21 research outputs found
Numerical Investigation of Strongly Interacting Bosons at Zero Temperature
We review some numerical works carried out within the department for Quantum
Optics and Statistics at the University of Freiburg’s Institute of Physics, between
September 2016 and June 2018. Our activities focus on quantum properties of
matter at zero temperature, i.e., a regime where the thermal energy kBT is negligible
with respect to the other energy scales of the considered system. This
area of research, related to ultracold gases, has attracted a great deal of interest,
both experimentally and theoretically, since the first realization of a Bose-Einstein
condensate in 1995. In a context where the theoretical understanding of these
systems still remains challenging, the growing power of computers offers a unique
and efficient way to tackle such challenges. In our theory group, we particularly
use powerful numerical methods that give exact results, in contrast to other theoretical
approaches based on an a priori assumption, e.g., mean field theory. To
illustrate it, we focus on few typical results that would not be available other
than by using high performance computing. These results have been obtained by
using three numerical methods: quantum Monte Carlo (QMC), Gutzwiller Monte
Carlo (GMC), and the Multiconfigurational Time-dependent Hartree method for
bosons (MCTDHX)
Quantum multifractality as a probe of phase space in the Dicke model
We study the multifractal behavior of coherent states projected in the energy
eigenbasis of the spin-boson Dicke Hamiltonian, a paradigmatic model describing
the collective interaction between a single bosonic mode and a set of two-level
systems. By examining the linear approximation and parabolic correction to the
mass exponents, we find ergodic and multifractal coherent states and show that
they reflect details of the structure of the classical phase space, including
chaos, regularity, and features of localization. The analysis of
multifractality stands as a sensitive tool to detect changes and structures in
phase space, complementary to classical tools to investigate it. We also
address the difficulties involved in the multifractal analyses of systems with
unbounded Hilbert spacesComment: 14 pages, 7 figure
Spectral Structure and Many-Body Dynamics of Ultracold Bosons in a Double-Well
We examine the spectral structure and many-body dynamics of two and three
repulsively interacting bosons trapped in a one-dimensional double-well, for
variable barrier height, inter-particle interaction strength, and initial
conditions. By exact diagonalization of the many-particle Hamiltonian, we
specifically explore the dynamical behaviour of the particles launched either
at the single particle ground state or saddle point energy, in a
time-independent potential. We complement these results by a characterisation
of the cross-over from diabatic to quasi-adiabatic evolution under finite-time
switching of the potential barrier, via the associated time-evolution of a
single particle's von Neumann entropy. This is achieved with the help of the
multiconfigurational time-dependent Hartree method for indistinguishable
particles (\textsc{Mctdh-x}) -- which also allows us to extrapolate our results
for increasing particle numbers.Comment: 20 pages, 14 figure