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arXiv:1111.1316 · New Journal of Physics

Disorder-driven loss of phase coherence in a quasi-2D cold atom system

M C Beeler, M E W Reed, T Hong, S. L. Rolston

Published Jul 12, 2012• 32 citations
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Abstract

We study the order parameter of a quasi-two-dimensional (quasi-2D) gas of ultracold atoms trapped in an optical potential in the presence of controllable disorder. Our results show that disorder drives phase fluctuations without significantly affecting the amplitude of the quasi-condensate order parameter. This is evidence that disorder can drive phase fluctuations in 2D systems, relevant to the phase-fluctuation mechanism for the superconductor-to-insulator phase transition (SIT) in disordered 2D superconductors.

DOI
10.1088/1367-2630/14/7/073024

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We study the order parameter of a quasi-two-dimensional (quasi-2D) gas of ultracold atoms trapped in an optical potential in the presence of controllable disorder. Our results show that disorder drives phase fluctuations without significantly affecting the amplitude of the quasi-condensate order parameter. This is evidence that disorder can drive phase fluctuations in 2D systems, relevant to the phase-fluctuation mechanism for the superconductor-to-insulator phase transition (SIT) in disordered 2D superconductors.
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.
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.
The effect of disorder on many-body physics is important for our understanding of real-world systems. In particular, the behaviour of phase transitions between superfluid, normal and insulating phases is an area with many unanswered questions and experimental evidence remains scarce in certain important cases. In this thesis, we focus on systems of two-dimensional (2D) Bose gases subjected to a pointlike disorder potential. We trap atoms in radiofrequency dressed potentials and apply the technique of multiple-radiofrequency dressing to create a double-well potential into which we load the ultracold atoms. Matter-wave interferometry allows us to directly probe the local relative phase and its fluctuations between the clouds in the two potential wells. A pointlike disordered optical potential is produced by a high-intensity laser beam which is shaped by a programmable mirror array and passes through clouds in both of the wells. We adiabatically apply disordered potentials of increasing strength to observe their effect on the superfluids in equilibrium in a double-well. We observe that above a critical disorder strength the superfluid undergoes a transition to the normal phase at a lower temperature than that of the disorder-free case, and we characterise this disorder-induced transition. We also study the flow of a 2D superfluid cloud around both a single defect and a random potential and measure the dissipation induced by the obstacles. The absence of dissipation is observed below a critical velocity in the case of a single defect but we find no such dissipationless regime for the disordered potential. We describe the development of a software simulation package for modelling cold-atom systems and the implementation of particle collisions, magnetic trapping and evaporative cooling. Finally, we report on the initial work towards construction of a new cold-atom apparatus, capable of faster sequence times and greater atom numbers, to continue our investigation of many-body physics.
We use the density-matrix renormalization group method to investigate the superconductor-insulator transition (SIT) in disordered quasi-one-dimensional systems. Focusing on the case of an interacting spinful Hamiltonian at quarter filling, we contrast the differences arising in the SIT when the parent noninteracting model features flat or dispersive bands. Furthermore, we unveil the critical disorder amplitude that triggers insulating behavior by comparing disorder distributions that preserve or not SU(2) symmetry. While scaling analysis suggests the transition be of a Berezinskii-Kosterlitz-Thouless type for all models (two lattices and two disorder types), only in the flat-band model with Zeeman-like disorder is the critical disorder nonvanishing. In this sense, the flat-band structure does strengthen superconductivity in the presence of attractive interactions. For both flat- and dispersive-band models, (i) in the presence of SU(2)-symmetric random chemical potentials, the disorder-induced transition is from superconductor to insulator of singlet pairs; (ii) for the Zeeman-type disorder, the transition is from superconductor to insulator of unpaired fermions. In all cases, our numerical results suggest no intermediate disorder-driven metallic phase.
We experimentally study the effect of disorder on trapped quasi-two-dimensional (2D) 87{}^{87}87Rb clouds in the vicinity of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition. The disorder correlation length is of the order of the Bose gas characteristic length scales (thermal de Broglie wavelength, healing length) and disorder thus modifies the physics at a microscopic level. We analyze the coherence properties of the cloud through measurements of the momentum distributions for two disorder strengths as a function of its degeneracy. For moderate disorder, the emergence of coherence remains steep but is shifted to a lower entropy. In contrast, for strong disorder, the growth of coherence is hindered. Our study is an experimental realization of the dirty boson problem in a well controlled atomic system suitable for quantitative analysis.
We investigate a dilute Bose gas confined in a tight one-dimensional (1D) optical lattice plus a superimposed random potential at zero temperature. Accordingly, the ground-state energy, quantum depletion, and superfluid density are calculated. The presence of the lattice introduces a crossover to the quasi-two-dimensional (2D) regime, where we analyze asymptotically the 2D behavior of the system, particularly the effects of disorder. We thereby offer an analytical expression for the ground-state energy of a purely 2D Bose gas in a random potential. The obtained disorder-induced normal fluid density nn{n}_{n}nn​ and quantum depletion nd{n}_{d}nd​ both exhibit a characteristic 1/ln(1/n2Da2D2)1/\mathrm{ln}(1/{n}_{2\mathrm{D}}{a}_{2\mathrm{D}}^{2})1/ln(1/n2D​a2D2​) dependence. Their ratio nn/nd{n}_{n}/{n}_{d}nn​/nd​ increases to 222 compared to the familiar 4/34/34/3 in lattice-free three-dimensional (3D) geometry, signifying a more pronounced contrast between superfluidity and Bose-Einstein condensation in low dimensions. The conditions for possible experimental realization of our scenario are also proposed.