Experiments have been conducted observing Anderson localisation in a two-dimensional ultracold gas. The atomic transport of a Rb87 Bose-Einstein condensate through a dumbbell shaped optical trap was examined, with a connecting channel containing impurities providing the only path. We have utilised a synthetic gauge field to demonstrate, theoretically, negative magneto-resistance in systems comparable to these experiments. This pro- vides us with strong evidence for the existence of Anderson localisation, an intriguing interference phenomenon, in these systems. Similar systems are examined with impurities distributed periodically, contrasting the ran- dom distributions required for Anderson localisation. It is demonstrated, through a comparison to the periodic case, that the negative magneto- resistance observed must be the result of the destruction of Anderson local- isation. Corresponding localisation lengths are also examined. We see that under that application of a synthetic gauge field, localisation lengths in- crease. A BEC localised within the channel can become delocalised on that scale with the application of a synthetic gauge field, with the correspond- ing localisation length transitioning from smaller than the channel length to larger. Experimental verification of our theoretical predictions would provide strong evidence confirming the existence of Anderson localisation in the experiments.
Experiments have been conducted observing Anderson localisation in a two-dimensional ultracold gas. The atomic transport of a Rb87 Bose-Einstein condensate through a dumbbell shaped optical trap was examined, with a connecting channel containing impurities providing the only path. We have utilised a synthetic gauge field to demonstrate, theoretically, negative magneto-resistance in systems comparable to these experiments. This pro- vides us with strong evidence for the existence of Anderson localisation, an intriguing interference phenomenon, in these systems. Similar systems are examined with impurities distributed periodically, contrasting the ran- dom distributions required for Anderson localisation. It is demonstrated, through a comparison to the periodic case, that the negative magneto- resistance observed must be the result of the destruction of Anderson local- isation. Corresponding localisation lengths are also examined. We see that under that application of a synthetic gauge field, localisation lengths in- crease. A BEC localised within the channel can become delocalised on that scale with the application of a synthetic gauge field, with the correspond- ing localisation length transitioning from smaller than the channel length to larger. Experimental verification of our theoretical predictions would provide strong evidence confirming the existence of Anderson localisation in the experiments.
Anderson localisation -the inhibition of wave propagation in disordered media- is a surprising interference phenomenon which is particularly intriguing in two-dimensional (2D) systems. While an ideal, non-interacting 2D system of infinite size is always localised, the localisation length-scale may be too large to be unambiguously observed in an experiment. In this sense, 2D is a marginal dimension between one-dimension, where all states are strongly localised, and three-dimensions, where a well-defined phase transition between localisation and delocalisation exists as the energy is increased. Here, we report the results of an experiment measuring the 2D transport of ultracold atoms between two reservoirs, which are connected by a channel containing pointlike disorder. The design overcomes many of the technical challenges that have hampered observation of localisation in previous works. We experimentally observe exponential localisation in a 2D ultracold atom system.
Anderson localization was first investigated in the context of electrons in solids. One of the successes was in explaining the puzzle of negative magneto-resistance - as early as the 1940s it had been observed that electron diffusion rates in some materials can increase with the application of a magnetic field. Anderson localization has now been demonstrated in ultra-cold atomic gases. We present a theoretical study of the two-dimensional ultra-cold Bose gas in the presence of disorder, to which we apply a synthetic magnetic field. We demonstrate that, in the ballistic transport regime this leads to positive magneto-resistance and that, in the diffusive and strong localization regimes, can also lead to negative magneto-resistance. We propose experimental scenarios to observe these effects.
Anderson localization in a two-dimensional ultracold Bose-gas has been demonstrated experimentally. Atoms were released within a dumbbell-shaped optical trap, where the channel of variable aspect ratio provided the only path for particles to travel between source and drain reservoirs. This channel can be populated with columnar (repulsive) optical potential spikes of square cross section with arbitrary pattern. These spikes constitute impurities, the scattering centers for the otherwise free propagation of the particles. This geometry does not allow for classical potential trapping which can be hard to exclude in other experimental setups. Here we add further theoretical evidence for Anderson localization in this system by comparing the transport processes within a regular and a random pattern of impurities. It is demonstrated that the transport within randomly distributed impurities is suppressed and the corresponding localization length becomes shorter than the channel length. However, if an equal density of impurities are distributed in a regular manner, the transport is only modestly disturbed. This observation corroborates the conclusions of the experimental observation: the localization is indeed attributed to the disorder. Beyond analyzing the density distribution and the localization length, we also calculate a quantum ``impedance'' exhibiting qualitatively different behavior for regular and random impurity patterns.
The transport of quantum particles in non ideal mate- rial media (eg the conduction of electrons in an imperfect crystal) is strongly affected by scattering from impurities of the medium. Even for a weak disorder, semi-classical theories, such as those based on the Boltzmann equation for matter-waves scattering from the impurities, often fail to describe transport properties and full quantum approaches are necessary. The properties of the quan- tum systems are of fundamental interest as they show intriguing and non-intuitive phenomena that are not yet fully understood such as Anderson localization, percola- tion, disorder-driven quantum phase transitions and the corresponding Bose-glass or spin-glass phases. Under- standing quantum transport in amorphous solids is one of the main issues in this context, related to electric and thermal conductivities. Ultracold atomic gases can now be considered to re- visit the problem of quantum conductivity and quan- tum transport under unique control possibilities. Dilute atomic Bose-Einstein condensates (BEC) and degener- ate Fermi gases (DFG) are produced routinely taking advantage of the recent progress in cooling and trap- ping of neutral atoms. Transport has been widely in- vestigated in controlled potentials with no defects, for instance periodic potentials (optical lattices). Controlled disordered potentials can also be produced with various techniques such as the use of magnetic traps designed on atomic chips with rough wires, the use of localized impurity atoms, the use of radio-frequency fields or the use of optical potentials. This recently lead to the ob- servation of the Anderson Localisation of a BEC and the measurement of the diffusion coefficient of a 2D gaz in the presence of disorder.
Since the realization of Bose-Einstein condensation in 1995, experimentalists in ultracold atomic gas community have developed a set of entirely new methods to study quantum gases. In ultracold atomic gases, implementation of synthetic gauge fields, the spin-orbit coupling, optical lattices and Feshbach resonances, provides a clean and highly controllable platform to tune the parameters of the system, which are typically fixed for real materials. Motivated by the rapid developments of experimental progresses, I investigate the ultracold atomic gases with synthetic gauge fields. \n \nIn this thesis, a bosonic gas in optical lattices in the presence of an effective staggered magnetic flux will be studied, using a generalized Bose-Hubbard model. Phase transition from the Mott insulating phase to the superfluid phase will be discussed. Novel superfluid phases including the stripe phase and the plane wave phase will be discussed. Furthermore, the existence of a tricritical point in the phase diagram is predicted. \n \nTo study Fermi systems with synthetic gauge fields, a spin-1=2 Fermi gas with Rashba spin-orbit coupling is investigated by studying the structure of vortex line through the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation (BCSBEC) crossover. Due to the spin-orbit coupling, the s-wave interacting Fermi gas behaves like an effective p-wave paired system. A discussion about the vortex line structure will be provided by calculating the spatial distribution of the gap function, the density, the particle current, and also the elementary excitations. It has been found that the most robust superfluid occurs around the unitary point, indicated by the smallest healing length and the largest critical current. \n \nFinally, motivated by the recent progress of p-wave resonantly Fermi gas in experiment, an extension of Nozières-Schmitt-Rink method to the p-wave case will be given. An investigation of the normal state properties will be given by calculating the equation of state and the p-wave contacts, which have been measured by the experiment. Furthermore, the superfluid transition temperature with realistic parameters appropriate for experiment is calculated and is found to be within experimental reach.
The transport of quantum particles in non ideal material media (eg the conduction of electrons in an imperfect crystal) is strongly affected by scattering from impurities of the medium. Even for a weak disorder, semi-classical theories, such as those based on the Boltzmann equation for matter-waves scattering from the impurities, often fail to describe transport properties and full quantum approaches are necessary. The properties of the quantum systems are of fundamental interest as they show intriguing and non-intuitive phenomena that are not yet fully understood such as Anderson localization, percolation, disorder-driven quantum phase transitions and the corresponding Bose-glass or spin-glass phases. Understanding quantum transport in amorphous solids is one of the main issues in this context, related to electric and thermal conductivities. Ultracold atomic gases can now be considered to revisit the problem of quantum conductivity and quantum transport under unique control possibilities. Dilute atomic Bose-Einstein condensates (BEC) and degenerate Fermi gases (DFG) are produced routinely taking advantage of the recent progress in cooling and trapping of neutral atoms. Transport has been widely investigated in controlled potentials with no defects, for instance periodic potentials (optical lattices). Controlled disordered potentials can also be produced with various techniques such as the use of magnetic traps designed on atomic chips with rough wires, the use of localized impurity atoms, the use of radio-frequency fields or the use of optical potentials. This recently lead to the observation of the Anderson Localisation of a BEC and the measurement of the diffusion coefficient of a 2D gaz in the presence of disorder.