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arXiv:1210.1096 · Physical Review A

Phase diagrams of two-dimensional and three-dimensional disordered Bose gases in the local density approximation

Thomas Bourdel

Published Dec 21, 2012• 9 citations
arXivHTMLPDF

Abstract

We study superfluid transitions in bidimensional (2D) and tridimensional (3D) disordered and interacting Bose gases. We work in the limit of long-range correlated disorder such that it can be treated in the local density approximation. We present superfluid transition curves in both the disorder-temperature plane and the disorder-entropy plane in 2D and 3D Bose gases. Surprisingly, we find that a small amount of disorder is always favorable to the apparition of a superfluid. Our results offer a quantitative comparison with recent experiments in 2D disordered ultracold gases, for which no exact theory exists.

DOI
10.1103/physreva.86.063626

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We study superfluid transitions in bidimensional (2D) and tridimensional (3D) disordered and interacting Bose gases. We work in the limit of long-range correlated disorder such that it can be treated in the local density approximation. We present superfluid transition curves in both the disorder-temperature plane and the disorder-entropy plane in 2D and 3D Bose gases. Surprisingly, we find that a small amount of disorder is always favorable to the apparition of a superfluid. Our results offer a quantitative comparison with recent experiments in 2D disordered ultracold gases, for which no exact theory exists.
In this thesis, we study the quantum phase transition triggered by an external random po- tential in ultra-cold low-dimensional weakly-interacting Bose gases at zero temperature. In one-dimensional systems, the quantum phases are characterized by the decay at long-range of the one-body density matrix. This decay exhibits an algebraic behaviour in the superfluid quasi-condensed phase while in the insulating Bose glass phase this it becomes exponen- tial, signaling the complete loss of coherence in the system. In two-dimensional systems, a characterization based on the long-range behaviour of the one-body density matrix appears to be highly demanding from a computational point of view. We therefore characterized the superfluid-insulator transition in two-dimensional systems by the low-energy behaviour of the cumulative density of states of the Bogoliubov excitations. While in the superfluid condensed phase this quantity grows as the square of the excitation energy in agreement with the existence of a finite velocity of sound, in the insulating Bose glass phase this power law is less than quadratic. This study is performed in the framework of an extended Bogoliubov approach properly adapted to treat low-dimensional Bose gases. Using a systematic numerical study, we draw the interaction-disorder phase diagrams of the superfluid-insulator transition in 1D and 2D. The phase boundary follows two different power- laws depending on the length scales characterizing the spatial correlations of the disorder and the strength of interactions. The power-law exponents were found to be in agreement with the ones predicted by scaling arguments, both in the white noise and the Thomas-Fermi regimes. In the two-dimensional system, the classical percolation threshold in the Thomas-Fermi limit was found to overestimate the critical disorder below which the onset of superfluidity should be observed for a given interaction strength.
Ultracold bose gase systems can perform quantum simulations of high temperature superconductors in certain parameter regimes. Specifically, 2D bose gases at low temperatures exhibit a superfluid to thermal gas phase transition analogous to the superconductor to insulator transition in certain superconductors. The unbinding of thermally activated vortex pairs drives this phase transition, and disorder is expected to affect vortex motion in this system. In addition, disorder itself can drive phase transitions in superconductors. We have designed and built a system which produces two 2D ultracold Bose gas systems separated by a few microns. In addition, we have also produced a disordered speckled laser intensity pattern with a grain size of ~1 μm, small enough to provide a disordered potential for the two systems. We have observed the superfluid phase transition with and without the presence of disorder. The coherence of the system, which is related to superfluidity, is strongly reduced by the presence of disorder, even at small disorder strength, but the effect of the disorder on observed vortices in the system is less clear.
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We study the two-dimensional weakly repulsive Bose gas at zero temperature in the presence of correlated disorder. Using large-scale simulations, we show that the low-energy Bogoliubov cumulative density of states remains quadratic up to a critical disorder strength, beyond which a power law with disorder-dependent exponent $\ensuremath{\beta}<2$ sets in. We associate this threshold behavior with the transition from superfluid to Bose glass, and compare the resulting mean-field phase diagram with scaling laws and the Thomas-Fermi percolation threshold of the mean-field density profile.
Thermal fluctuations, the microscopic fluctuations of things due to their temperature, counteract order in many-body systems. Thermal fluctuations often lead to high-temperature disordered phases and low-temperature ordered ones. In lower dimensions, thermal fluctuations are relatively stronger with two-dimensional materials being just on the brink of thermal fluctuations destroying their order. Twodimensional materials therefore display unique behaviour, for example undergoing a superfluid phase transition driven by point-like topological defects. In this work, we realise two-dimensional bosonic quantum gases of the isotope Rb-87 in precisely controlled potentials to study how quantum-tunnelling and spatially disordered potentials affect the phases of matter they form. We also present a new scheme for cooling quantum gases directly in the finely tuned radiofrequency-dressed traps confining the gases in our experiments. To study tunnel-coupled gases, this work utilises a novel method to read out information from bilayer quantum gas experiments by analysing noise patterns arising from interference effects. We find that quantum-tunnelling between the two layers in a bilayer system can cause both layers to remain superfluid at higher temperatures than without quantum tunnelling. We compare our results to predictions using renormalisation-group theory and numerical simulations. We experimentally observe the predicted double-layer superfluid phase, a novel phase where the U(1) symmetry of the relative phase is broken and relative excitations are suppressed. Separately, we investigate the topological Berezinskii-Kosterlitz-Thouless phase transition in disordered two-dimensional Bose gases. We find that such systems can be driven across this phase transition by increasing the strength of an applied disordered potential. We experimentally map out the phase diagram for a continuous 2D Bose gas in the presence of disorder, which has not previously been carried out to the best of our knowledge. We find that the presence of disorder increases the number of topological defects at a given temperature while reducing the rate at which the number of defects increases with temperature. The experimental results for 2D disordered Bose gases are in qualitative agreement with numerical simulations for the parameter regime studied.