We use an effective one-dimensional Gross-Pitaevskii equation to study bright matter-wave solitons held in a tightly confining toroidal trapping potential, in a rotating frame of reference, as they are split and recombined on narrow barrier potential
s. In particular, we present an analytical and numerical analysis of the phase evolution of the solitons and delimit a velocity regime in which soliton Sagnac interferometry is possible, taking account of the effect of quantum uncertainty.
We investigate the mean--field equilibrium solutions for a two--species immiscible Bose--Einstein condensate confined by a harmonic confinement with additional linear perturbations. We observe a range of equilibrium density structures, including `bal
l and shell formations and axially/radially separated states, with a marked sensitivity to the potential perturbations and the relative atom number in each species. Incorporation of linear trap perturbations, albeit weak, are found to be essential to match the range of equilibrium density profiles observed in a recent Rb-87 - Cs-133 Bose-Einstein condensate experiment [D. J. McCarron et al., Phys. Rev. A, 84, 011603(R) (2011)]. Our analysis of this experiment demonstrates that sensitivity to linear trap perturbations is likely to be important factor in interpreting the results of similar experiments in the future.
While the Gross--Pitaevskii equation is well-established as the canonical dynamical description of atomic Bose-Einstein condensates (BECs) at zero-temperature, describing the dynamics of BECs at finite temperatures remains a difficult theoretical pro
blem, particularly when considering low-temperature, non-equilibrium systems in which depletion of the condensate occurs dynamically as a result of external driving. In this paper, we describe a fully time-dependent numerical implementation of a second-order, number-conserving description of finite-temperature BEC dynamics. This description consists of equations of motion describing the coupled dynamics of the condensate and non-condensate fractions in a self-consistent manner, and is ideally suited for the study of low-temperature, non-equilibrium, driven systems. The delta-kicked-rotor BEC provides a prototypical example of such a system, and we demonstrate the efficacy of our numerical implementation by investigating its dynamics at finite temperature. We demonstrate that the qualitative features of the system dynamics at zero temperature are generally preserved at finite temperatures, and predict a quantitative finite-temperature shift of resonance frequencies which would be relevant for, and could be verified by, future experiments.
We consider the ground state of an attractively-interacting atomic Bose-Einstein condensate in a prolate, cylindrically symmetric harmonic trap. If a true quasi-one-dimensional limit is realized, then for sufficiently weak axial trapping this ground
state takes the form of a bright soliton solution of the nonlinear Schroedinger equation. Using analytic variational and highly accurate numerical solutions of the Gross-Pitaevskii equation we systematically and quantitatively assess how soliton-like this ground state is, over a wide range of trap and interaction strengths. Our analysis reveals that the regime in which the ground state is highly soliton-like is significantly restricted, and occurs only for experimentally challenging trap anisotropies. This result, and our broader identification of regimes in which the ground state is well-approximated by our simple analytic variational solution, are relevant to a range of potential experiments involving attractively-interacting Bose-Einstein condensates.
We consider a Bose-Einstein condensate driven by periodic delta-kicks. In contrast to first-order descriptions, which predict rapid, unbounded growth of the noncondensate in resonant parameter regimes, the consistent treatment of condensate depletion
in our fully-time-dependent, second-order description acts to damp this growth, leading to oscillations in the (non)condensate population and the coherence of the system.
We propose a method to split the ground state of an attractively interacting atomic Bose-Einstein condensate into two bright solitary waves with controlled relative phase and velocity. We analyze the stability of these waves against their subsequent
re-collisions at the center of a cylindrically symmetric, prolate harmonic trap as a function of relative phase, velocity, and trap anisotropy. We show that the collisional stability is strongly dependent on relative phase at low velocity, and we identify previously unobserved oscillations in the collisional stability as a function of the trap anisotropy. An experimental implementation of our method would determine the validity of the mean field description of bright solitary waves, and could prove an important step towards atom interferometry experiments involving bright solitary waves.
We consider a two-component Bose-Einstein condensate (BEC) in a ring trap in a rotating frame, and show how to determine the response of such a configuration to being in a rotating frame, via accumulation of a Sagnac phase. This may be accomplished e
ither through population oscillations, or the motion of spatial density fringes. We explicitly include the effect of interactions via a mean-field description, and study the fidelity of the dynamics relative to an ideal configuration.
Under certain conditions, the quantum delta-kicked harmonic oscillator displays quantum resonances. We consider an atom-optical realization of the delta-kicked harmonic oscillator, and present a theoretical discussion of the quantum resonances that c
ould be observed in such a system. Having outlined our model of the physical system we derive the values at which quantum resonances occur and relate these to potential experimental parameters. We discuss the observable effects of the quantum resonances, using the results of numerical simulations. We develop a physical explanation for the quantum resonances based on symmetries shared between the classical phase space and the quantum-mechanical time evolution operator. We explore the evolution of coherent states in the system by reformulating the dynamics in terms of a mapping over an infinite, two-dimensional set of coefficients, from which we derive an analytic expression for the evolution of a coherent state at quantum resonance.
