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