Tunneling Dynamics in Open Ultracold Bosonic Systems

Abstract

Abstract:This thesis explores the quantum many-body tunneling dynamics of open ultracold bosonic systems with the recently developed multiconfigurational timedependent Hartree for bosons (MCTDHB) method. The capabilities of MCTDHB to provide solutions to the full time-dependent many-body problem are assessed in a benchmark using the analytically solvable harmonic interaction Hamiltonian and a generalization of it with time-dependent both one-and two-body potentials. In a comparison with numerically exact MCTDHB results, it is shown that e.g. lattice methods fail qualitatively to describe the tunneling dynamics. A model assembling the many-body physics of the process from basic simultaneously happening single-particle processes is derived and verified with a numerically exact MCTDHB description. The generality of the model is demonstrated even for strong interactions and large particle numbers. The ejection of the bosons from the source occurs with characteristic velocities. These velocities are defined by the chemical potentials of systems with different particle numbers which are converted to kinetic energy. The tunneling process is accompanied by fragmentation: the ejected bosons lose their coherence with the source and among each other. It is shown that the various aspects of the tunneling dynamics' can be controlled well with the interaction and the potential threshold.

Time-dependent restricted-active-space self-consistent-field theory for bosonic many-body systems

“…The analytical ground state wavefunction and energy are used to ensure the convergence of the imaginary time propagation and, as expected, are the same for all methods. The dynamics is initiated at t=0 by quenching instantaneously the strength of the two-body interaction, as performed in [25,26], leading to the evolution of the system under the action of the following Hamiltonian,…”

“…One model uses an inverse-harmonic interaction between the particles and can be solved exactly with a harmonic trapping potential [22], while an other model considers a harmonic interaction potential [23,24]. The latter model has the peculiarity that it can be solved exactly numerically also for time-dependent Hamiltonians with a time-dependent trapping potential or a time-dependent interaction potential for bosons [25,26] and fermions [27].These exact models, unfortunately, do not cover the large variety of interaction or trapping potentials that are encountered in experiments. Nonetheless, they are of primary interest as they provide a unique way to benchmark numerical methods and approximations.…”

Management of the correlations of UltracoldBosons in triple wells

“…We found that the effect appears at larger tilts (α=7.1) for the case of M=4. We therefore speculate that the next-to-nearest neighbor coherence results from a resonance condition involving two-or many-particle correlated tunneling processes [39,62,63]; the lowered energy at the M= 4-level of MCTDHB (footnote 5) seems to cause the resonance condition to be fulfilled at a different tilt.…”

“…are a complete basis set of N-body Hilbert space for M  ¥, the variational principle [45] guarantees that the solutions of the time-dependent manybody problem provided by the MCTDHB method gradually improve towards exactness when the number of considered creation operators M in the ansatz, equation (5), is increased [36,39]. To derive the MCTDHB equations, the time-dependent variational principle [45] is employed to determine the time-evolution of the expansion coefficients C t [37,38].…”

“…MCTDHB represents a generalization beyond exact diagonalization approaches with static basis sets like the Bose-Hubbard approach that uses Wannier functions. Necessarily, the self-consistent basis of MCTDHB is superior to a fixed static (Wannier) basis as shown directly in [36,39,[51][52][53][54].…”