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 Gross–Pitaevskii 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 non-perturbative 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 Thomas–Fermi 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.
Highlights
The dirty boson problem is defined as a system of interacting bosons in a random potential [1]
The results presented correspond to a dirty BoseEinstein condensation (BEC) with N = 106 atoms of 87Rb, with the s
From the discussion in the previous section, we conclude that the TF approximation yields good results for the quasi-one-dimensional dirty bosons in the weak disorder regime, which agree well with the numerical ones, especially in the centre of the bosonic cloud, where the kinetic energy can be neglected
Summary
The dirty boson problem is defined as a system of interacting bosons in a random potential [1]. Within a BoseEinstein condensation (BEC), which is a many-particle interacting system, the presence of disorder causes the emergence of a new phase besides the superfluid phase (SF), which is called a Bose-glass phase due to the localisation of bosons in the respective minima of the random potential landscape. Indications for the existence of the Bose-glass phase were found, for instance, in the experiments of references [6, 7, 9, 19] There it was shown within the superfluid phase that an increasing disorder strength yields first a fragmentation of the condensate due to the formation of tiny BEC droplets in the minima of the random environment. Whereas for small disorder bosons tend to localise at the border of the trap, for intermediate disorder strength they concentrate in the trap centre
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