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arXiv:1511.03768 · Physical Review A

Persistent currents in coherently coupled Bose-Einstein condensates in a ring trap

Marta Abad

Published Mar 1, 2016• 10 citations
arXivHTMLPDF

Abstract

We study the stability of persistent currents in a coherently coupled quasi-two-dimensional Bose-Einstein condensate confined in a ring trap at $T=0$. By numerically solving Gross-Pitaevskii equations and by analyzing the excitation spectrum obtained from diagonalization of the Bogoliubov--de Gennes matrix, we describe the mechanisms responsible for the decay of the persistent currents depending on the values of the interaction coupling constants and the Rabi frequency. When the unpolarized system decays due to an energetic instability in the density channel, the spectrum may develop a rotonlike minimum, which gives rise to the finite wavelength excitation necessary for vortex nucleation at the inner surface. When decay in the unpolarized system is driven by spin-density excitations, the finite wavelength naturally arises from the existence of a gap in the excitation spectrum. In the polarized phase of the coherently coupled condensate, there is a hybridization of the excitation modes that leads to complex decay dynamics. In particular, close to the phase transition, a state of broken rotational symmetry is found to be stationary and stable.

DOI
10.1103/physreva.93.033603

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We study the stability of persistent currents in a coherently coupled quasi-two-dimensional Bose-Einstein condensate confined in a ring trap at T=0T=0T=0. By numerically solving Gross-Pitaevskii equations and by analyzing the excitation spectrum obtained from diagonalization of the Bogoliubov--de Gennes matrix, we describe the mechanisms responsible for the decay of the persistent currents depending on the values of the interaction coupling constants and the Rabi frequency. When the unpolarized system decays due to an energetic instability in the density channel, the spectrum may develop a rotonlike minimum, which gives rise to the finite wavelength excitation necessary for vortex nucleation at the inner surface. When decay in the unpolarized system is driven by spin-density excitations, the finite wavelength naturally arises from the existence of a gap in the excitation spectrum. In the polarized phase of the coherently coupled condensate, there is a hybridization of the excitation modes that leads to complex decay dynamics. In particular, close to the phase transition, a state of broken rotational symmetry is found to be stationary and stable.
Abstract We present a kinetic description of superfluid currents in ring-shaped Bose-Einstein condensates based on the Wigner phase-space formalism. Starting from the Gross-Pitaevskii equation in a toroidal geometry, we derive a Vlasov-type equation for the angular Wigner function, in which the mean-field interaction generates an effective force proportional to the density gradient. Within this framework, we obtain the dispersion relation of collective modes and recover the Bogoliubov spectrum in the long-wavelength limit. We show that the Landau criterion for superfluidity can be interpreted as the absence of resonant phase-space trajectories satisfying the condition ω=qvℓ\omega = q v_\ell ω=qvℓ​ ω = q v ℓ . In a ring geometry, the quantization of angular momentum leads to a discrete set of velocities, which suppresses the availability of resonant states and strongly inhibits Landau damping. In contrast, in the continuous limit R→∞R \rightarrow \infty R→∞ R → ∞ , the spectrum becomes quasi-continuous and the standard Landau damping mechanism is recovered, establishing a direct connection between kinetic resonances and the energetic criterion for superfluidity. We further analyze the role of Bogoliubov depletion by considering a finite-width angular momentum distribution. Although resonant states formally exist in this case, we show that, for flow velocities below the sound velocity, the phase-space distribution does not provide the gradients required for energy transfer, and the superfluid current remains dynamically stable. Our results provide a unified phase-space interpretation of superfluidity, highlighting the role of angular momentum quantization and the structure of the distribution function in determining the stability of persistent currents. Graphic abstract Phase-space interpretation of superfluid stability in a ring Bose-Einstein condensate. For flow velocities below the sound velocity, resonant phase-space trajectories are unavailable and the superflow remains stable, whereas above the sound velocity resonant coupling becomes possible, leading to kinetic instability
We investigate the dynamics of a two-component Bose-Einstein condensate trapped in two coupled rings in ladder configuration. First, we derive from the two-component Gross-Pitaevskii equation a few state model for the angular momentum modes. Then, we analyse the stability of the stationary states by solving the Bogoliubov-de Gennes equations. Also, we study the dynamics of the system for an arbitrary population imbalance between the rings, characterizing the transition from Josephson oscillations to quantum self-trapping. We also derive the self-trapping condition for the bosonic mixture, finding simultaneous self-trapping of the two components.
The stability of persistent currents in a two-component Bose-Einstein condensate in a toroidal trap is studied in both the miscible and the immiscible regimes. In the miscible regime we show that superflow decay is related to linear instabilities of the spin-density Bogoliubov mode. We find a region of partial stability, where the flow is stable in the majority component while it decays in the minority component. We also characterize the dynamical instability appearing for a large relative velocity between the two components. In the immiscible regime the stability criterion is modified and depends on the specific density distribution of the two components. The effect of a coherent coupling between the two components is also discussed.
In this thesis we solve the Gross-Pitaevskii equation numerically in order to model the response of trapped Bose-Einstein condensed gases to perturbations by electromagnetic fields. First, we simulate output coupling of pulses from the condensate and compare our results to experiments. The excitation and separation of eigenmodes on flow through a constriction is also studied. We then move on to the main theme of this thesis: the important subject of quantised vortices in Bose condensates, and the relation between Bose-Einstein condensation and superfluidity. We propose methods of producing vortex pairs and rings by controlled motion of objects. Full three-dimensional simulations under realistic experimental conditions are performed in order to test the validity of these ideas. We link vortex formation to drag forces on the object, which in turn is connected with energy transfer to the condensate. We therefore argue that vortex formation by moving objects is intimately related to the onset of dissipation in superfluids. We discuss this idea in the context of a recent experiment, using simulations to provide evidence of vortex formation in the experimental scenario. Superfluidity is also manifest in the property of persistent currents, which is linked to vortex stability and dynamics. We simulate vortex line and ring motion, and find in both cases precessional motion and thermodynamic instability to dissipation. Strictly speaking, the Gross-Pitaevskii equation is valid only for temperatures far below the BEC transition. We end the thesis by describing a simple finite-temperature model to describe mean-field coupling between condensed and non-condensed components of the gas. We show that our hybrid Monte-Carlo/FFT technique can describe damping of the lowest energy excitations of the system. Extensions to this model and future research directions are discussed in the conclusion. (author)
In the present work, motivated by numerous recent experimental developments we revisit the dynamics of a single vortex ring in anisotropic harmonic traps. At the theoretical level, we start from a general Lagrangian dynamically capturing the evolution of a vortex ring and not only consider its spectrum of linearized excitations, but also explore the full nonlinear dynamical evolution of the ring as a vortical filament. The theory predicts that the ring is stable for $1\ensuremath{\le}\ensuremath{\lambda}\ensuremath{\le}2$, where $\ensuremath{\lambda}={\ensuremath{\omega}}_{z}/{\ensuremath{\omega}}_{r}$ is the ratio of the trapping frequencies along the zzz and rrr axes, i.e., for spherical to slightly oblate condensates. We compare this prediction with direct numerical simulations of the full three-dimensional Gross-Pitaevskii equation (GPE) capturing the linearization spectrum of the ring for different values of the chemical potential and as a function of the anisotropy parameter $\ensuremath{\lambda}$. We identify this result as being only asymptotically valid as the chemical potential $\ensuremath{\mu}\ensuremath{\rightarrow}\ensuremath{\infty}$, revealing how the stability interval narrows and, in particular, its upper bound decreases for finite $\ensuremath{\mu}$. Finally, we compare at the dynamical level the results of the GPE with the ones effectively capturing the ring dynamics, revealing the unstable evolution for different values of $\ensuremath{\lambda}$, as well as the good agreement between the two.