University of Hamburg Library · PDF
Quantum gases of ultracold atoms are ubiquitous in modern physics as they offer excellent isolation from the environment as well as fine-grained control over their relevant characteristics such as interparticle interactions. Almost arbitrary spatial arrangements of these particles can be realized and manipulated by employing external potentials. This versatility renders ultracold atoms an ideal platform for the simulation of other quantum system as well as promising candidates in the field of quantum information. However, the corresponding theoretical description usually involves complex many-body problems which can rarely be solved analytically, thus rendering the development of powerful numerical approaches crucial.
The present thesis employs the family of multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) methods in order to simulate ultracold quantum many-body systems. While this class of ab-initio approaches originates from the description of molecular dynamics in quantum chemistry, it was later applied to a plethora of other problems and extended to capture indistinguishable particles such as ultracold atoms. The strength of this class of algorithms stems from the fact that they employ variationally optimal, time-dependent basis functions in order to obtain a compact representation of the many-body wave function. The construction of hierarchical multi-layer ansätze allows for the treatment of large and complex composite quantum systems. The present thesis focuses on the development of methodological and implementational improvements as well as the application of the method to novel scenarios.
Even though ML-MCTDH methods can often yield compact representations of the many-body wave function, they too cannot escape the exponential scaling of computational complexity as the number of particles increases or when strong correlations in the system require numerous basis functions in order to obtain accurate results. In recent years, various different approaches have been proposed to tackle this problem and reduce the numerical effort. Unfortunately, these schemes cannot be easily transferred to ultracold atom setups or are unable to adapt to non-trivial dynamics. Hence, a novel dynamical pruning approach targeting bosonic particles is developed in the scope of the present thesis. The scheme automatically selects the most relevant many-body states and adapts to the time-evolution of the system. The algorithm is benchmarked using two typical scenarios motivated from ultracold atom physics and found to capture the physics accurately while significantly reducing the computational effort in some cases.
A particularly fascinating aspect of quantum simulation is the emulation ultrafast processes such as electronic dynamics with slower-moving atomic particles. In light of this strategy, controlled collisions of ultracold atoms confined in moving potential wells may serve as a test bed to unravel the fundamental processes in atom-atom collisions by taking on the role of electrons. Furthermore, similar scenarios have been proposed as a means to generate entanglement and implement quantum gates in the context of quantum computing. Therefore, the second focus of the present dissertation is to investigate the nonequilibrium dynamics of bosonic particles in colliding potential wells which can be realized experimentally using optical tweezers. This study illuminates the main signatures of the dynamics such as entanglement build-up as well as the transport and untrapping of particles.
Quantum spin models are relevant in many areas of physics such as quantum information or condensed matter physics and have been realized experimentally using ultracold atoms or in the related field of Rydberg atoms, among others. The theoretical description of these systems is often challenging, especially when disorder comes into play. Disorder can result in a high level of degeneracy in the low-energy spectrum and the violation of the so-called area law of entanglement entropy which is a fundamental assumption of many numerical approaches, such as those based on matrix product states. The present thesis studies how the ML-MCTDH method can handle such scenarios by computing the ground states of different disordered models and comparing the results with other established numerical approaches. ML-MCTDH is found to yield accurate results even in the presence of strong disorder and should be considered as another promising approach for the investigation of quantum spin systems.