Inhomogeneities and instabilities of Bose-Einstein condensates in rough potential landscapes

In this work we investigate the dynamics of Bose-Einstein condensates (BECs) in inhomogeneous potential landscapes. As this research field continues to develop, more attention will focus on non-equilibrium systems, on potential applications that use condensates, and on the integration of cold atoms with other physical systems. This thesis covers all of these areas. We begin by recapping the historical background of condensate physics, with a definition of the condensed phase and discussion of various analytical quantities of relevance to this work. The Landau picture of supefluidity and predictions of its breakdown, given by the Landau criterion, is particularly pertinent to the results on supersonic flow in an inhomogeneous system. After outlining current experimental procedures, we present a computationally efficient modelling technique, used in our numerical simulations of atomic condensates. We then use this technique to study the dynamics of supersonic condensate flow, in the presence of a perturbing potential. Normally one would expect this situation to introduce disturbances, known as Landau excitations into the system, potentially destroying it. However, we find, under certain circumstances, complete suppression of Landau excitations: a behaviour that has not, to our knowledge, been previously observed. The efficiency of our chosen modeling technique allowed the possibility to conduct the large phase space campaigns necessary to find these special circumstances. On investigation, the mechanism resulting in the suppression of these Landau excitations is continuously related to the presence of transmission resonances in an equivalent linear quantum system. This demonstration of a link between linear and non-linear quantum regimes is of great interest in understanding possible behaviour in other non-equilibrium superfluid systems. Finally, we consider the magnetic fields from small scale (~ 1 µm) quantum electronic devices fabricated within a two-dimensional electron gas (2DEG). We demonstrate that atomic condensates provide a powerful tool for imaging these fields, or indeed similar fields created by other structures. Using a Fourier method, we show that the field profile that would be measured by the condensate can be used to recreate the current density of the 2DEG structure. The spatial resolution of this current mapping technique is limited only by the separation of the condensate from the current-carrying structure. We also show that quantum electronic conductors in 2DEGs are well suited to form a new generation of atom chips capable of trapping atoms < 1 µm away, thereby reducing both the size and power requirements of chip-trap potentials

Inhomogeneities and instabilities of Bose-Einstein condensates in rough potential landscapes

In this work we investigate the dynamics of Bose-Einstein condensates (BECs) in inhomogeneous potential landscapes. As this research field continues to develop, more attention will focus on non-equilibrium systems, on potential applications that use condensates, and on the integration of cold atoms with other physical systems. This thesis covers all of these areas. We begin by recapping the historical background of condensate physics, with a definition of the condensed phase and discussion of various analytical quantities of relevance to this work. The Landau picture of supefluidity and predictions of its breakdown, given by the Landau criterion, is particularly pertinent to the results on supersonic flow in an inhomogeneous system. After outlining current experimental procedures, we present a computationally efficient modelling technique, used in our numerical simulations of atomic condensates. We then use this technique to study the dynamics of supersonic condensate flow, in the presence of a perturbing potential. Normally one would expect this situation to introduce disturbances, known as Landau excitations into the system, potentially destroying it. However, we find, under certain circumstances, complete suppression of Landau excitations: a behaviour that has not, to our knowledge, been previously observed. The efficiency of our chosen modeling technique allowed the possibility to conduct the large phase space campaigns necessary to find these special circumstances. On investigation, the mechanism resulting in the suppression of these Landau excitations is continuously related to the presence of transmission resonances in an equivalent linear quantum system. This demonstration of a link between linear and non-linear quantum regimes is of great interest in understanding possible behaviour in other non-equilibrium superfluid systems. Finally, we consider the magnetic fields from small scale (~ 1 µm) quantum electronic devices fabricated within a two-dimensional electron gas (2DEG). We demonstrate that atomic condensates provide a powerful tool for imaging these fields, or indeed similar fields created by other structures. Using a Fourier method, we show that the field profile that would be measured by the condensate can be used to recreate the current density of the 2DEG structure. The spatial resolution of this current mapping technique is limited only by the separation of the condensate from the current-carrying structure. We also show that quantum electronic conductors in 2DEGs are well suited to form a new generation of atom chips capable of trapping atoms < 1 µm away, thereby reducing both the size and power requirements of chip-trap potentials

Superfluid flow above the critical velocity

Superfluidity and superconductivity have been widely studied since the last century in many different contexts ranging from nuclear matter to atomic quantum gases. The rigidity of these systems with respect to external perturbations results in frictionless motion for superfluids and resistance-free electric current flow in superconductors. This peculiar behaviour is lost when external perturbations overcome a critical threshold, i.e. above a critical magnetic field or a critical current for superconductors. In superfluids, such as liquid helium or ultracold gases, the corresponding quantities are a critical rotation rate and a critical velocity respectively. Enhancing the critical values is of great fundamental and practical value. Here we demonstrate that superfluidity can be completely restored for specific, arbitrarily large flow velocities above the critical velocity through quantum interference-induced resonances providing a nonlinear counterpart of the Ramsauer-Townsend effect occurring in ordinary quantum mechanics. We illustrate the robustness of this phenomenon through a thorough analysis in one dimension and prove its generality by showing the persistence of the effect in non-trivial 2d systems. This has far reaching consequences for the fundamental understanding of superfluidity and superconductivity and opens up new application possibilities in quantum metrology, e.g. in rotation sensing