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arXiv:1204.6183 · Physical Review A

Critical rotation of an annular superfluid Bose-Einstein condensate

Romain Dubessy, Thomas Liennard, P. Pedri, Hélène Perrin

Published Jul 12, 2012• 54 citations
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Abstract

We analyze the excitation spectrum of a superfluid Bose-Einstein condensate rotating in a ring trap. We identify two important branches of the spectrum related to outer and inner edge surface modes that lead to the instability of the superfluid. Depending on the initial circulation of the annular condensate, either the outer or the inner modes become first unstable. This instability is crucially related to the superfluid nature of the rotating gas. In particular, we point out the existence of a maximal circulation above which the superflow decays spontaneously, which cannot be explained by invoking the average speed of sound.

DOI
10.1103/physreva.86.011602

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We analyze the excitation spectrum of a superfluid Bose-Einstein condensate rotating in a ring trap. We identify two important branches of the spectrum related to outer and inner edge surface modes that lead to the instability of the superfluid. Depending on the initial circulation of the annular condensate, either the outer or the inner modes become first unstable. This instability is crucially related to the superfluid nature of the rotating gas. In particular, we point out the existence of a maximal circulation above which the superflow decays spontaneously, which cannot be explained by invoking the average speed of sound.
We theoretically show that the topology of a nonsimply connected annular atomic Bose-Einstein condensate enforces the inner surface waves to be always excited with outer surface excitations and that the inner surface modes are associated with induced vortex dipoles unlike the surface waves of a simply connected one with vortex monopoles. Consequently, under stirring to drive an inner surface wave, a peculiar population oscillation between the inner and outer surface is generated regardless of annulus thickness. Moreover, a vortex nucleation process by stirring is observed that can merge the inner vortex dipoles and outer vortex into a single vortex inside the annulus. The energy spectrum for a rotating annular condensate with a vortex at the center also reveals the distinct connection of the Tkachenko modes of a vortex lattice to its inner surface excitations.
The irrotational nature of superfluids leads to spectacular rotational properties. For the fluid to rotate, its density must locally vanish at a singular point called a quantum vortex. The annular geometry is of great interest for studying superfluidity as the gas can rotate in this geometry around a central hole without requiring any singularity, allowing the existence of persistent currents along the ring with a quantized circulation. In out experiment, we confine cold atoms dressed by a radiofrequency field in an adiabatic potential based on a quadrupolar magnetic trap. The resulting bubble-shaped potential, both very smooth and easily tunable, allows us to produce two types of ring-shaped Bose-Einstein condensates. A first strategy consists in adding a far-detuned light sheet to confine the atoms at the intersection between the bubble and the horizontal plane imposed by the light field – i.e. a ring. We present the implementation and optimization of this trap and demonstrate the possibility to prepare and observe superfluid currents in the ring. A second path exploits the centrifugal force and the anharmonicity of the adiabatic potential to create an effective Mexican hat potential by rotating the trapped atoms at the bottom of the bubble faster than the trap frequency. After having realized such a system, we probe its quadrupolar modes to characterize the rotation. The study of vortex distribution in the rotating gas also shows a thermal melting effect of the finite temperature vortex lattice.
Abstract We investigate the flow of a one-dimensional nonlinear Schrödinger model with periodic boundary conditions past an obstacle, motivated by recent experiments with Bose–Einstein condensates in ring traps. Above certain rotation velocities, localized solutions with a nontrivial phase profile appear. In striking difference from the infinite domain, in this case there are many critical velocities. At each critical velocity, the steady flow solutions disappear in a saddle-center bifurcation. These interconnected branches of the bifurcation diagram lead to additions of circulation quanta to the phase of the associated solution. This, in turn, relates to the manifestation of persistent current in numerous recent experimental and theoretical works, the connections to which we touch upon. The complex dynamics of the identified waveforms and the instability of unstable solution branches are demonstrated.
A two-dimensional rapidly rotating Bose-Einstein condensate in a harmonic plus quartic trap is expected to have unusual vortex states that do not occur in a pure harmonic trap. At a critical rotation speed ${\ensuremath{\Omega}}_{h}$, a central hole appears in the condensate, and at some faster rotation speed ${\ensuremath{\Omega}}_{g}$, the system undergoes a transition to a giant vortex state with pure irrotational flow. Using a time-dependent variational analysis, we study the behavior of an annular condensate with a single concentric ring of vortices. The transition to a giant vortex state is investigated by comparing the energy of the two equilibrium states (the ring of vortices and the giant vortex) and also by studying the dynamical stability of small excitation modes of the ring of vortices.
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