Browsing by Author "Büchler, Hans Peter (Prof. Dr.)"

Now showing 1 - 4 of 4

Open Access
Collective effects of light-matter interactions in Rydberg superatoms
(2021) Kumlin, Jan; Büchler, Hans Peter (Prof. Dr.)
Open Access
Quantum Monte Carlo studies of strongly correlated systems for quantum simulators
(2018) Humeniuk, Stephan; Büchler, Hans Peter (Prof. Dr.)
Many strongly correlated quantum systems are difficult to study numerically because of the exponential growth of the Hilbert space combined with the failure of numerical methods in important parameter regimes. This includes the long-standing problems of high-temperature superconductivity and frustrated magnetism. A promising solution to this dilemma are quantum simulators, well-controlled (synthetic) quantum systems, emulating model Hamiltonians not only of condensed matter systems, where parameters can be tuned at will and model complexity can be added step by step. This dissertation presents numerical simulation studies that are motivated by quantum simulators. Using large-scale quantum Monte Carlo computer simulations and mean-field theory the semiquantitative ground state phase diagram of a Penning ion trap quantum simulator, realizing a two-dimensional model of quantum magnetism with long-range interactions, is obtained. We study also thermal and quantum phase transitions in one-dimensional transverse-field Ising models with long-range interactions, which exhibit a Kosterlitz-Thouless transition and universality classes with continuously varying critical exponents. The second part of this thesis is concerned with the Fermi-Hubbard model, which has been realized recently with ultracold atoms in optical lattices, both for repulsive and attractive interactions. Equipped with a quantum gas microscope, which allows single-site single-atom detection, these experimental setups can collect histograms of the particle number from repeated projective measurements. This dissertation presents a method to compute such full counting statistics for quadratic operators such as particle number or magnetization in the framework of determinantal quantum Monte Carlo. From an analysis of the full counting statistics of the particle number for different subsystem sizes the size of preformed pairs or Cooper pairs in the attractive Hubbard model is inferred. Furthermore, excellent agreement of the numerically computed probability distribution of the staggered magnetization with a recent quantum gas experiment demonstrates that current experiments are capable of resolving the differences between the Hubbard model and its limiting Heisenberg model. An extensive method section reviews the stochastic series expansion quantum Monte Carlo method for Ising models in a transverse field, which is free of the sign problem for arbitrary interactions, with special emphasis on the efficient simulation of long-range interactions. Also a self-contained introduction to the determinantal quantum Monte Carlo method is provided.
Open Access
Quantum simulator for spin-orbital magnetism
(2015) Bühler, Adam; Büchler, Hans Peter (Prof. Dr.)
In this dissertation we focus on many-body phenomena on a quantum level. In particular fermionic quantum gases in a temperature regime approaching absolute zero. Ultracold quantum gases have proven to be a versatile framework for Theorists and Experimentalists to probe many-body quantum mechanics. They also serve to quantum simulate solid state problems in a clean and controllable environment. The use of optical lattices include the advantage of tuning the required lattice structure nearly at will and lack the experimental shortcomings compared to the solid state, like the presence of lattice dislocations. The relevant lattice parameters can be easily tuned without changing the setup. In recent years many goals within theory and experiments of ultracold quantum gases in optical lattices were achieved. This emphasizes the significance of ongoing research with ultracold quantum gases on optical lattices. We present two aspects of modern theory of ultracold quantum gases in optical lattices. On the one hand, we implement orbital physics in a setup of optical lattices and on the other, we find elusive Majorana fermions in a setup with ultracold fermionic gases. Both aspects are well-known in solid state systems, but did not make the step towards ultracold quantum gases so far. We propose and investigate setups to quantum simulate these challenges in the framework of optical lattices. The first part of this work concerns the implementation of orbital physics in optical lattices. The orbital structure of atoms reveals novel phenomena in solid state systems. This raises the interest in creating optical lattice systems exhibiting analog behavior, as dictated by the orbitals in the solid state. We derive the microscopic Hamiltonian for a p-orbital system and investigate it in detail. For this Hamiltonian we perform a mean-field treatment and discover novel phase transitions including a possible tricritical point. In the analysis of the strong coupling regime we find an additional phase transition towards an antiferromagnet and then extend the mean-field phase diagram. Concluding the investigations is a proposal of an experimental setup to achieve orbital physics with state-of-the-art experimental tools. The second part of this work considers Majorana modes and p-wave superfluids. Majorana modes are not only present in high-energy physics, but also in condensed matter systems. Here we demonstrate a setup in order to simulate Majorana modes and p-wave superfluids in optical lattices. We derive an effective Hamiltonian and investigate it on a mean-field level as well as give the mean-field phase diagram. It contains a rich manifold of different p-wave phases. In addition, we extend our investigations to topological properties of our system and provide the topological phase diagram. We discover the special phenomena that the mean-field and topological phase transitions are decoupled in our system. The proposed system is suited to have Majorana modes at vortices and dislocations, which are injected into the system in controllable experimental manner. We conclude the considerations by giving a protocol for braiding in order to demonstrate non-Abelian statistics of Majorana modes.
Open Access
Strongly interacting many-body systems in cold atomic gases
(2013) Honer, Jens Daniel; Büchler, Hans Peter (Prof. Dr.)
The remarkable progress in control over cold atomic gases has led to a point where people are no longer satisfied with merely studying these systems, but rather put them to use to understand complex quantum many-body systems. The basis of this development is a deep understanding of the interaction between atoms, and how to exploit those in order to engineer interesting and novel quantum-systems. The aim of this particular thesis is to contribute to this third quantum revolution [1] and hence help to understand the inner workings of complex many-body systems. We present a method to control the shape and character of the interaction between cold atoms based on dressing the atomic ground-state with a Rydberg-state. The latter induces a van der Waals interaction between all the atoms in the ensemble, and allows for control via the coupling light-field. We find that with increasing atom densities the ensemble shows a direct transition into a collective regime that preempts the onset of three-body interactions associated with a break-down of the first Born-approximation. The reason for this intriguing behavior is the strong interaction between Rydberg atoms that gives rise to the blockade-mechanism, and prevents the simultaneous excitation to the Rydberg-state for spatially close atoms. The non-trivial behavior of the interaction-potential within the collective regime yields a novel tool for shaping the interaction between ground-state atoms beyond s-wave scattering. We study this collective regime and the resulting interaction-potential between the atoms within a variational/mean-field approach, and discuss its effects on a trapped Bose-Einstein condensate. Artificial atoms show remarkable properties, that are often superior to real atoms. In particular, since they are built out of many constituents, such systems often exhibit an enhanced coupling to the light-field as well as strong optical non-linearities even for small light-fields. On the other hand, noise in quantum-mechanical systems can not only destroy coherence, but rather can be used in order to robustly drive a system into an interesting state. We study the effect of a controlled dephasing onto an artificial atom in the context of an ensemble of atoms coherently coupled to a Rydberg state and demonstrate that such an enhanced artificial atom allows for the deterministic absorption of a single photon from an arbitrary incoming probe field. Such behavior yields a unique tool in light-matter interaction, and opens the path to realise quantum-networks or to fabricate novel quantum-devices. Here, we discuss the applicability of this single-photon absorber as a single-photon transistor, a high fidelity n-photon counter, and a device that allows for the deterministic creation of non-classical states of light via photon-subtraction. A non-trivial topological order of quantum-states leads to conservation of certain properties and, hence, increases their robustness against external perturbations. This can even stabilize quantum-states against local fluctuations. The latter usually corrupts the coherence within a macroscopic object and thereby prevents quantum-phenomena to occur in our macroscopic world. As an example of such a topological state, we study the behavior of vortex-excitations in a two-dimensional superfluid confined to a periodic potential, as can be realised within a cold atomic gas in an optical lattice. For large superfluid filling factors and strong interactions, the healing-length and, accordingly, the vortex core is much smaller than the lattice spacing. As a result, vortices are confined to the plaquettes of the lattice, and can be described in the framework of an effective tight-binding Hamiltonian. Via a first-principle calculation based on coherent-state path-integrals we derive the microscopic parameters of this model and provide an analytic expression for the vortex mass. Moreover, we show that such a quantum vortex is not obliged to follow the superfluid flow, but rather exhibits Bloch-oscillations perpendicular to it, which is a telltale sign for quantum interference of this macroscopic many-body excitation. Recently, Jonathan Simon et al. [2] performed a major step towards simulating quantum many-body systems in cold atomic gases by simulating the paramagnet-antiferro-magnet transition of a one-dimensional Ising-model. Fundamental excitations in the phase with broken translational symmetry are domain-walls carrying fractional statistics. The question is, whether experimentally accessible single-particle excitations, which correspond to two closely-bound domain-walls, decay into fractional excitations or remain closely-bound. By use of perturbation theory, we derive an analytic model for the time-evolution of these fractional excitations in the framework of a tilted Bose-Hubbard model, and demonstrate the existence of a repulsively bound state above a critical center-of-mass momentum. The validity of the perturbative approach is confirmed by the use of t-DMRG simulations. Together with the recent demonstration of single-site addressing and readout in optical lattices, these findings open the path for experimental observation of fractional excitations within cold atomic gases.