Elementary excitations of chiral Bose-Einstein condensates

We study the collective modes of a Bose-Einstein condensate subject to an optically induced density-dependent gauge potential. The corresponding interacting gauge theory lacks Galilean invariance, yielding an exotic superfluid state. The nonlinear dynamics in the presence of a current nonlinearity and an external harmonic trap are found to give rise to dynamics which violate Kohn's theorem; where the frequency of the dipole mode strongly depends on the strength of the mass current in the gas. The linearised spectrum reveals how the centre of mass and shape oscillations are coupled, whereas in the strongly nonlinear regime the dynamics is irregular.Comment: General improvements, corrections and references adde

Dark quantum droplets in beyond-mean-field Bose-Einstein condensate mixtures

Quantum liquid-like states of matter have been realized in an ongoing series of experiments with ultracold Bose gases. By means of analytical and theoretical methods we identify the specific criteria for the existence of dark solitons in beyond-mean-field condensates, revealing how these excitations exist for both repulsive and attractive interactions, the latter leading to dark quantum droplets with properties intermediate between a dark soliton and a quantum droplet. The dark quantum droplet's physical characteristics are investigated, including calculation of the integrals of motion, revealing their sensitive dependence on physical parameters relevant to the current generation of experiments with quantum gases in the beyond-mean-field limit.Comment: 8 pages, 5 figures. Comments welcom

Simulation of single and many particle gauge theories with ultracold atomic gases

The study of systems formed from ultracold atomic gases has emerged to become one of the most active research elds within the condensed matter landscape. These highly controllable macroscopic systems amalgamate ideas from many sub disciplines of physics, including the study of low temperatures, quantum optics and quantum information theory as well as the seemingly disparate eld of high energy physics. The central concept of this thesis is gauge theories as applied to systems of bosonic atoms, which at temperatures close to absolute zero form Bose-Einstein condensates. To simulate the mathematical structure of a gauge theory, the geometric (Berry) phase formalism is adopted. This is in turn accomplished by considering the adiabatic following of the eigenstates of the light-matter coupling for an ensemble of atoms forming a Bose-Einstein condensate. These concepts are then applied to show how one can generate a spin-orbit coupling in a one-dimensional condensate, which additionally features a random mass term that allows us to study the physics of Anderson localization in an intriguing \quasi" relativistic regime. One of the features of light induced gauge potentials is that they are static; in the sense that there is no feedback between the light-matter interaction and the matter eld. In the second part of this thesis it is demonstrated how such a feedback mechanism can be induced by the appropriate modi cation of the light-matter interaction. The consequences this has for the condensate are then described at the mean- eld level, including the expected experimental signatures of the resulting `interacting' gauge theory, in terms of the expansion of the condensate and also the structure of the solitons of this nonlinear system. Finally, this nonlinear model is applied to a double well system, from which the associated Bose-Hubbard model is derived and analysed; and the nonlinear Josephson problem studied

Simulating an interacting gauge theory with ultracold Bose gases

We show how density dependent gauge potentials can be induced in dilute gases of ultracold atoms using light-matter interactions. We study the effect of the resulting interacting gauge theory and show how it gives rise to novel topological states in the ultracold gas. We find in particular that the onset of persistent currents in a ring geometry is governed by a critical number of particles. The density-dependent gauge potential is also found to support chiral solitons in a quasi-one-dimensional ultracold Bose gas.Comment: General improvements. Published version: Phys. Rev. Lett. 110, 085301 (2013

Quantum vacuum effects in non-relativistic quantum field theory

Nonlinearities in the dispersion relations associated with different interactions designs, boundary conditions and the existence of a physical cut-off scale can alter the quantum vacuum energy of a nonrelativistic system nontrivially. As a material realization of this, we consider a 1D-periodic rotating, interacting non-relativistic setup. The quantum vacuum energy of such a system is expected to comprise two contributions: a fluctuation-induced quantum contribution and a repulsive centrifugal-like term. We analyze the problem in detail within a complex Schoedinger quantum field theory with a quartic interaction potential and perform the calculations non-perturbatively in the interaction strength by exploiting the nonlinear structure of the associated nonlinear Schroedinger equation. Calculations are done in both zeta-regularization, as well as by introducing a cut-off scale. We find a generic, regularization-independent behavior, where the competition between the interaction and rotation can be balanced at some critical ring-size, where the quantum vacuum energy has a maxima and the force changes sign. The inclusion of a cut-off smoothes out the vacuum energy at small distance but leaves unaltered the long distance behavior. We discuss how this behavior can be tested with ultracold-atoms.Comment: 10 pages, 3 figure