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.
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.
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.
The properties of phase transitions and the types of order present in the low-temperature states of matter are fundamentally dependent on the dimensionality of physical systems. Generally, highly ordered states are more robust in higher dimensions, while thermal and quantum fluctuations, which favour disordered states, play a more important role in lower dimensions. The case of a two-dimensional (2d) Bose fluid is particularly fascinating because of its "marginal" behaviour. In an infinite uniform 2d fluid thermal fluctuations at any non-zero temperature are strong enough to destroy the fully ordered state associated with Bose--Einstein condensation, but are not strong enough to suppress superfluidity in an interacting system at low, but non-zero temperatures. Further, the presence of residual "quasi-long-range" order at low temperatures leads to an interesting interplay between superfluidity and condensation in all experimentally relevant finite-size systems. In these notes we give an introduction to the physics of 2d Bose fluids from an atomic physics perspective. Our goal is to summarize the recent progress in theoretical understanding and experimental investigation of ultra-cold atomic gases confined to 2d geometry, and we also hope to provide a useful introduction to these systems for researchers working on related topics in other fields of physics.
We study the phase diagram of two-dimensional, interacting bosons in the presence of a correlated disorder in continuous space, by using large-scale quantum Monte Carlo simulations at finite temperature. We show that the superfluid transition is strongly protected against disorder. It remains of the Berezinskii-Kosterlitz-Thouless type up to disorder strengths comparable to the chemical potential. Moreover, we study the transport properties in the strong disorder regime where a zero-temperature Bose-glass phase is expected. We show that the conductance exhibits a thermally activated behavior vanishing only at zero temperature. Our results point towards the existence of a Bose bad-metal phase as a precursor of the Bose-glass phase.
Abstract The physics of two-dimensional (2D) quantum gases can be revealed in strongly confining optical lattices. Upon cooling, 2D bosonic quantum gases as well as Fermi gases where pairing is present, become superfluid. The superfluid-to-normal transition is no longer governed by the presence or absence of a condensate, but by the Berezinskii–Kosterlitz–Thouless (BKT) mechanism: above a critical temperature, vortices and antivortices proliferate and destroy phase coherence. We investigate the BKT transition for superfluid 2D Fermi gases in the whole range of the BCS–BEC crossover, from weakly bound Cooper pairing (the BCS state), up to strongly bound molecules (the BEC state). Using a path-integral description, we then focus on the case of imbalanced gases: when the number of ‘spin-up’ and ‘spin-down’ fermions that form the pair is no longer equal. When an excess of one spin species exists, pairing is frustrated and the vortex energetics is strongly affected, influencing the KT mechanism. In the present work we are concentrated on the effect of both phase and amplitude fluctuations on phase diagrams of the fermion system. The amplitude fluctuations only slightly influence the BKT phase transition temperature. However, they lead to a substantial modification of the complete phase diagram for the Fermi gas in 2D with respect to that obtained taking into account only phase fluctuations.
Current experiments on atomic gases in highly anisotropic traps present the opportunity to study in detail the low temperature phases of two-dimensional inhomogeneous systems. Although, in an ideal gas, the trapping potential favors Bose-Einstein condensation at finite temperature, interactions tend to destabilize the condensate, leading to a superfluid Kosterlitz-Thouless-Berezinskii phase with a finite superfluid mass density but no long-range order, as in homogeneous fluids. The transition in homogeneous systems is conveniently described in terms of dissociation of topological defects (vortex-antivortex pairs). However, trapped two-dimensional gases are more directly approached by generalizing the microscopic theory of the homogeneous gas. In this paper, we first derive, via a diagrammatic expansion, the scaling structure near the phase transition in a homogeneous system, and then study the effects of a trapping potential in the local density approximation. We find that a weakly interacting trapped gas undergoes a Kosterlitz-Thouless-Berezinskii transition from the normal state at a temperature slightly below the Bose-Einstein transition temperature of the ideal gas. The characteristic finite superfluid mass density of a homogeneous system just below the transition becomes strongly suppressed in a trapped gas.