Nanoscale Magnetic Resonance Spectroscopy with Nitrogen-Vacancy Centers in Diamond Von der Fakultät 8 Mathematik und Physik der Universität Stuttgart zur Erlangung der Würde eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigte Abhandlung vorgelegt von Domenico Paone aus Ludwigsburg Hauptberichter: Prof. Dr. Jörg Wrachtrup Mitberichter: Prof. Dr. Klaus Kern 2. Mitberichter: Prof. Dr. Harald Giessen Tag der mündlichen Prüfung: 05.10.2021 3. Physikalisches Institut der Universität Stuttgart 2021 Summary Summary The detection of magnetic fields plays an important role in diverse areas ranging from fundamental science to applications in data storage and medicine. Consequently, a variety of magnetic field sensors have been developed including Hall sensors, anisotropic magnetoresistive (AMR) sensors, supercon- ducting quantum interference devices (SQUIDs) and magnetic resonance sensors. However, modern technologies are becoming more inclined towards effects occurring at the nanometer length scale. Examples can be found in the field of biomedical science, where properties of single proteins are in- vestigated which play a crucial role in medicine and pharmaceutics. For a better understanding of such biological compounds, spatial conformations and structures have to be revealed on the single molecule level. Therefore, sensors are required which are able to detect weak magnetic fields with high spatial resolution by implementing nano-magnetic resonance imaging (nano-MRI) techniques. Another ex- ample in modern condensed-matter physics comes from superconductivity. Due to the wide range of applications connected to superconductors, including the production of sensitive magnetometers, digital circuits and electromagnets, superconducting systems are catching a huge amount of interest in physics. Indeed, the macroscopic theory of superconductors is able to explain unique phenomena like the Meissner effect. However, microscopic studies on superconductors play an important role in un- derstanding the mechanisms underlying superconductivity. A nanometer scale magnetic sensor could investigate the Meissner state of a superconductor locally, detecting dynamical phenomena such as the formation and motion of single magnetic vortices. A promising approach for nanoscale magnetic field detection and imaging can be enabled by exploit- ing quantum effects in the nitrogen-vacancy (NV) defect center in diamond. This point defect shows a spin dependent photoluminescence (PL). The sensing principle relies on microwave excitations which allow coherent manipulation within different spin sublevels in the ground state. These transitions show a Zeemann effect which is dependent to the applied magnetic field and can be read out by recording the corresponding PL of the NV defect. The sensing approach, known as optically detected magnetic resonance (ODMR) spectroscopy, can be used for sensing nuclear and electron spins in a nanometer- sized volume. Applications of NV center based quantum sensing have been shown by electron spin resonance (ESR) of spin labeled molecular chains and nuclear magnetic resonance (NMR) of organic samples. Furthermore, magnetic properties like spin waves, ferromagnetism and superconductivity have been investigated with this approach locally on the �m scale. Therefore, the single spin sensi- tivity of the NV center is a powerful tool for revealing a deeper understanding in the composition of single molecules and the formation of magnetic domains in solids. This thesis demonstrates NV center based magnetometry for the detection of single external spins and I Summary the local resolution of collective spin phenomena. All presented experiments have been performed in an ultra-high vacuum (UHV) cryogenic setup operating at a base pressure of 2 ⋅ 10−10mbar and at a base temperature of 4.7K. More specifically, the presented work shows a successful NV center based readout of single optically dark molecules which are usually difficult to address with spectroscopy methods in the optical wave- length region. Two systems have been investigated in this context, namely long-chain spin labeled polyphenols and endofullerene N@C60 buckyballs. Thereby, the dipolar coupling between the NV center spin and the corresponding individual target spin has been observed in terms of double elec- tron electron resonance (DEER) spectroscopy. With this technique, the structure of optically dark molecules can be investigated even at the nanometer length scale. Both external spin systems were identified by the usual NV center sensing protocol which relies on the application of microwave excitation. However, such excitations are often accompanied by lo- cal heating effects which could cause undesired changes in the properties of the investigated system. While for molecular spin sensing the local microwave heating has a minor impact on the observed system, the characterization of spin phenomena in solids could be influenced. Prime examples are two-dimensional superconductors which are accompanied by magnetic phases at certain critical tem- peratures. This problem can be circumvented by utilizing an all-optical, microwave-free measurement scheme. Therefore, this thesis also introduces the direct fluorescence emitted by an NV ensemble for the detec- tion of the Meissner state in a thin film La2−xSrxCuO4 (LSCO) sample. The measured magnetic field profile along the LSCO thin film can be analytically reproduced by Brandt’s model, revealing a critical current density jc of 1.4 ⋅ 108A∕cm2. The good agreement between the measured jc and the corre- sponding literature values for LSCO suggests that the all-optical, microwave-free PL rate of the NV center can be utilized as a reliable quantity for the observation of magnetic properties in solids. These measurement schemes can be potentially extended further with optical pump-probe spectroscopy en- abling access to dynamical phenomena in nanomagnetic materials with ps time resolution. Finally, the last part of this thesis highlights experimental attempts for enhancing the spin properties of single shallow NV centers. The spatial resolution of an NV center sensor is defined by the sensor-to- sample distance. Therefore, near-surface NVs are beneficial for sensing purposes. However, shallow NV centers often suffer from spin state instabilities due to charge traps available on the diamond sur- face. To overcome this limitation, controlled in situ dosing procedures have been implemented. Our results exhibit that surface-modification provides a viable route to enhance the optical properties of shallow NV centers in diamond. Thus altogether, the results presented in this thesis provide major advances in the field of nanoscale magnetometry. II Zusammenfassung Zusammenfassung Die Detektion von magnetischen Feldern spielt in verschiedenen Bereichen eine wichtige Rolle, die von fundamentalen Wissenschaften bis hin zu Anwendungen in der Datenspeicherung und Medizin weit reichen. Folglich wurde eine Vielzahl von magnetischen Sensoren entwickelt, zu denen Hall Sensoren, anisotropische magnetoresistive (AMR) Sensoren, supraleitende Quanteninterferenzein- heiten (SQUIDs) und magnetische Resonanzsensoren gehören. Dennoch fokussieren sich moderne Technologien immer mehr auf Effekte, die auf der Nanometerskala relevant sind. Beispiele kön- nen im Bereich der Biomedizin gefunden werden, in welcher Eigenschaften einzelner Proteine un- tersucht werden, die eine entscheidende Rolle in der Medizin und Pharmazeutik spielen. Um ein besseres Verständnis solcher biologischer Zusammensetzungen zu erhalten, ist es wichtig, die räum- liche Orientierung und Struktur auf Ebene einzelner Moleküle zu enthüllen. Daher werden Sensoren benötigt, die in der Lage sind, schwache Magnetfelder mit hoher räumlicher Auflösung in Form der nano-Magnetresonanztomographie (MRT) zu detektieren. Ein weiteres Beispiel kann in der Fes- tkörperforschung im Bereich der Supraleiung gefunden werden. Dank den weitreichenden Anwen- dungsbereichen von Supraleitern, zu denen die Produktion von sensitiven Magnetometern, digitalen Schaltkreisen und Elektromagneten gehört, haben supraleitende Systeme große Aufmerksamkeit in der Physik erhalten. In der Tat ist die makroskopische Theorie von Supraleitern in der Lage, einzigar- tige Phänomene, wie den Meissner Effekt, zu erklären. Dennoch spielen mikroskopische Studien eine wichtige Rolle, um die Mechanismen zu verstehen, welche grundlegend für die Supraleitung sind. Ein magnetischer Sensor, der im Nanometerbereich arbeitet, könnte lokal die Meissner Phase eines Supraleiters untersuchen um dynamische Phänomene, wie die Formation und Bewegung magnetis- cher Wirbelschläuche, zu detektieren. Ein vielversprechendes Vorgehen für die Detektion von Magnetfeldern auf der Nanometerskala kann durch das Ausnutzen von Quanteneffekten im Stickstoff-Fehlstellen (NV) Defekt Zentrum in Dia- manten ermöglicht werden. Dieser Punktdefekt besitzt eine spinabhängige Lumineszenze (PL). Das Sensorenprinzip basiet auf resonanten Mikrowellenanregungen, die kohärente Manipulationen inner- halb des Spin Grundzustandes ermöglichen. Diese Übergänge weisen einen Zeeman Effekt auf, der linear vom angewandten Magnetfeld abhängt und optisch ausgelesen werden kann indem die NV Fluoreszenz aufgenommen wird. Das Detektionsvorgehen, bekannt als optische magnetische Reso- nanzspektroskopie (ODMR), kann genutzt werden um Kern- und Elektronenspins in Nanometervol- umen wahrzunehmen. Anwendungen von Detektionen, die auf dem NV Zentrum basieren, wurden als Elektronenspinresonanz (ESR) in Spin-gekennzeichneten Molekülketten und Kernspinresonanz in organischen Proben aufgezeigt. Zusätzlich wurden magnetische Eigenschaften wie Spin-Wellen, Fer- III Zusammenfassung romagnetismus und Supraleitung auf �m-Skalen mit dieser Vorgehensweise untersucht. Deshalb ist die Sensitivität des NV Zentrums ein wichtiges Werkzeug um ein tieferes Verständins in der Zusam- mensetzung einzelner Moleküle und der Formation magnetischer Bereiche zu erhalten. Diese Doktorarbeit veranschaulicht Magnetometermessungen, die auf dem NV Zentrum basieren, um einzelne externe Moleküle zu detektieren und kollektive Elektronenphänomene aufzulösen. Alle präsentierten Experimente wurden in einem Hochvakuum-Kryostaten durchgeführt, welcher in einem Druckbereich von 2 ⋅ 10−10mbar und einer Temperatur von 4.7K arbeitet. Genauer gesagt zeigt diese Arbeit die erfolgreiche Detektion von optisch dunklen Molekülen, die mit einzelnen NV Zentren charakterisiert wurden und üblicherweise schwer mit Spektroskopiemethoden im optischen Wellenlängenbereich zu adressieren sind. Zwei Systeme wurden dabei untersucht und zwar langkettige Spin-gekennzeichnete Polyphenole und endohedrale N@C60 "buckyballs". Dabei wurde die dipolare Koppulng zwischen dem NV Zentrum Spin und dem jeweiligen individuellen Ziel- spin mithilfe von doppelter Elektronenspinresonanz Spektroskopie (DEER) untersucht. Mit dieser Methode kann die Struktur von optischen dunklen Moleküle, einschließlich ihrer Nanometer Längen- skalen, untersucht werden. Beide Spinsysteme wurden mit den üblichen NV Zentren Detektionsprotokolle untersucht, welche auf den Gebrauch von Mikrowellenanregungen basieren. Solche Anregungen werden oft von lokalen Erhitzungseffekten begleitet, die unerwünschte Änderungen der Eigenschaften des zu untersuchen- den Systems induzieren. Während dies auf die Detektion von Molekülen nur geringe Auswirkungen hat, lässt sich die Charakterisierung von Spin Phänomenen in Festkörpern stark davon beeinflussen. Beispiele sind zwei dimensionale Supraleiter, welche einen magnetischen Phasenübergang ab einer bestimmten kritischen Temperatur vollziehen. Dieses Problem kann verhindert werden, indem rein optische, mikrowellen-freie Messungen durchgeführt werden. Daher leitet diese Arbeit ebenfalls die direkte Fluoreszenz ein, welche von einem NV Zentrum Ensem- ble emittiert wird, um die Meissner Phase einer dünnen La2−xSrxCuO4 (LSCO) Probe zu detektieren. Das Profil des gemessenenmagnetischen Feldes kannmit Hilfe des analytischen BrandtModells rekon- struiert werden um eine kritische Stromdichte jc = 1.4 ⋅ 108A∕cm2 der Probe zu erhalten. Da dieser Wert mit den Literaturwerten für LSCO übereinstimmt, kann die rein optische, Mikrowellen freie NV Fluoreszenz als zuverlässliche Messgröße bewertet werden, mit welcher magnetische Eigenschaften in Festkörpern untersucht werden können. Zudem kann die NV Fluoreszenz potentiell mit optischen "pump-probe" Spektroskopie Methoden erweiter werden, um dynamische Prozesse im Pikosekunden Bereich zu untersuchen. Letztendlich zeigt Kapitel 7 experimentelle Versuche auf, welche die Spineigenschaften sehr ober- flächennahen NV Zentren verbessern sollen. Die räumliche Auflösung eines NV Zentrum Sen- sors ist durch den Abstand zwischen dem Sensor und der Probe definiert. Daher sind NV Zen- tren, welche nah an der Diamantenoberfläche lokalisiert sind, vorteilhaft für Detektionsanwendun- gen. Dennoch zeigen oberflächennahe NV Zentren oft Spininstabilitäten auf, die mit Ladungspoten- tialen auf der Diamantenoberfläche zusammenhängen. Um diese Beschränkung zu bewältigen, wurden IV Zusammenfassung Dosierungsvorgänge, innerhalb des Hochvakuums, auf der Diamantenoberfläche implementiert. Die experimentellen Ergebnisse zeigen, dass Oberflächenmodifikation durchaus in der Lage sind, die op- tischen Eigenschaften von oberflächennahen NV Zentren zu verbessern. Die präsentierten Ergebnisse dieser Doktorarbeit erzielen wichtige Fortschritte in Bereichen der Mag- netfelmessung auf Nanometerskalen. V Publications Publications From the presented PhD thesis, two scientific articles have been published and one more publication is in the process of being drafted. Furthermore, two additional articles have been published during this time period from former experiments which were performed within the scope of my Master thesis at the PI4 of the University of Stuttgart. Publications from my Master Thesis • T. Teutsch, N. Strohfeldt, F. Sterl, A. Warsewa, E. Herkert, D. Paone, H. Giessen and Christina Tarin, Mathematical Modeling of a Plasmonic Palladium-Based Hydrogen Sensor, IEEE Sen- sors Journal 18, 1946-1959 (2018). • Q. Ai, L. Gui, D. Paone, B. Metzger, M.Mayer, K.Weber, A. Fery and H. Giessen, Ultranarrow Second-Harmonic Resonances in Hybrid Plasmon-Fiber Cavities, NanoLett. 18, 5576-5582 (2018). Publications from this PhD Thesis • D. Pinto, D. Paone, B. Kern, T. Dierker, R. Wieczorek, A. Singha, D. Dasari, A. Finkler, W. Harneit, J. Wrachtrup and K. Kern, Readout and Control of an Endofullerne Electronic Spin, Nature Communications 11, 6405 (2020). • D. Paone, D. Pinto, G. Kim, L. Feng, M.-J. Kim, R. Stöhr, A. Singha, S. Kaiser, G. Logvenov, B. Keimer, J. Wrachtrup and K. Kern, All-Optical and Microwave-Free Detection of Meissner Screening using Nitrogen-Vacancy Centers in Diamond, J. Appl. Phys. 129, 024306 (2021). • D. Paone, J. Neethirajan, D. Pinto, A. Denisenko, R. Stöhr, A. Singha, J. Wrachtrup and K. Kern, Charge State Instabilities of Nitrogen-Vacancy Centers in Diamond at Cryogenic Ultra- High-Vacuum Conditions, in preparation. VI Curriculum Vitae Curriculum Vitae • 09/2011 - 09/2014 Bachelor of Science, thesis at the PI4 of the University of Stuttgart on plas- monic gas sensing • 2013 - 2017 Trainee at the PI4 of the University of Stuttgart, research topic: Plasmonic gas sensing • 10/2014 - 04/2015 Research internship at CSIRO Sydney Australia, research topic: Plasmonic photovoltaic cells • 04/2015 - 08/2017 Master of Science, thesis at the PI4 of the University of Stuttgart on chemical growth of plasmonic nanostructures • 09/2017 - 10/2021 Doctor Rerum Naturalium, thesis at the Max Planck Institute for Solid State Research in Stuttgart on magnetic field sensing with NV centers in diamond VII Declaration Declaration I, Domenico Paone, hereby declare that this dissertation entitled "Nanoscale Magnetic Resonance Spectroscopy with NV Centers in Diamond" is entirely my own work expect where otherwise in- dicated. Passages from other sources have been clearly cited within the bibliography. The contents of this thesis have not been submitted to any other examination institution. Furthermore, the printed version fully accords with the submitted portable document format (pdf) version which can be found online. Stuttgart, VIII Contents Contents Summary I Zusammenfassung III Publications VI Curriculum Vitae VII Declaration VIII Contents IX List of Abbreviations XII 1 Introduction 1 2 The Nitrogen Vacancy Center in Diamond 5 2.1 General Properties of the NV Center . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1 Defect Centers in Diamond . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.2 The NV Center Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.3 Electronic Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.4 Optical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Magnetic Resonance Spectroscopy with NV Centers . . . . . . . . . . . . . . . . . 11 2.2.1 ODMR Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.2 Lifetime Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2.3 Spectral Filter Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.4 ESR Measurement Schemes with NV Centers . . . . . . . . . . . . . . . . . 20 2.2.5 NMR Measurement Schemes with NV Centers . . . . . . . . . . . . . . . . 22 2.3 NV Center Implantation into Diamond Samples . . . . . . . . . . . . . . . . . . . . 24 2.3.1 Artificial Diamonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.3.2 Single NV Center Implantation . . . . . . . . . . . . . . . . . . . . . . . . 25 2.3.3 NV Center Ensemble Implantation . . . . . . . . . . . . . . . . . . . . . . . 25 2.3.4 Diamond Nano-Structuring . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 IX Contents 3 Experimental Setup 27 3.1 Overview Scheme of the Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 The Cryo-UHV Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.2.1 Load Lock and Preparation Chamber . . . . . . . . . . . . . . . . . . . . . 28 3.2.2 Main Chamber and Cryostat . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2.3 Measurement Head . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.3 Microwave Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.4 Optical Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.5 Implemented Improvements in the System Performance . . . . . . . . . . . . . . . . 37 4 Detection of Individual External Spins with Single NV Centers 41 4.1 Molecular Ruler Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.1.1 Bulk ESR Measurements of Spin Labeled Polyphenols . . . . . . . . . . . . 43 4.1.2 Magnetic Dipole-Dipole Interaction . . . . . . . . . . . . . . . . . . . . . . 45 4.1.3 Nanoscale ESR Measurements Using a Single NV Center . . . . . . . . . . 46 4.1.4 Measurement Limitations with the Polyphenols . . . . . . . . . . . . . . . . 51 4.2 Endofullerene Spin Qubits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.2.1 Endofullerene N@C60 Molecules . . . . . . . . . . . . . . . . . . . . . . . 54 4.2.2 Sensing N@C60 Molecules with a Single NV Center . . . . . . . . . . . . . 56 4.2.3 Coherent Control of N@C60 Spins . . . . . . . . . . . . . . . . . . . . . . . 59 4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 5 Measuring Nitrogen Spin Qubits with NV Center Ensembles 64 5.1 The P1 Center in Diamond as Spin Qubit . . . . . . . . . . . . . . . . . . . . . . . 65 5.1.1 Structural Properties of the P1 Center . . . . . . . . . . . . . . . . . . . . . 65 5.1.2 Energy Structure and Selection Rules . . . . . . . . . . . . . . . . . . . . . 66 5.1.3 The P1 Center Spin Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . 67 5.2 Measuring P1 Centers with an NV Ensemble . . . . . . . . . . . . . . . . . . . . . 67 5.2.1 NV Ensemble Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5.2.2 Sensing P1 Ensembles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.2.3 Detection of P1 Center Forbidden Transitions . . . . . . . . . . . . . . . . . 71 5.2.4 Measurements at Ambient Conditions . . . . . . . . . . . . . . . . . . . . . 72 5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 6 Observation of Superconducting Phase Transitions with NV Centers 74 6.1 Measuring the Meissner State with NV Centers . . . . . . . . . . . . . . . . . . . . 75 6.2 Thin Film LSCO Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 6.2.1 Fabrication and Characterization of the LSCO Sample . . . . . . . . . . . . 79 6.2.2 Detecting the Meissner State with an NV Ensemble . . . . . . . . . . . . . . 81 X Contents 6.3 All-Optical Characterization by Using the NV Fluorescence . . . . . . . . . . . . . 85 6.3.1 The Magnetic Field Dependent Photoluminescence Drop . . . . . . . . . . . 85 6.3.2 Microwave-Free Measurements . . . . . . . . . . . . . . . . . . . . . . . . 86 6.4 Investigation of Superconducting Vortices in LSCO . . . . . . . . . . . . . . . . . . 91 6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 7 Towards Stabilizing the Spin Properties of Near-Surface NVs 95 7.1 Charge State Dynamics of the NV Center . . . . . . . . . . . . . . . . . . . . . . . 96 7.2 Near-Surface NVs at Ambient Conditions . . . . . . . . . . . . . . . . . . . . . . . 99 7.3 Measurements at UHV and Cryogenic Conditions . . . . . . . . . . . . . . . . . . . 102 7.4 Surface Modifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 7.4.1 Nitrogen Dosing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 7.4.2 Formation of an Atmospheric Water Layer . . . . . . . . . . . . . . . . . . 106 7.4.3 IR Laser Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 7.4.4 Carbon Monoxide Dosing . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 7.4.5 Water Dosing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 7.4.6 Fluorescence Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 8 Alternatives to NV Centers as Quantum Sensors 115 8.1 A Novel Defect Center in Diamond . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 8.1.1 Optical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 8.1.2 High Frequency Measurements . . . . . . . . . . . . . . . . . . . . . . . . 118 8.1.3 Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 9 Conclusion 123 9.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 9.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 10 Appendix 132 11 Bibliography 139 Acknowledgments 156 XI List of Abbreviations List of Abbreviations AO Atomic orbitals APD Avalanche Photo diode BDS BeiDous navigation system CO Carbon monoxide Co Cobalt CR Charge reservoir Cu Copper CuBe Beryllium Copper CuO2 Copper Oxides CVD Chemical vapour deposition cw Continious wave DEER Double electron electron resonance DMAP Dymethylaminopyridine DQT Double quantum transition ENDOR Electron nuclear double resonance EPR Electron paramagnetic resonance ESR Electron spin resonance fcc Face-centered cubic FFT Fast Fourier transformation FID Free induction decay FPGA Field programmable gate array XII List of Abbreviations GLONASS Global’naya Navigatsionnaya Sputnikovaya Sistema GNSS Global navigation satellite systems GPS Global positioning system HF High frequency H2O Water HPHLC High-performance liquid chromatography HPHT High pressure and high temperature IR Infrared ISC Inter-system crossing JTE Jahn-Teller effect LBCO Lanthanum barium copper oxide LCAO Linear combination atomic orbitals LP Longpass LSAO Lanthanum strontium aluminum oxide LSCO Lanthanum strontium copper oxide MBE Molecular beam epitaxy MFM Magnetic force microscopy MO Molecular orbitals MRFM Magnetic resonance force microscopy MRI Magnetic resonance imaging MW Microwave N Nitrogen NA Numerical aperture nanoSQUID Nano superconducting interference device Nb Niobium XIII List of Abbreviations Nb3Si Niobium silicon NbTi Niobium titanium NMR Nuclear magnetic resonance NO Nitric oxide N2O Nitrous oxide NV Nitrogen-vacancy NV− Negatively charged nitrogen-vacancy NV+ Positively charged nitrogen-vacancy NV0 Neutral nitrogen-vacancy O Oxygen ODMR Optically detected magnetic resonance P Phosphorous P5C-NR Tetramethylpyrolline carboxylic nitroxide radical PL Photoluminescence PMT Photomultiplier tube Qdyne Quantum heterodyne detection RF Radio frequency RHEED Reflection high energy diffraction SiV Silicon-vacancy SMP Sub-miniature-P SQUID Superconducting interference device STM Scanning tunneling microscopy TEER Triple electron electron resonance UHV Ultra high vacuum UV Ultraviolet XIV List of Abbreviations V Vanadium V3In Vanadium indium YBCO Yttrium barium copper oxide ZPL Zero phonon line XV Introduction 1 Introduction Magnetic sensors are widely used in a large number of practical and essential applications. Of great importance among these are recording heads for magnetic storage and memory elements of modern devices [1]. Furthermore, magnetometers form the fundamental basis for compass schemes [2] which play a crucial role in Global Navigation Satellite Systems (GNSS), including the Global Position- ing System (GPS), the Global’naya Navigatsionnaya Sputnikovaya Sistema (GLONASS), the BeiDou Navigation Satellite System (BDS) and the Galileo positioning system (Galileo). In addition to that, the detection, discrimination and localization of magnetic fields are essential for many security appli- cations [3] as research studies identified several effects on the human health under high magnetic field exposures [4]. These include minor symptoms such as headaches up to serious impacts in increasing the risk of childhood leukemia [5, 6]. As magnetic fields are invisible and penetrate through nearly all materials, a reliable detection plays a crucial role for human safety [3]. The detection of magnetic signals also plays a significant role in magnetic resonance imaging (MRI) which reveals high resolution images of defective tissues in human body [7, 8]. The technique is a con- sequence of nuclear magnetic resonance (NMR) which is a physical phenomenon of the behavior of nuclei in a strong constant magnetic field [9]. Thereby, the nuclei respond by accumulating an electro- magnetic signal with a characteristic frequency. With this, certain compounds within the human tissue can be distinguished for medical diagnosis. Typically, MRI schemes utilize magnetic field gradients of ≈ 70mT∕m which are able to detect nuclear spin concentrations within a volume of 1mm3 [10, 11]. However, a measurable signal requires a contribution of ≈ 1015 nuclear spins within the investigated compound [12]. A complementary method is formed by electron spin resonance (ESR) (also termed as electron paramagnetic resonance (EPR)), which utilizes electromagnetic signals gathered by excited electron spins instead of atomic nuclear spins [13]. As the gyromagnetic ratio of an electron spin is higher compared to a nuclear spin, lower magnetic field strengths (≈ 20mT) are already sufficient for the acquisition of a spin signal. Nevertheless, similar to the case of MRI, also in traditional ESR setups a huge number of spins (≈ 108 − 1014 [12]) are required to ensure an acceptable signal to noise ra- tio. Notably, these standard EPR and NMR techniques are not readily available with nanoscale spatial resolution which is often of great interests for investigating the properties and spatial conformations of single cells, proteins or even molecules for gaining more insights into biochemical processes which highly influence the human behavior. In order to achieve nanoscale spatial resolution, magnetic field sensors have to be down-scaled to the nanometer level. Furthermore, the sensors have to be brought in close proximity to the sample as the magnetic dipole moment and thereby the dominant term in the magnetic dipole-dipole interaction 1 Introduction decreases with 1∕r3 (where are r defines the sensor-to-sample distance). The detection of magnetic fields at the nanoscale is also crucial for advancements and developments of other modern scientific applications, for instance, in the field of quantum information processing for the realization of quantum computers [14, 15, 16]. As classical computers are entering the quantum realm, quantum properties can be utilized for increasing the computational power as well as the efficiency for specific tasks. The structure of a quantum computing device is based on interacting quantum spin networks [17]. Thereby, single spins take the role of classical bits as so called quantum bits (qubits). While the state of a clas- sical bit can only be 0 or 1, a qubit according to quantum mechanics can take the values |0⟩, |1⟩ and all possible coherent superposition states of these two states. As a result, the break of solely binary states reveals the potential to perform calculations in more efficient manners. However, coherent superposi- tion states of an individual qubit attend to obtain certain instabilities due to environmental magnetic noise or exchange interactions with other qubits within the quantum network [18]. Therefore, the local readout of specific magnetic spins inside the quantum network could reveal information for controlling and stabilizing the coherence of the individual quantum states. There are several techniques which pave the way towards nanoscale magnetic field sensing. For in- stance, magnetic resonance force microscopy (MRFM) methods are able to detect single electronic spins [19, 20]. Thereby, the interaction force between a spin specimen and magnetic tip is measured as a shift of the mechanical resonance frequency of the utilized tuning fork. With this, an image of the magnetic distribution of a sample can be reconstructed by scanning the magnetic tip over a certain area. However, the disadvantage of this technique, is the high complexity of the experimental instrument which requires sensitive cantilevers for the detection of forces in the attonewton range. Furthermore, most of the experiments have to be performed at mK temperatures for reducing drifts and instabilities of the magnetic tip. Other promising attempts include magnetometers based on superconducting quantum interference de- vices (SQUIDs) which consist of a superconducting loop interrupted by two weak links forming a Josephson junction [21]. By applying an external magnetic field, an electrical current is induced through the superconducting loop and a magnetic flux is generated inside the loop which must be an integer multiple of the magnetic flux quantum Φ0 = 2.07 ⋅ 10−15Vs. A change of the externally applied field leads to a variation of the induced current and magnetic flux within the superconducting ring. As such a slight shift is challenging to detect, the implemented Josephson junction can be utilized for obtaining a measurable signal. In order to achieve this, a current can be applied across the SQUID. As a result, a certain voltage can be measured on the device which mainly depends on the applied cur- rent but also on the magnetic field induced current within the superconductor. Observing the variations of the measurable voltage leads to a qualitative detection of external magnetic fields with a sensitivity of ≈ 10 aT∕Hz1∕2. However, the realization of nanoscale measurements is challenging as the whole superconducting circuit has to be miniaturized to nanometer length scales. Nevertheless, nanoscaled SQUIDs (nanoSQUIDs) have been successfully developed recently with a loop-diameter of ≈ 40 nm [22]. A more problematic drawback is that SQUIDs are only able to operator at low temperatures due 2 Introduction to the superconducting phenomena which are exploited for the magnetic field measurement. This issue avoids experiments at ambient temperature conditions. In addition to that, another class of nanoscale magnetic field sensors have emerged over recent years based on single spins in solids including systems as semiconductor quantum dots [23] or phosphorous in silicon [24]. Thereby, the spins originate by certain impurities within a specific material and form stable quantum sensors due to their reliable response to weak external magnetic fields. One of the best studied spin system in solids is the nitrogen-vacancy (NV) defect in diamond [26] which forms the main focus within the scope of this thesis. The impurity consist of a substitutional nitrogen atom and a neighboring carbon vacancy within the diamond crystal. Several experiments demonstrated its ability to detect small magnetic fields at the nanoscale [25]. As a result, the NV center received an increased attention. Measurements can be performed at both cryogenic as well as ambient conditions with a magnetic field sensitivity of 10 pT∕Hz1∕2 [26]. Furthermore, it can be brought in close proximity to a spin system achieving a spatial resolution in the nm regime. The fundamental sensing principle relies on the spin state dependent photoluminescence (PL) of the NV defect which forms a S = 1 ground state [27]. Consequently, three different sublevels (mS = 0, mS = −1 and mS = +1) are involved within the ground state. Thereby, the mS = 0 sublevel exhibits a higher emission compared to the mS = −1 and mS = +1 substates. According to the energy level diagram, microwave (MW) excita- tions allow coherent manipulations within these spin sublevels. The resulting MW transitions show a Zeeman effect which linearly depends on the applied magnetic field and realizes the performance of optically detected magnetic resonance (ODMR) spectroscopy. Thereby, the resonance lines can be observed as sharp dips within the ODMR spectrum due to the different fluorescence yield of the NV center spin states. These non-invasive and reliable properties make the NV center to a very promising quantum sensor for discovering physical processes at the nanoscale. Indeed, applications of NV center based sensing schemes have been shown in single molecular spin systems in terms of ESR and NMR spectroscopy revealing molecular distances in the nm region [28]. Additionally, magnetic properties of materials have been investigated including ferromagnetism in permalloys and cobalt (Co) nanowires [29, 30] and superconductivity at the nanoscale [31] giving local insights into magnetic domains. Furthermore, op- timizations on the NV center sensing protocols are able to locally detect fast magnetic dynamics in a narrow �s time resolution [32]. This Thesis The presented thesis describes NV center based measurement schemes for the characterization of molecules and superconductivity in a cryogenic, ultra high vacuum (UHV) environment. The work is separated into 8 chapters. Chapter 2 describes the fundamental physics of the NV center in diamond and explains measurement schemes which have been implemented to characterize its spin properties. Furthermore, sensing proto- cols are reviewed which utilize the NV center for performing ESR and NMR spectroscopy on external 3 Introduction spin systems. Chapter 3 introduces the experimental setup which has been used for performing NV center based measurements at cryogenic (4.7K) and UHV (2 ⋅ 10−10mbar) conditions. The whole assembly of the existing instrument, as well as the upgradations made to the existing setup, are described in this chapter. In chapter 4 the first experimental results of this thesis are shown. Thereby, single NV centers are utilized for the characterization of nitroxide spin labeled polyphenols and endofullerene N@C60 spins. A detection of less than 10 external spins is demonstrated. Furthermore, chapter 5 describes the readout of a spin bath by an NV center ensemble. The spin bath is formed by P1 defect centers within the diamond lattice. It is demonstrated that a neighboring NV center ensemble is able to control and manipulate the spin state of the dense P1 center spin bath. In chapter 6 an NV center ensemble is utilized for the characterization of a superconducting La2−xSrxCuO4 (LSCO) thin film sample. Thereby, an all-optical, MW-free measurement scheme is presented which relies on the pure fluorescence yield of the NV center ensemble. This circumvents local heating effects which can originate from applying MW fields. The spatial resolution of the thin film Meissner screening is shown. Afterwards, chapter 7 describes a statistical study for enhancing and stabilizing the spin properties of shallow implanted NV centers. Thereby, autocorrelation measurements, ODMR signals, and emission spectra are obtained for individual NV centers under different diamond surface treatments including nitrogen, carbon monoxide and water dosing. A slight increase of the NV fluorescence yield is re- ported by utilizing protection layers with strong dipole moments. In addition to that, chapter 8 presents other alternative defect centers in diamond to the NV center as quantum sensors. Furthermore, the characterization of a novel defect center in diamond is described in terms of an optical study and high frequency (HF) spectroscopy. Finally, chapter 9 summarizes the demonstrated experiments and presents an outlook on future inves- tigations for revealing interesting magnetic phenomena in nanomagnetic materials. 4 The Nitrogen Vacancy Center in Diamond 2 The Nitrogen Vacancy Center in Diamond As this thesis is focused on NV center based magnetometry it is crucial to introduce the fundamentals of the NV center in this chapter. Therefore, the first section describes the general properties of the NV center in diamond like the crystallographic structure, the electronic structure and the resulting optical properties. The second section of this chapter is dedicated to measurement protocols which use the NV center as magnetic field sensor. These schemes can be utilized for the realization of ESR and NMR experiments at the nanoscale. In the third section, techniques for the fabrication of NV implanted diamond samples are described. Both, the single NV and the NV center ensemble implantation into a diamond matrix are highlighted. Finally, the last section summarizes this theoretical background around the NV center which will be used throughout the whole thesis for the realization and analysis of NV based experiments. 2.1 General Properties of the NV Center Diamond is a solid form of carbon in which the atoms are arranged in a crystal structure consisted by a repeating tetrahedral pattern of 4 carbon atoms [33]. At standard temperature and pressure, diamond is a stable compound. However, under extreme conditions (1300C◦ [34] and 100GPa [35]) diamond is able to transform to graphite which is another chemically stable form of carbon. The first discovered diamonds were found in India in the 4tℎ century BC., and until the 18tℎ century, India was thought to be the only source of diamond [36]. In 1725, the first deposit of diamond outside India was found in Brazil [36]. In contrary to the Dark Ages, in which diamonds served as talisman and medical aid, today the most uses of diamonds are as gemstones utilized as adornments or in industry as abrasives for cutting hard materials. From a scientific point of view, diamond induced a whole research field for its ability to host stable atomic defects with interesting physical properties. One of the most explored atomic defect in diamond is the NV center which forms the basis of this thesis. The most important aspects of the NV center will be presented in this section including structural, electronic and optical properties. 2.1.1 Defect Centers in Diamond The diamond crystal is defined by carbon atoms arranged in a face-centered cubic (fcc) lattice struc- ture [33] with a lattice constant of a = 3.57 Å [37]. To form a crystal, the four valence electrons of 5 The Nitrogen Vacancy Center in Diamond the sp3-hybridized carbon bond to the neighboring atoms. The resulting chemical bonds give rise to the extraordinary hardness and thermal conductivity (22Wcm−1K−1 [38]) of diamond. Due to the large band gap of 5.48 eV [39], diamond is regarded as an electrical insulator and optically transparent material up to ultraviolet (UV) wavelengths. Furthermore, the diamond matrix is able to host incor- porated atomic defects which are often denoted as impurities. Therefore, diamonds can be classified according to the amount and type of impurities they contain. The four commonly used classes are the Type Ia, Type Ib, Type IIa and Type IIb diamonds [40, 41]. Type Ia diamonds contain a high amount of nitrogen impurities (< 3000 ppm) in the form of aggregated nitrogen clusters. Type Ib diamonds also contain nitrogen impurities (< 500 ppm). However, the impurities appear in the form of paramagnetic single nitrogen defects. In contrary, Type IIa diamonds show a low nitrogen concentration < 1 ppm. In case of a significant boron content, the diamond is classified as Type IIb. Beside nitrogen and boron defects, diamond can also host phosphorous, hydrogen, nickel, cobalt, chromium, silicon, germanium, tin, lead and sulfur atoms. Typically, the defect centers can be detected by optical spectroscopy or EPR methods. One of the most studied defect in diamond is the NV center which gives an unique combination of optical and spin properties [42]. Fig. 2.1 shows the structure of this defect within the diamond lattice. The NV center is formed by a substitutional nitrogen atom and a carbon vacancy on an adjacent lattice site, possessing a C3v-symmetry [43]. The symmetry axis is given by the vector between the nitrogen atom and the vacancy. Figure 2.1: Schematic picture of the NV center in the diamond unit cell in which the carbon atoms are represented as gray spheres. The lattice constant of the unit cell is a = 3.57 Å and the C-C bond distance is 1.57 Å. A nitrogen atom, depicted as red sphere, substitutes one of the carbon atoms. By removing one of the near-neighbor carbon atoms, a vacancy is created which is depicted in white. The sketch is adapted from [44]. 6 The Nitrogen Vacancy Center in Diamond Due to the tetrahedral geometry of the diamond lattice, the NV center can be oriented in four different directions (corresponding to the four equivalent [111] directions of the diamond lattice). The first identification of the NV center was noted in 1965 [45]. Afterwards, several optical and electron spin resonance experiments were performed for understanding its physical properties [42]. These properties will be explained in the following subsections. 2.1.2 The NV Center Hamiltonian The fundamental for describing physical properties of a quantum system, like a molecule or a localized defect, is the full electronic Hamiltonian. Following the Born-Oppenheimer approximation [46], in which the nuclear motion is fixed and can be separated from the electronic motion, the NV center Hamiltonian can be written as Hfull NV = ∑ i ( H i kinetic +H i Coulomb−crystal +H i spin−orbit +H i ℎyperfine ) (2.1) + ∑ i,j ( H i,j Coulomb−ee +H i,j spin−spin ) , whereH i kinetic is the kinetic energy of the i-th electron of the NV electrons,H i Coulomb−crystal describes the Coulomb interaction between the crystal nuclei and the NV electrons,H i spin−orbit is the electronic spin-orbit coupling and H i ℎyperfine defines the hyperfine interaction between the NV electrons and crystal nuclei [47]. Furthermore,H i,j Coulomb−ee andH i,j spin−spin describe the Coulomb potential and spin- spin potential between the NV electrons [47]. As this Hamiltonian can not be solved exactly, different approaches can be used for partly tackling the equation. Figure 2.2: Molecular orbitals of the NV center which result from a linear combination of the atomic orbitals of the carbon and nitrogen. The positive parts of the wavefunction are depicted red. Instead, the blue sections show the negative parts of the wavefunction. Especially the a1 orbital shows the resided electron density close on the vacancy. The figure is adapted from [48]. 7 The Nitrogen Vacancy Center in Diamond One method is to use atomic orbitals (AO), which are solutions of the one-electron problem and con- struct molecular orbitals (MO) as a linear combination of them [43]. These linear combination atomic orbitals (LCAO) are then filled up with electrons. In case of the NV center, the LCAOs are sp3- hybridized orbitals from the three carbon atoms and one nitrogen atom as depicted in Fig.2.2. The combined orbitals are named corresponding to the representation of the C3v symmetry group a1, ex and ey. Furthermore, group theoretical symmetry approximations, ab initio calculations and experi- ments can be connected for revealing the full electronic energy spectrum of the NV center [47]. For describing the interaction of the NV center with electromagnetic fields or materials, the Hamil- tonian in Eq. 2.1 can even be simplified by the spin Hamiltonian hypothesis [49]. Therefore, only terms containing the electron spin are regarded and thus kinetic and Coulomb interaction terms can be neglected. Furthermore, we can solely focus on the ground state in which the spin-orbit coupling is zero (L = 0). Taking these simplifications into account the NV center Hamiltonian from Eq. 2.1 can be written as: Hspin NV = HZFS +HHF +HNQ +HEZ +HNZ +Hcpl. (2.2) The zero field splitting (ZFS) due to the spin-spin interaction of the two electrons in the highest oc- cupied molecular orbital is defined by the HZFS term. The ZFS interaction can be expressed as SDS = DS2z+E ( S2x − S 2 y ) , whereS = (Sx, Sy, Sz) is the electron spin operator andD = 2.87GHz the axial ZFS parameter [42]. The transverse ZFS paramter or strain factor E is, compared to D, very small but highly dependent on lattice distortions. In general, the strain term is negligible and can be considered to E ( S2x − S 2 y ) = 0. The second term in Eq. 2.2, HHF , describes the hyperfine interaction with the nitrogen nuclear spin. This can be either an 14N atom with a nuclear spin of I = 1 or an 15N isotope with a nuclear spin of I = 1∕2. The hyperfine term can be expressed as SAI = A∥SzIz + A⟂ ( SxIx + SyIy ), in which I = (Ix, Iy, Iz) is the nuclear spin operator and A∥ and A⟂ correspond to the hyperfine constants. In case of the 14N atom the hyperfine constants are A∥ = 2.3MHz and A⟂ = 0 [42]. Instead, for the 15N case, the constants are A∥ = 3.1MHz and A⟂ ≈ 2.3 − 3.6MHz [42]. Furthermore, HNQ stands for the quadrupole term and is only present for 14N with the nuclear quadrupole interaction of P = 5.2MHz [50]. For the 15N nucleus, this term can be discarded. The Zeeman interaction of the NV center with an external magnetic field B0 is described with HEZ = �BB0gS∕ℏ. The orbital contributions to the g-tensor can be neglected. Therefore, the tensor can be written as g = g ⋅1. Furthermore, if the magnetic field vector B0 is oriented along the NV axis, the Zeeman interaction can be expressed asHEZ = BNV Sz. Thereby, is the electron gyromagnetic ratio and can be written as = g�B∕ℏ. In general, the Zeeman term is described by the dot product between the magnetic field vector and the spin vector expressed asHEZ = |B0||S| cos � , including the angle between the two vector orientations �. HNZ represents the nuclear Zeeman interaction. In general, this term can be neglected since the nu- clear magneton �N = eℏ∕2mp is orders of magnituded smaller than any other term. 8 The Nitrogen Vacancy Center in Diamond In summary, the NV center spin Hamiltonian can be simplified to [47]: Hspin NV = DS2z + A∥SzIz + BNV Sz +Hcpl. (2.3) Note that theHamiltonianH = H ′∕ℏ is written in units of frequency instead of energy. The last term in Eq. 2.3,Hcpl, describes the coupling of the NV center spin to magnetic elements in its environment. In this thesis, we focus on the interaction of the NV center with isolated spins which give rise to a dipole- dipole coupling term. This dipole-dipole interactionHdip will be discussed in detail in chapter 4. 2.1.3 Electronic Structure After we introduced the full NV center Hamiltonian, we can extract its physical properties like the electronic charge or optical behavior. The electronic structure of the NV center can be understood by the electron configuration in the LCAO. Thereby, three different electronic charge states have been theoretically suggested and experimentally verified [43, 51]. The ground states of these are depicted in Fig.2.3. Figure 2.3: NV center charge states and the corresponding energy level diagrams of their ground state. The first a1 orbital lies within the valence band of diamond. Instead, the other three orbitals lie withing the bandgap. The figure is adapted from [47]. The NV center system consists of three electrons in the dangling sp3 vacancy orbitals and two addi- tional free electrons in the nitrogen impurity orbitals. This fact gives rise to five electrons that fill up the molecular NV orbitals. The resulting configuration is termed as the neutral NV0 state and has a total electronic spin quantum number of S = 1∕2. Two other electronic states of the NV center are the NV+ and NV− states. It is naturally possible for the NV defect to trap or release electrons from or into the energy bands in diamond. Therefore, a posi- tively charged version of the NV center (NV+) can be realized when the NV defect acts as an electron donor. The total spin quantum number of the NV+ charge state is S = 0. On the other side, the NV center is able to act as an electron receptor, forming the negatively charged 9 The Nitrogen Vacancy Center in Diamond NV− state. The additional electron forms an electronic S = 1 system. The NV− center is the most prominent and well-studied defect in diamond, due to its unique spin properties and optical accessibil- ity. All NV center based magnetometry schemes are based on the negatively charged NV center. Also in this thesis, the NV− forms the nanoscale magnetic field sensor. Therefore, the negative sign will be omitted from now and the general NV expression will stand for the NV− state. 2.1.4 Optical Properties For describing the optical properties of the NV center we want to have a closer observation on its ground and excited state. As already discussed in the last subsection, the negatively charged NV center is a S = 1 triplet system, formed by the unpaired electrons in the ex and ey orbitals. From this 3A2 ground state, one electron can be promoted from the a1 orbital to the ex,y orbitals, forming the excited 3E triplet state. Both states are shown in Fig. 2.4(a) for comparison. The resulting energy gap between the NV ground and excited state is 1.945 eV. Figure 2.4: Optical Properties of the NV center in diamond. (a) Electronic structure of the NV ground state and the first excited state for comparison. One electron of the a1(2) orbital can be pro- moted to one of the ex,y orbitals. The figure is adapted from [37]. (b) Allowed transitions between the ground and excited state which define the optical properties of the NV center. Green laser irradiation promotes the electrons to the excited state. The decay results in a ZPL of 637 nm. Furthermore, a non-radiative decay is possible over metastable singlet states. A simplified energy level diagram is depicted in Fig. 2.4(b), showing the optical transitions between the 3A2 and 3E state of the NV center. In general radiative transitions with a zero-phonon line (ZPL) 10 The Nitrogen Vacancy Center in Diamond at 637 nm can be induced [52]. However, only about 4% of the photons are found in the ZPL while the rest stems from relaxation into the phonon sideband [52]. In fact, it has been shown that it is more efficient to excite the NV center off-resonantly with lower wavelengths between 512 nm − 532 nm for increasing its fluorescence counts [53]. Beside these general optical properties, the NV center obtains unique characteristics in its 3A2 ground state. As already discussed, the spin-spin interaction between the two unpaired electrons gives rise to a ZFS of the spin triplets. The resulting splitting between the mS = 0 state and the degeneratedmS = ±1 states is 2.87GHz as noted in Fig. 2.4(b). In addition, there is also a non-radiative relaxation channel processed by an inter-system crossing (ISC) [42]. The strong spin state dependence of this ISC leads to the optical spin polarization and optical spin readout of the NV center. For the mS = 0 sublevels the ISC is strongly suppressed. This results in a predominantly radiative decay from the mS = 0 sublevel of the 3E state into the mS = 0 sublevel of the 3A2 state. Instead, for the mS = ±1 states the ISC is comparable to the radiative decay rate. Therefore, the mS = ±1 sublevels of the 3E excited state relax into the singlet system by the ISC. From there, they cross over predominantly to the mS = 0 sublevel of the 3A2 ground state. As the ISC relaxation emits in the wavelength range of 1024 nm, it does not contribute to the 637 nm ZPL emission. Therefore, the fluorescence of the mS = 0 sublevels is higher than for the mS = ±1 subsystem. As a result, a fluorescence contrast of up to 30% can be observed [47]. This spin dependent fluorescence mechanism forms the fundamentals of NV center based magnetic resonance spectroscopy which will be discussed in the next section. 2.2 Magnetic Resonance Spectroscopy with NV Centers After the properties of the NV center have been introduced in the last section, we can now focus on applying the NV center spin system into magnetic resonance spectroscopy methods. The fundamental technique in terms of NV center based magnetomtery are ODMR measurement schemes which com- bine the NV center fluorescence and the electron spin resonance [54, 55]. Instead of detecting the MW absorption of the NV center, the changes in fluorescence upon spin state manipulations are detected. The spin states are controlled via resonant microwave excitation matching the ZFS of the NV center ground state spin. 2.2.1 ODMR Spectroscopy The simplest approach for realizing magnetic measurements on NV centers, is the continuous appli- cation of microwave and laser radiation for promoting the NV spin into the excited state. Such a measurement scheme is called continuous wave (cw) ODMR spectroscopy and reveals information about the Zeeman interactions on the NV center. As already discussed, the mS = 0 sublevels of the NV center result into a high fluorescence count rate. However, the NV center spin is able to flip from the mS = 0 state to one of the mS = ±1 states under resonant microwave excitation. In case of the absence of an external magnetic field, this resonant condition is fulfilled by a microwave frequency 11 The Nitrogen Vacancy Center in Diamond matching the ZFS constant ofD = 2.87GHz. Thus, sweeping the microwave frequency and matching the resonance condition provide a mS = 0 → mS = ±1 transition of the NV spin. As the excited mS = ±1 sublevels decay via the non-radiative singlet states, a decrease of the NV fluorescence can be observed. However, cw ODMR spectroscopy methods include several drawbacks due to microwave power broadening and laser frequency fluctuations [47]. Such issues prevent for example the resolu- tion of hyperfine interactions within the NV spin system. Therefore, NV center based spectroscopy methods typically rely on pulsed measurement techniques. Pulsed ODMR Pulsed ODMR spectroscopy measurements on NV centers are shown in Fig. 2.5. The basic principle is to polarize the NV spin state via laser radiation and to subsequently manipulate it with microwave excitation. Afterwards, the spin state is read out by an additional laser pulse. Figure 2.5: ODMR spectroscopy with NV centers in diamond. (a) Pulse scheme for the realization of an ODMR measurement set. The NV defect is initialized with a green laser pulse. After that, a microwave pulse is implemented for exciting the mS = 0 spin substate to one of the mS = ±1 sublevels. Therefore, the microwave frequency is swept for matching the ZFS of the ground state spin system. The readout is based on the fluorescence contrast between the mS = 0 state and mS = ±1 states. The readout sketch is adapted from [37]. (b) ODMR spectra of an NV center ensemble for different applied magnetic fields. Without magnetic field a resonant line at 2.87GHz can be observed, indicating the ZFS of the groundstate. By applying a magnetic field, a splitting of the line can be investigated due to the removed degeneracy of the mS = ±1 spin sublevels. As the NV spin is manipulated in absence of the laser illumination, the measurement technique is more robust against laser frequency instabilities. Furthermore, the NV center spin can be coherently manip- ulated due to the microwave pulses. Such a coherent spin manipulation can be achieved by adjusting 12 The Nitrogen Vacancy Center in Diamond the microwave pulses in a certain length in time. Than, the microwave pulse length corresponds to a certain phase of the quantum spin state. Typically, the resulting fluorescence photons need to be detected in the first ≈ 400 ns after the onset of the read out laser pulse for evaluating the spin state with high fidelity [37]. This fact is connected with the timescale of the 3E singlet level lifetime of about � = 250 ns [56]. Very interesting is the magnetic field dependent behavior of the fluorescence drop in the resulting ODMR spectra which are depicted in Fig. 2.5(b). In presence of an external magnetic field, the mS = ±1 degeneracy is removed following a Zeeman splitting. As already described, the Zeeman term can be written asHEZ = BNV Sz when the magnetic field is aligned parallel to the NV axis. For this case, the full frequency splitting in an NV center ODMR spectrum can be written as Δf = 2 BNV , (2.4) in which the gyromagnetic ratio is 28MHz∕mT for the NV center spin [42]. In case of a misaligned field, the frequency splitting depends on the angle between the magnetic orientation and the NV center axis. Also this has already been discussed and can be represented as the dot product in the frequency splittingΔf = 2 B0 cos �. By rising the external magnetic field, an increase of the frequency splitting in the ODMR spectrum can be observed. Thus, ODMR spectroscopy is a very fundamental tool for measuring a static magnetic field experienced by the NV center spin system. Therefore, all other measurement schemes which will be discussed in this thesis build up on pulsed ODMR spectroscopy methods. Rabi Oscillations Based on the fluorescence drop in the ODMR spectrum, we are able obtain the resonance frequency for the realization of mS = 0 → mS = −1 or mS = 0 → mS = +1 transitions. Instead of applying a microwave frequency sweep, we can now fix the excitation frequency and sweep the duration length of the pulse [57]. Such a measurement scheme is depicted in Fig. 2.6(a) and results in a oscillatory behavior called Rabi oscillation as shown in Fig. 2.6 [58]. The oscillation reveals the coherent ma- nipulation of the NV center spin state between the mS = 0 and mS = −1 sublevels or mS = 0 and mS = +1 sublevels, depending on the fixed frequency of the applied microwave pulse. Typically, the behavior of the spin state within the Rabi oscillation can be depicted by the Bloch sphere representa- tion in which the two Eigenstates |0⟩ and |1⟩ (or |−1⟩) lie at the poles of the sphere. Note that, |0⟩ and |±1⟩ represent the Eigenstates of the mS = 0 and mS = ±1 sublevels, respectively. Any superposition of the Eigenstates |Ψ⟩ = � |0⟩ + � |1⟩ can be created and visualized as a vector between the poles of the Bloch sphere. Especially the coherent superposition states |�⟩ = 1 √ 2 ( |0⟩ + ei� |1⟩ ) , (2.5) 13 The Nitrogen Vacancy Center in Diamond which are points on the equator of the Bloch sphere, are of great importance for spin sensing. Here, � is the complex phase and determines the direction along the x and y axis of the Bloch sphere. Figure 2.6: Rabi oscillation of the NV center spin. (a) Pulse sequence for driving a Rabi oscillation of the NV center spin. The microwave resonance frequency is fixed at 2.87GHz and varied in the duration time �. (b) Resulting Rabi oscillation between the |0⟩ and |+1⟩ states of the NV center ground state spin. The different emitted fluorescence of the spin sublevels makes the detection of the oscillation possible. Each point of the graph can be interpreted as a spin orientation on the Bloch sphere. The Bloch sphere sketch is adapted from [47]. With this, the Rabi oscillation measurement reveals information about the duration length of a mi- crowave pulse for exciting a certain electron spin transition. The two most relevant outcomes are the �∕2 and � pulse parameters. The �∕2 parameter denotes the resonant microwave pulse duration for achieving a transition from the |0⟩ state to the coherent super position state |�⟩ = 1 √ 2 ( |0⟩ + ei� |1⟩ ) [37]. Instead, the � pulse denotes the excitation duration for obtaining a full spin transition |0⟩ → |1⟩ [37]. It is worth to mention that the pulse durations depend on the applied MW power. Usually, an increase of the MW power leads to a higher frequency of the Rabi oscillation which can be inter- preted as a decrease of the �∕2 and � pulse lengths. The revelation of the resonance frequencies from ODMR spectroscopy and the pulse duration lengths from the Rabi oscillation is the key for advanced measurement protocols which will be discussed in the next subsection. 14 The Nitrogen Vacancy Center in Diamond 2.2.2 Lifetime Measurements So far we focused on the absorption properties of the spin states of the NV center. We have described the microwave excitation within different sublevels and the laser illumination for promoting the ground state to an excited state. However, the temporal spin dynamics involving the lifetime of the NV center spin has not been discussed. As the spin lifetime yields information about the environment of the NV center it is crucial to introduce its behavior. The most important quantities are the longitudinal spin life time (T1), the transverse relaxation time (T ∗2 ) and the coherence decay time (T2). Longitudinal Spin State Lifetime T1 The longitudinal spin life time T1 describes the duration of the preservation of a quantum state before it decays into its thermal equilibrium population due interactions with the environment [59]. In case of the NV center, several processes within the diamond lattice can contribute to such spin decays. Typi- cally, lattice phonons can act as relaxation channels for spin polarization [47]. Furthermore, inelastic scattering processes or dipolar coupling with paramagnetic impurities can provide a random energy for spin flips [47]. Therefore, measuring the T1 time could give estimates about paramagnetic con- tributions close to the NV center. A measurement scheme which is able to probe the T1 relaxation is shown in Fig. 2.7(a) [60]. Figure 2.7: Longitudinal spin state lifetime of an individual NV center. (a) Pulse sequence for reveal- ing the T1 time of the NV center consisting of two laser pulses for initialization and readout. An additional resonant microwave � pulse can be utilized for spin substate control. (b) Re- sulting fluorescence behavior of the NV center under the described pulse sequence without an additional � pulse (readout of the mS = 0 state) at ambient conditions. The T1 time of the investigated system can be estimated with an exponential approach to ≈ 12ms. The scheme consists of two variably delayed laser pulses. The first laser pulse is used for initialization of the NV center spin. For controlling the spin state, a resonant � pulse can be implemented at the beginning of the waiting time. The fluorescence read out is achieved by the second laser pulse and 15 The Nitrogen Vacancy Center in Diamond measures the remaining population in the corresponding spin state after a time �. A typical T1 mea- surement result is shown in Fig. 2.7(b) and can be described by an exponential fit. In that particular case, the measurement has been performed without a � pulse. Therefore, the mS = 0 has been read out. As a result, the fluorescence level decreases as the |0⟩ state corresponds to the brightest NV center level and the spin decays into an optically darker mixed ground state. Single NV centers are able reach T1 times in the ms range [60]. Transverse Relaxation Time T ∗2 Figure 2.8: Measurement set for estimating the T ∗2 time of a single NV center. (a) Phase pick-up of the NV center spin represented in the Block sphere picture. The spin can be excited to the superposition state with a resonant �∕2 pulse. In the coherent state, the spin is able to evolve in the xy-plane of the Bloch sphere due to magnetic noise in the NV environment. The Bloch sphere sketch is adapted from [47]. (b) FID pulse scheme for measuring the T2 ∗ time. The first �∕2 pulse creates the superposition state. This state is evolved in time. After a certain duration �, the second �∕2 pulse converts the phase pick-up to a population difference which is read out by a laser pulse. (c) Measurement on a single NV center at ambient conditions. A decrease of the NV fluorescence is observed due to the decoherence of the superposition state. A T ∗2 time of ≈ 300 ns can be estimated by an exponential envelope function. Besides investigating the timescale in which the population remains in a certain spin substate of the NV center, there are also other time quantities which are more sensitive towards external magnetic fields. Therefore, we have to evaluate the quantum coherence from Eq. 2.5 in a more detailed manner. Commonly, the phase � is time dependent (�(�)) and is affected by magnetic fields. The resulting magnetic field dependent phase pick-up is �(�) = ∫ � 0 beff (t) dt. (2.6) 16 The Nitrogen Vacancy Center in Diamond beff is the sum over all sources of magnetic fields which tune the position of the phase and can be written as beff (t) = 1 n ∑ i !0 − !i(t), (2.7) where! denotes the specific frequencies of the external magnetic fields. The influence of the magnetic field on the phase pick-up is sketched in Fig.2.8(a). Typical sources for such phase pick-ups are nuclear spins or paramagnetic species close to the NV center which are able to generate a magnetic field oscillating at their characteristic Larmor frequency. The coherent behavior of the NV center can be probed with a free induction decay (FID) measurement sequence (also called Ramsey pulse sequence) as shown in Fig. 2.8(b) [61], [62]. The scheme consist of two resonant �∕2 pulses with a variable time delay of �. The first �∕2 creates the superposition state |�⟩ of Eq. 2.5. In the beginning, the phase is zero. However, during the variable delay time a phase is picked up due to the multiple magnetic field sources in the NV environment. The second �∕2 converts the phase pick-up to a population difference which is readable by a laser pulse. The phase information is transferred to an actual fluorescence signal of the NV center. A corresponding measurement data set is shown in Fig. 2.8(c) which shows the decay of the fluorescence contrast over time caused by random magnetic field noise including the decoherence of the phase. The resulting decay envelope of the Ramsey measurement has a timescale in the order of few ns for NV centers and is termed as T ∗2 time [63]. One of the main sources for decoherence mechanisms in diamond are nuclear spins from 13C carbon atoms [47]. Coherence Time T2 Typically, the NV center T ∗2 timescale of few ns is too short for realizing reasonable sensing protocols [47]. Therefore, it is crucial to extend the coherence of the superposition state |�⟩. A powerful method for achieving this goal is to refocus the spin dephasing mechanism by applying an additional � pulse into the Ramsey measurement scheme. As a result the magnetic interactions are inverted, leading to a sign change of the phase pick-up, and a spin echo will occur when the acquired phase has been canceled. In its simplest form the technique is referred as Hahn echo measurement [64]. The pulse sequence is depicted in Fig. 2.9(a). At the half evolution period, a refocusing � pulse is added which corresponds to a flip of the time evolved spin state by 180◦ around the x-axis. Mathematically, this can be interpreted as a sign change and the accumulated phase during the second free evolution period can then be written as �(�) = ∫ �∕2 0 beff (t) dt − ∫ � �∕2 beff (t) dt. (2.8) Consequently, the phase pick-up is canceled if both evolution periods are equal in time length. Thus, the original superposition state |�⟩ will be restored. At the end of the sequence, a final �∕2 pulse converts the remaining phase difference to a population difference. A typical Hahn echo measurement 17 The Nitrogen Vacancy Center in Diamond on a single NV is shown in Fig. 2.9(b). Again, a decay envelope of the decoherence can be observed. However, the resulting coherence decay constant, termed as T2, is larger than the T ∗2 time gained from the Ramsey measurement scheme. For single NV centers the T2 time can reach up to 100�s [65]. In practice, the Hahn Echo pulse scheme is slightly modified for removing artifacts from the measured curves. This is achieved, by implementing simultaneously a 3�∕2 pulse to the final �∕2 pulse. With this, the coherent state is once flipped to the bright |0⟩ state and on the following pulse sequence to one of the dark |±1⟩ states. A contrast curve is created by substracting the two resulting data sets of pure fluorescence. This pulse sequence will be discussed more detailed in chapter 4. Such refocusing pulse schemes build up the fundamental principle of NV center based spin sensing. Figure 2.9: Hahn Echo measurement set on an NV center. (a) Pulse sequence and corresponding spin evolution depicted in the Bloch sphere. The first �∕2 pulse creates the superposition state of the NV center spin. After a certain time amount �∕2, the spin evolves and picks up a phase which is dependent on the magnetic noise. A resonant � pulse flips the evolved spin by 180◦. After the second free evolution period the phase pick-up is canceled. The final �∕2 pulse converts the remaining phase difference to a population difference. (b) Resulting data from a Hahn Echo Measurement on a single NV center at ambient conditions. Like in the FID measurement scheme, a decrease of the fluorescence can be observed due to the decoherence of the superposition state. However, the exponential envelope yields a higher time constant of 14�s that is denoted as coherence time T2. 18 The Nitrogen Vacancy Center in Diamond 2.2.3 Spectral Filter Functions After we described experimental measurement schemes on manipulating the NV center spin state, we want to assign theoretical expressions of how the NV is influenced by the magnetic noise in its envi- ronment under these pulse schemes. This issue can be mathematically defined by the spectral filter function  (!) which is a specific formula for each applied sequence. In general, the filter function denotes a selective transmittance of a wavelength specific signal. Together with the spectral density �(!) of the environmental magnetic noise, the sequence specific filter function  (!) forms the envi- ronmental relaxation rate Γenv of the spin system [47]: Γenv ∝ ∫ ∞ 0  (!)�(!) dt. (2.9) Therefore, the filter function is an important expression for evaluating the influence of different fre- quency regimes on the NV center lifetime. Filter Function for a T1 Measurement The spectral filter function for a T1 measurement pulse sequence can be formed by utilizing Fermi’s golden rule which describes the transition rate between different energy Eigenstates in a quantum system [66]. As a result,  (!) consists of two Lorentzians at the frequencies !± = D ± Bz [47]: T1(!) = � ��2 + (! − !+)2 + � ��2 + (! − !−)2 . (2.10) The linewidth Δ� of the Lorentzians are dependent on the T ∗2 related inhomogeneous broadening Δ� = 1∕T ∗2 . As the ZFS parameter D is in the GHz regime, magnetic noise need to fluctuate at GHz frequencies for having an influence on the T1 time of the NV center. Filter Function for an FID Measurement The filter function for an FID pulse sequence is defined by an oscillation magnetic field with a charac- teristical frequency ! [47]: FID(!) = ( sin !�2 ! 2 )2 . (2.11) The sensitivity of the FID sequence is limited by the dephasing T ∗2 time of the investigated system. Filter Function for a Hahn Measurement In case of a Hahnmeasurement, the sign of themagnetic field sensitivity is switched by an implemented � pulse within the sequence. Therefore, the sensitivity function alternates between +1 and −1 in the 19 The Nitrogen Vacancy Center in Diamond time domain. By applying a Fourier transformation to this alternating square function, the spectral filter function can be derived to [47] Haℎn = ( sin2 !�4 ! 4 )2 . (2.12) As the Han echo pulse sequence decouples the NV center from its environment, the measurement scheme is only sensitive to a narrow frequency range. This spectral regime can be narrowed further by applying multiple decoupling pulses which benefits NV center based NMR measurements and will be discussed in subsection 2.2.5. 2.2.4 ESR Measurement Schemes with NV Centers One of themost demonstrated applications of NV center sensors is the investigation of single molecular systems with ESR spectroscopy. In general, ESR measurements are widely used in various scientific fields for the detection of free radicals and the identification of paramagnetic complexes revealing their electronic structures [67]. The origin of the ESR signal of a sample can be explained by the Zeeman effect. An unpaired electron in an observable system obtains a spin quantum number of s = 1∕2 and with this the magnetic components ms = ±1∕2. In presence of an external magnetic field B0, a separation of these two magnetic components occurs due to the Zeeman effect with an energy gap of ΔE = ge�BB0, (2.13) in which ge is the free electron g-factor and �B the Bohr magneton. Furthermore, the electron spin can flip by absorbing or emitting photons with an energy value of ΔE = ℎ�. Therefore, Eq. 2.13 can be written as ℎ� = ge�BB0, (2.14) forming the fundamental EPR equation [67]. The mathematical term shows that an external magnetic field is able to induce a precession of the electron magnetic moment (called Larmor precession) which can be investigated in form of absorption measurements. However, the major limitation of such ESR techniques is the huge number of spins (≈ 1012 [68]) which are necessary for the measurements, preventing the investigations on nanometer sized samples or single molecules. One way to solve this problem is to implement quantum sensors as the NV center into ESR measurement schemes. In fact, NV center based ESR experiments have been successfully achieved by using double electron electron resonance (DEER) measurement protocols. 20 The Nitrogen Vacancy Center in Diamond DEER Spectroscopy DEER measurements are able to identify couplings between electronic spins [69]. The resulting cou- pling strength contains information about the distance between the measured spins and with this the structure of molecules can be studied [70]. NV center based DEER spectroscopy can be realized by implementing an additional � pulse within the NV Hahn echo measurement scheme which we discussed in Fig. 2.9 [71]. Figure 2.10: DEER measurement set on an NV center realizing ESR spectroscopy. (a) Pulse scheme of the DEER measurement technique consisting of an additional � pulse compared to the Hahn Echo sequence. The additional � pulse is varied in frequency and excites an external spin in the NV environment. Furthermore, it is crucial to time the pulse in the second evolution period of the NV center superposition spin. A resonant excitation of the external spin results into a drop of the recorded NV center fluorescence. (b) DEER spectrum measured by a single NV center at ambient conditions. The sharp fluorescence drop indicates a spin signal of electrons in the NV environment. The modified pulse sequence is shown in Fig. 2.10(a). The frequency of the additional � pulse is swept in a certain frequency range for matching the resonance condition of the external spin. In resonance, the external spin reverses its Sz component which also inverts the sign of the NV center phase pickup. By timing the additional � pulse right after the NV spin � pulse, the new magnetic field dependent phase pick-up is �(�) = ∫ �∕2 0 beff (t) dt − ∫ � �∕2 beff ,2(t) dt. (2.15) As beff = −beff ,2, the phase pick-up is not canceled to zero like in the scenario of the pure Hahn echo measurement on the NV. Therefore, a change in the NV center fluorescence can be observed by matching the resonance frequency of the investigated spin as shown in Fig. 2.10(b). This phase accumulation is solely permitted for the resonant excitation of the external spins. Depending on the applied magnetic field strength, the resonance frequency of an external electron spin is in the order of 21 The Nitrogen Vacancy Center in Diamond ≈ 100MHz. Based on the DEER pulse sequence, the coupling between the NV center spin and an external spin can be investigated more detailed in form of DEER Double Quantum Transition (DQT), DEERRabi and DEERDelay measurements. However, these sequences will be discussed in chapter 4, in which we utilize a single NV center for sensing individual molecules. 2.2.5 NMR Measurement Schemes with NV Centers Besides ESR measurements, also NMR experiments have a great impact in modern science. The magnetic field dependent Larmor precession of the atomic nuclei is extensively used in medicine for magnetic resonance imaging [67]. However, also here the number of nuclear spins has to be huge for gaining a measurable signal. Again, the NV center can be utilized as nanoscale quantum sensor. Nevertheless, more complicated dynamical decoupling schemes have to be implemented by inserting more refocusing � pulses [72]. The reason for this are the different characteristics between electron and nuclear spins. Typically, the electron larmor precession is on the order of≈ 100MHz−9000MHz [70] leading to a realtively high ΔE which can be measured. Instead, nuclear spin frequencies are on the order of ≈ 200 kHz − 1.2MHz [72] resulting in a significantly decreased ΔE. Therefore, the NV center as sensor has to be decoupled from its magnetic environment in a more robust manner. XY8-N Dynamical Decoupling A frequently used concept, for increasing the robustness of the NV center is the XY8-N pulse scheme, which is depicted in Fig. 2.11(a) [73]. The measurement sequence consists of N = 8n refocusing pulses which are able to cancel out pulse errors in a very efficient way. Furthermore, the symmetrical shape of the sequence decouples the NV against all possible phase noise. Depending on the total number of microwave pulses, the sequence acts as a filter function for a certain frequency �: XY 8−N = 2 ( sin ��2 � 2 sin2 �� 4N cos �� 2N )2 . (2.16) The sensitivity can be described the width Δ� of the filter function: Δ� = 1 N� . (2.17) A typical result of this technique is shown in Fig. 2.11(b) which presents the NMR signal of carbon and hydrogen atoms measured with an NV center. However, a drawback of this technique is the limitation of the frequency resolution (≈ 50 − 100 kHz [73]) as the measurement protocol is limited by the NV center coherence time [74]. As a consequence, important quantities in the field of NMR can not be observed with the NV center sensor like the chemical shift or the J-coupling which obtain a spectral width on the order of 10Hz [75]. 22 The Nitrogen Vacancy Center in Diamond Figure 2.11: NMR spectroscopy with NV centers in diamond. (a) Microwave pulse scheme of the XY8-N sequence. The number and timing of the � pulse train defines the frequency selection and resolution of the measurement technique. (b) Resulting NMR spectrum of the carbon and hydrogen signals recorded by an NV center. The different atomic species of the sample are clearly observable. The resolution of the spectral features is on the order of 50 − 100 kHz. Quantum Heterodyne Detection Scheme An ultrahigh resolution sensing scheme based on the NV center can be realized with the Quantum Heterodyne Detection (Qdyne) by combining several XY8 sequences as shown in Fig. 2.12(a) [76]. In this pulse scheme, the NV center fluorescence is measured after each XY8 sequence as a function of time. Each sampling instance consists of an initialization, a phase measurement and a read out of the NV center [76]. The time trace of the measured fluorescence is able to reconstruct the wave form of the magnetic field experienced by the NV center. With a Fast Fourier Transformation (FFT), the time trace can be converted to a frequency scale revealing the Larmor precession of the observed nuclei. Fig. 2.12(b) shows a Qdyne spectrum of a 1MHz test signal with a resolution of about 5Hz. The test signal was generated by a cw radio frequency (RF) running through a copper coil which has been positioned close to the NV center diamond sample. Modifications of the Qdyne measurement scheme have achieved a frequency resolution of even 600�Hz [74]. 23 The Nitrogen Vacancy Center in Diamond Figure 2.12: NMR spectroscopy using a single NV center based on the Qdyne measurement scheme. (a) Pulse sequence of the Qdyne measurement protocol. A train of XY8-N sequences are attached to each other. After each readout pulse, the fluorescence is measured and recorded as a function of time. The resulting fluorescence time trace can be converted with a FFT into the frequency domain containing spectral information of the magnetic noise in the NV environment. The figure is adapted from [76]. (b) Resulting Qdyne spectrum of a 1MHZ test signal measured with a single NV center at ambient conditions. The frequency resolution is in the 5Hz regime. 2.3 NV Center Implantation into Diamond Samples After we described the theoretical background of the NV center in diamond and its usage in nanoscale magnetometry, we want to briefly introduce fabrication processes which are able to implant NV centers into a diamond sample. However, before we focus on that, the artificial diamond growth is explained. 2.3.1 Arti�cial Diamonds Diamonds can nowadays be readily produced artificially in two different approaches. The first fabrica- tion technique relies on the application of high pressure and high temperature (HPHT) to graphite or 24 The Nitrogen Vacancy Center in Diamond another form of carbon for a certain amount of time, forming a diamond sample [77]. An advantage of this technique is the large quantity of diamonds which can be produced. However, the resulting samples contain often a poor quality with many uncontrolled impurities. Instead, clean diamonds can be created using chemical vapor deposition (CVD) [78]. In this fabrica- tion method, a high quality carbon seed crystal is exposed to a high temperature gas of hydrocarbons which are able to bond to the carbon surface dangling bonds. NV centers can be created after the diamond fabrication by the implantation of nitrogen ions into the diamond matrix and subsequent annealing by the incorporation of nitrogen during the CVD growth. 2.3.2 Single NV Center Implantation Typically for single NV membranes, the nitrogen ions are implanted after the diamond sample fabri- cation. This approach allows the control of the NV center depth which is defined by the kinetic energy of the implanted ions [79]. The vacancies are formed by a subsequent annealing step at temperatures above 650 ◦C. However, the ion straggling creates a large amount of crystal faults which can influence the NV center spin properties. 2.3.3 NV Center Ensemble Implantation Also NV ensembles can be fabricated by the direct nitrogen ion implantation. Therefore, the ion beam diameter has to be enlarged for increasing the nitrogen concentration withing the carbon crystal. How- ever, ensembles of NV defects can also be created by the incorporation of nitrogen atoms during the diamond growth process. This fabrication technique is called �-doping [80]. Afterwards, irradiation with high energy particles or subsequent annealing steps have to be involved for creating vacancies. This approach creates less unwanted crystal defects which influence the NV spin properties. However, a precise location of the incorporated nitrogen atoms is not possible. Nevertheless both fabrication methods have the ability to create shallow NV centers few nanometers below the diamond surface which is the key for sensing applications. 2.3.4 Diamond Nano-Structuring The key quantity for NV center based magnetometry is the fluorescence of the defects. Therefore, it is crucial to obtain NV centers with high emission rates. In case of NV center ensembles, a high countrate is achieved by the density of the NV cluster. Regions on the diamond sample with an high NV center density exhibit an intense emission. However, individual NV centers usually obtain a low number of collected photons [81]. For increasing the single NV emission, nanofabrication processes can be performed. An efficient attempt, is the implementation of nanopillars on the diamond surface in which single NV centers are located. The pillar structure acts as an waveguide for the NV emission and increases the collection number of photons [81]. Typically, nanopillars can be fabricated by etching the diamond surface with O2∕O2+CF4 plasma [81]. Before of that, the diamond has to be coated with a 25 The Nitrogen Vacancy Center in Diamond plasma resistive mask which defines the pillar geometry. Afterwards, the NV centers can be implanted within the pillars. A corresponding SEM image is shown in Fig. 2.13. Figure 2.13: SEM image of a nano-structured diamond surface. Due to specific plasma resistivemasks, nanopillars can be formed after etching the diamond surface. Afterwards, single NV center can implanted within the pillars. The nanostructure acts as a waveguide for the NV fluorescence and increases the resulting collection photons. The figure is adapted from [81]. 2.4 Summary In this chapter we introduced the NV center in diamond as a nanoscalemagnetic field sensor. A detailed overview of the NV properties was given by evaluating its Hamiltonian resulting into the electronic structure and the optical behavior. Most importantly it was shown that resonant microwave pulses can excite different sublevels within the NV center spin ground state. Furthermore, the fluorescence shows a spin dependence which can be used for sensing applications. The simplest measurement scheme can be realized by ODMR spectroscopy revealing static magnetic fields experienced by the NV center. In addition, more sophisticated pulse sequences like DEER schemes can be implemented for the detection of single electrons in the NV environment. NMR spectroscopy can be achieved by modifying the DEER pulse sequences towards dynamical decoupling schemes which is sensitive for nuclei Larmor frequencies. Finally, a short description was given regarding different fabrication processes of NV implanted diamond samples. Artificial diamonds can be created by HPHT or CVD growth methods. Thereby, NV defects can be inserted after the diamond fabrication by nitrogen ion implantation or during the CVD growth process in form of �-doping. For both techniques, the vacancies are formed via heat exposure or high energy irradiation. The theoretical background of this chapter is crucial for a better understanding of the experimental results of this thesis. 26 Experimental Setup 3 Experimental Setup This chapter presents the experimental setup which was utilized for performing the measurements of this thesis. The first section describes an overview of the setup which consists of a cryostat connected to an UHV chamber. The structure of the cryo-UHV instrument is explained in a more detailed manner in the second section by highlighting the load lock, preparation and main chamber. Furthermore, the measurement head which is positioned within the cryostat is described. The third section is dedicated to the microwave pulse generation which is crucial for realizing spin manipulation measurements on the NV center. In the last section, we focus on the optical elements of the instrument. These are of great importance as the NV center has to be initialized and read out optically. It is also worth to mention that a detailed technical description of the setup can be found in the works [37] and [82] which fully focus on the instrument. 3.1 Overview Scheme of the Setup The architecture of the experimental setup consists of four different subsystems, namely the confocal microscope, the microwave generation, the vacuum chamber and the cryogenic system. A simplified diagram of the setup is illustrated in Fig. 3.1(a). For promoting the NV center ground state into its excited level, a pulsed laser with a frequency of 512 nm is used. The NV center emission is collected with avalanche photo diodes (APDs) which are characterized by an efficiency maximum at around 650 nm. These parts, form together with refocusing lenses, a dichroic mirror and a 75�m pinhole the confocal microscope which is able to image the NV center fluorescence. Apart from the objective which is positioned inside the cryostat, the whole optical setup is assembled outside the vacuum system. Besides optically exciting the NV center, the spin states have to be manipulated with microwave and RF fields. Therefore, HF sources are coupled into a waveguide on the sample via impedance matched transmission lines within the cryostat. The control of the pulse sequences is achieved by a Field Programmable Gate Array (FPGA) which is able to trigger the switches between the laser and microwave signals [47]. 27 Experimental Setup Figure 3.1: Overview of the experimental setup. (a) Simplified sketch of the setup which consists of an UHV-cryostat. The NV-diamond sample is located inside the instrument. Below the UHV chamber, an optical confocal microscope is assembled for exciting and reading out the NV center. Furthermore, a microwave line is implemented for NV center spin manipulation. (b) Photograph of the experimental setup. For realizing measurements in a cryogenic-UHV environment, a helium bath cryostat is attached to a vacuum chamber. The cryostat is able to reach a base temperature of 4.7K. Furthermore, different pumps are able to create an UHV environment with a pressure of about 2 ⋅ 10−10mbar. The vacuum chamber obtains several ports with optically accessible windows in the visible wavelength range for ensuring a transmission of the 512 nm laser light and the 637 nm − 750 nm NV emission. These subsystems will be explained in a more detailed way in the following sections. 3.2 The Cryo-UHV Setup After giving a general overview of the experimental setup, we want to focus on the cryo-UHV part of the instrument in this section. In the first part, the vacuum setup is described which consists of three separated vacuum chambers named load lock, preparation and main chamber. After that, the cryostat structure and the measurement head are explained. 3.2.1 Load Lock and Preparation Chamber The first two parts of the UHV setup are the load lock and the preparation chambers. Both are separated from each other by a gate valve. The load lock chamber provides the first step for introducing a sample 28 Experimental Setup from an ambient environment into an UHV system. Typically, a load lock chamber ensures a vacuum of about 2 ⋅ 10−8mbar. Figure 3.2: Overview of the preparation chamber. (a) Side view photograph of the preparation chamber on which a gas line is connected to it for surface treatments. A leak valve is used for controlling the gas flow. Furthermore, a CO2 laser is guided to the chamber for cleaning the diamond surface. (b) Top view photograph of the preparation chamber. The sampleholder is stably located into a manufactured mount which is screwed into the magnetic transfer rod. Before a sample can be introduced into such a chamber, the load lock system has to be vented with pure nitrogen gas. After that, the sample can be mounted on the magnetically coupled linear transfer rod [37]. Amembrane pump is used for generating a pre-vacuum state of fewmbar. When this is achieved, the system including the sample can be evacuated via turbomolecular pumps down to 10−8mbar [83]. The pressure is read out by cold cathode gauges. The advantage of implementing a load lock chamber into the vacuum system is the in situ sample exchange, as the preparation and main chambers are not vented during the sample transfer. When the load lock pressure is in the range of 10−8mbar, the sample can be transferred into the 29 Experimental Setup preparation chamber. For this, the gate valve can be opened and the magnetic transfer rod can be introduced into the preparation chamber. Also this system contains a magnetic transfer rod with a stage which is able to hold the introduced sample. In contrary to the load lock, the preparation chamber is equippedwith a turbomolecular pump and an ion getter vacuum pump [84]. This pumping combination is able to realize an UHV environment on the order of 10−10mbar. Furthermore, the preparation chamber enables the deposition of different gas molecules upon the diamond surface for modifying the NV center spin properties. Therefore, a leak valve is attached to one port of the chamber. The corresponding gas bottles are connected with steal pipes to the leak valve for ensuring a controllable introduction of the gas. Additionally, a ZnSe vacuum viewport is attached on the preparation chamber which transmits infrared light (IR). A high power 10�m IR laser beam can be introduced through this port for cleaning the diamond surface. The top and side views of the preparation chamber are shown in Fig. 3.2 highlighting the explained features. After the surface treatment of the diamond, the sample holder can be transferred to the main chamber. 3.2.2 Main Chamber and Cryostat The main chamber is separated by a gate valve from the preparation chamber and is equipped with a turbomolecular pump and an ion getter vacuum pump. Typically, the readout pressure is at about 2 ⋅ 10−10mbar confirming the UHV environment in which the sample is located. The central part of the main chamber is the attached cryostat which consist of two stages with distinct base temperatures as shown in Fig. 3.3. The outer part (depicted in green) forms the liquid nitrogen reservoir with a volume of 30 liters and acts as a protection jacket for the 10 liters helium reservoir (inner part depicted in blue) [37]. Due to the extremely low boiling temperatures of the used gases, the nitrogen reservoir reaches a base temperature of 77K and the helium stage obtains a temperature of 4.7K [85, 86]. For controlling thermal fluctuations, the cryostat is fabricated from stainless steel which is a poor thermal conductor [37]. In addition, the UHV surrounding decreases thermal conduction from the environment. Therefore, the heat transfer is dominated by thermal radiation and conduction between the electrical wires which are connected to the measurement head. The thermal radiation is suppressed by the implementation of two gold-plated copper shields which are mounted around the measurement head. A shutter mechanism enables the sample transfer and view ports provide optical access. The heat transfer from the electrical connections is minimized by the chosen wire materials. Bronze wires with a thermal conductivity of 1.6 W m⋅K have been inserted for controlling the piezomotor of the sample stage [37, 87]. Furthermore, the microwave transmission lines are formed by semi-rigid coaxial cables with stainless steel shielding obtaining a thermal conductivity of 2 �W m⋅K [37, 88]. The resulting liquid helium consumption is of about 2.4 liters∕day by inserting the described thermal shielding and optimized wiring. However, laser and high frequency applications during extensive measurement sets increase the helium consumption to almost 4 liters∕day. 30 Experimental Setup Figure 3.3: Cross-section of the cryostat. The instrument consists of two reservoirs which operate at 77K (green part) and 4.7K (blue part). The operation temperature is achieved by filling the reservoirs with liquid nitrogen and helium. The sketch is adapted from [37]. 3.2.3 Measurement Head In the last part of this section, we want to focus on the measurement head as this element combines the key components for the investigation of NV centers, namely the optical and high frequency excitation. Therefore, it is crucial to provide an optical access to the mounted sample with a high collection efficiency. This can be realized by utilizing high numerical aperture (NA) objectives consisting of sophisticated multi-lens systems for correcting chromatic aberration [89]. However, the performance of such lens systems are highly affected by the ultra cold environment as the refractive index and the dispersion of the glasses depends on the temperature [37]. Furthermore, the glass curvature contracts at low temperatures resulting in a change of the lens radius and thickness [37]. Therefore it is crucial to implement a cryogenic compatible high NA objective [90]. Another important part of the measurement head is the home-built sample stage which consists of piezo actuators for three dimensional sample positioning, a mounting fixture for the sample holder and the high frequency transmission lines. The transmission for the MW excitation is crucial for precise NV center spin manipulation. This is achieved by coupling the waveguides of the sample holder with the MW transmission lines of the measurement head by spring-loaded contacts. These connections are assembled by sub-miniature-P (SMP) connectors, a glass-ceramic body and beryllium copper (CuBe) springs on which halfed copper (Cu) spheres are glued. Finally, the spring contacts are interconnected by flexible coaxial cables to the cryostat mount plate from where semi-rigid transmission lines go to the cryostat top plate. A sketch of the measurement head and a corresponding photograph is shown 31 Experimental Setup in Fig. 3.4. Figure 3.4: Overview of the measurement head. (a) Sketch of the measurement head assembly illus- trating the sample mount (in red) and the piezo stage (in blue) adapted from [82]. The inset shows a photograph of the sample holder. The copper waveguides are crucial for the MW transmission. (b) Photograph of the measurement head fixed to the cryostat cold plate. In addition, an electromagnet is installed inside the measurement head for controlling the orientation and the magnitude of the magnetic f