Analytical and numerical study of dirty bosons in a quasi-one-dimensional harmonic trap

Abstract

The emergence of a Bose-glass region in a quasi one-dimensional Bose-Einstein-condensed gas in a harmonic trapping potential with an additional delta-correlated disorder potential at zero temperature is studied using three approaches. At first, the corresponding time-independent GrossPitaevskii equation is numerically solved for the condensate wave function, and disorder ensemble averages are evaluated. In particular, we analyse quantitatively the emergence of mini-condensates in the local minima of the random potential, which occurs for weak disorder preferentially at the border of the condensate, while for intermediate disorder strength this happens in the trap centre. Second, in view of a more detailed physical understanding of this phenomenon, we extend a quite recent nonperturbative approach towards the weakly interacting dirty boson problem, which relies on the Hartree-Fock theory and is worked out on the basis of the replica method, from the homogeneous case to a harmonic confinement. Finally, in the weak disorder regime we also apply the ThomasFermi approximation, while in the intermediate disorder regime we additionally use a variational ansatz in order to describe analytically the numerically observed redistribution of the fragmented mini-condensates with increasing disorder strength.

Hartree–Fock mean-field theory for trapped dirty bosons

“…[58]. Analytical calculations based on the present Hartree-Fock mean-field theory as well as detailed numerical simulations show unambiguously the existence of a Bose-glass region, whose spatial distribution turns out to change with the disorder strength.…”

Excitation spectra of a Bose-Einstein condensate with an angular spin-orbit coupling

“…In future work, we plan to address bosonic excitations for spin-asymmetric interactions as well as to treat interactions for spin-orbit coupled system in more detail [48]. Another interesting direction would be to investigate the role of disorder [35,[49][50][51][52][53], or the phenomenon of Faraday waves [54][55][56] in this type of systems.…”

Green's function approach to the Bose-Hubbard model with disorder

“…As explained in the last section, for sufficiently weak disorder, ∆ < U , the Mott states should always appear in the insulating part of the phase diagram. Therefore, based on (47), the Mott lobes would correspond to the regions satisfying the following condition to the hopping parameter…”

“…Further analysis of the energy behaviour inside that region could also lead to a determination of an accurate phase boundary. An effective-action approach, similar to the one of [26,27,28], should also be of use in this respect, where an Edwards-Anderson like order parameter, such as the one suggested in [45] and used in [22,46,47,48], could be applied to identify the Bose-glass phase, allowing also to obtain information on the nature its collective excitations. The investigation of these questions characterizes a natural progression of this work.…”