The glass to superfluid transition in dirty bosons on a lattice

Abstract

We investigate the interplay between disorder and interactions in a Bose gas on a lattice in the presence of randomly localized impurities. We compare the performance of two theoretical methods, namely the simple version of multi-orbital Hartree-Fock and the common Gross-Pitaevskii approach, and show how the former gives a very good approximation to the ground state in the limit of weak interactions, where the superfluid fraction is small. We further prove rigorously that for this class of disorder the fractal dimension of the ground state d * tends to the physical dimension in the thermodynamic limit. This allows us to introduce a quantity called the fractional occupation, which gives useful information on the crossover from a Lifshits to a Bose glass. Finally, we compare the temperature and interaction effects and highlight their similarities and intrinsic differences.

Decay of correlations and absence of superfluidity in the disordered Tonks–Girardeau gas

“…This statement concerns the usual thermodynamic limit. We note that other limiting regimes are possible, corresponding to mean-field type interactions, where both BEC and superfluidity can prevail at zero temperature [30,50] (see also [8,29,54] for related results). The proof of theorem 2.4 will be given in section 4.…”

Superfluid behavior of a Bose–Einstein condensate in a random potential

“…In recent years the interplay between interactions and disorder in many body systems has been studied in many works, both theoretically and experimentally. It is not the intention here to give a review of the subject but we mention the references [12][13][14][15][16][17][18][19][20][21][22][23][24] as a representative sample. In [25] (see also [26]) a one-dimensional model of an interacting Bose gas was studied and it was shown that complete BEC in the ground state may survive a strong random potential in an appropriate limit.…”

Bose-Hubbard model with random impurities: Multiband and nonlinear hopping effects

“…By pinning a secondary type of atoms in an optical potential we obtain the disorder with binary (or Bernoulli) distribution. Such proposal, originating from the work of Gavish and Castin [29], has been frequently discussed theoretically [30][31][32][33]36], and only recently implemented experimentally [37] (note that in the early papers [38] the impurities were mobile). This is the type of disorder we consider in this paper.…”