Mean-field phase diagram of the one-dimensional Bose gas in a disorder potential

Abstract

We study the quantum phase transition of the 1D weakly interacting Bose gas in the presence of disorder. We characterize the phase transition as a function of disorder and interaction strengths, by inspecting the long-range behavior of the one-body density matrix as well as the drop in the superfluid fraction. We focus on the properties of the low-energy Bogoliubov excitations that drive the phase transition and find that the transition to the insulator state is marked by a diverging density of states and a localization length that diverges as a power-law with power 1. We draw the phase diagram and we observe that the boundary between the superfluid and the insulator phase is characterized by two different algebraic relations. These can be explained analytically by considering the limiting cases of zero and infinite disorder correlation length.

Density of states in an optical speckle potential

“…Choosing the value β ∼ 0.5 the modified semiclassical method based on Eqs. (22) and (23) reproduces very well the data for s = −1, as shown in Fig. 7.…”

“…These include classical localization and fragmentation effects, frequency shifts and damping of collective excitations, and inhibition of transport properties [3][4][5][6][7][8][9][10][11][12][13][14][15][16] and have culminated with the observation of Anderson localization for a BEC [12][13][14]. Also, the superfluid-insulator transition [17][18][19][20][21][22][23][24] and the transport of coherent matter waves have been recently investigated from the theoretical point of view for speckles in higher dimensions [25][26][27][28].…”

Superfluid-insulator transition of ultracold bosons in disordered one-dimensional traps

“…4) in the space of microscopic parameters, disorder and interaction strength, which is valid in the regime of weak interactions. The transition line is modified compared to that previously inferred from mean field (Gross-Pitaevskii) theory 24,26 and from estimates based on typical values of the Josephson coupling compared to interaction strength 6 . Note that the critical point in this regime is different in nature from the weak disorder transition considered by Giamarchi and Schulz 9 , shown as a separate transition line in the strong interaction range of Fig.…”

“…This mean field transition line, previously found in Refs. [24] and [6] is also plotted on Fig. 4 for comparison with the actual transition.…”

Normal and superfluid fractions of inhomogeneous nonequilibrium quantum fluids

“…A reduction in superfluid fraction due to disorder is due to the pinning of the fluid in the potential minima and a first theoretical estimate can be obtained at the mean field level 13,14 . In the theoretical study of Ref.…”