Anderson localization of a Tonks-Girardeau gas in potentials with controlled disorder

Abstract

We theoretically demonstrate features of Anderson localization in the Tonks-Girardeau gas confined in one-dimensional (1D) potentials with controlled disorder. That is, we investigate the evolution of the single particle density and correlations of a Tonks-Girardeau wave packet in such disordered potentials. The wave packet is initially trapped, the trap is suddenly turned off, and after some time the system evolves into a localized steady state due to Anderson localization. The density tails of the steady state decay exponentially, while the coherence in these tails increases. The latter phenomenon corresponds to the same effect found in incoherent optical solitons.

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

“…and then released from the trap at t=0. The localization bound(2.9) then guarantees that the total number of particles will remain small on average away from the initial location, uniformly in time (confirming numerical simulations in [45].) A related bound for the XY-model can be found in [2, theorem 1.1].…”

Many-body localization for disordered Bosons

“…increase of the ground state energy under twisting the boundary condition). Finally, [27] derives dynamical stability of particle density profiles for the disordered TG gas, uniformly in time and up to exponentially small corrections in the spatial distance, in particular confirming numerical simulations in [26].…”

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

“…We conclude that in the GP limit the superfluid fraction Note that in (18) the order in which the limits are taken is important in general. Also, there is no factor 2 on the right side of (18) because with our choice of units the mass is1/2.…”

“…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.…”