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arXiv:1105.1189 · Physical Review A

Suppression of Kelvon-induced decay of quantized vortices in oblate Bose-Einstein condensates

S. J. Rooney, P. B. Blakie, Brian P. Anderson, Ashton S. Bradley

Published Aug 29, 2011• 68 citations
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Abstract

We study the Kelvin mode excitations on a vortex line in a three-dimensional trapped Bose-Einstein condensate at finite temperature. Our stochastic Gross-Pitaevskii simulations show that the activation of these modes can be suppressed by tightening the confinement along the direction of the vortex line, leading to a strong suppression in the vortex decay rate as the system enters a regime of two-dimensional vortex dynamics. As the system approaches the condensation transition temperature, we find that the vortex decay rate is strongly sensitive to dimensionality and temperature, observing a large enhancement for quasi-two-dimensional traps. Three-dimensional simulations of the recent vortex dipole decay experiment of Neely et al. [Phys. Rev. Lett. 104, 160401 (2010)] confirm two-dimensional vortex dynamics and predict a dipole lifetime consistent with experimental observations and suppression of Kelvon-induced vortex decay in highly oblate condensates.

DOI
10.1103/physreva.84.023637

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We study the Kelvin mode excitations on a vortex line in a three-dimensional trapped Bose-Einstein condensate at finite temperature. Our stochastic Gross-Pitaevskii simulations show that the activation of these modes can be suppressed by tightening the confinement along the direction of the vortex line, leading to a strong suppression in the vortex decay rate as the system enters a regime of two-dimensional vortex dynamics. As the system approaches the condensation transition temperature, we find that the vortex decay rate is strongly sensitive to dimensionality and temperature, observing a large enhancement for quasi-two-dimensional traps. Three-dimensional simulations of the recent vortex dipole decay experiment of Neely et al. [Phys. Rev. Lett. 104, 160401 (2010)] confirm two-dimensional vortex dynamics and predict a dipole lifetime consistent with experimental observations and suppression of Kelvon-induced vortex decay in highly oblate condensates.
We study the Kelvin mode excitations on a vortex line in a three-dimensional trapped Bose-Einstein condensate at finite temperature. Our stochastic Gross-Pitaevskii simulations show that the activation of these modes can be suppressed by tightening the confinement along the direction of the vortex line, leading to a strong suppression in the vortex decay rate as the system enters a regime of two dimensional vortex dynamics. As the system approached the transition temperature we find that the vortex decay rate is strongly sensitive to dimensionality and temperature, observing a large enhancement for quasi-two-dimensional traps.
Recent experiments at the University of Arizona have demonstrated superb control and imaging of flattened superfluids revealing a rich landscape of vortex dynamics. Vortex dipoles have been created and their dynamics observed [Neely et al. Phys. Rev. Lett. 104, 160410 (2010)], and highly charged persistent currents have been formed through a clever combination of stirring and dissipation [T. W. Neely, PhD thesis, (2010)]. Many ultra-cold gas systems, including these, are in a regime that we may characterize as quasi-equilibrium: despite some external forcing, a large fraction of the gas remains in thermal equilibrium. In this thesis we use the stochastic projected Gross-Pitaevskii equation (SPGPE) to make quantitative predictions of the quasi-equilibrium Bose gas. \n\nWe quantitatively compare the SPGPE with experiment by modeling the persistent current formation experiment performed at the University of Arizona [T. W. Neely, PhD thesis, (2010)]. We determine all SPGPE parameters for the toroidal system prior to simulation, enabling quantitative modeling of the experiment with no fitting parameters, giving a true test of the SPGPE theory. We find the SPGPE gives quantitative agreement with experiment, accurately predicting the size of the persistent current as well as the decay time of the vortices. We also observe the crucial role that thermal fluctuations have on enabling this agreement, showing the comprehensive SPGPE treatment is necessary to make quantitatively accurate calculations of quasi-equilibrium systems. This is the first quantitative agreement with experimental observations of vortex dynamics obtained with a theory of dissipation from first principles using no fitting parameters.\n\nWe then systematically study the Kelvin mode excitations on a vortex line in a three dimensional Bose-Einstein condensate using the SPGPE. We give a quantitative measure of the magnitude of vortex bending caused by the activation of Kelvin modes, and find that vortex bending can be suppressed by tightening the confinement along the direction of the vortex line. This leads to a strong suppression of the vortex decay rate as the system enters a regime of two-dimensional vortex dynamics, characterized by a critical oblateness.\n\nIn our final application of the SPGPE we simulate the decay of a vortex dipole. We model a recent experiment of Neely et al. [Neely et al. Phys. Rev. Lett. 104, 160410 (2010)], finding the SPGPE predicts a dipole lifetime consistent with experimental observations. We also show the experiment lies in the two-dimensional regime of vortex dynamics, validating our critical oblateness calculation.
In a recent experiment, Kwon et al. [Phys. Rev. A 90, 063627 (2014)] generated a disordered state of quantum vortices by translating an oblate Bose-Einstein condensate past a laser-induced obstacle and studied the subsequent decay of vortex number. Using mean-field simulations of the Gross-Pitaevskii equation, we shed light on the various stages of the observed dynamics. We find that the flow of the superfluid past the obstacle leads initially to the formation of a classical-like wake, which later becomes disordered. Following removal of the obstacle, the vortex number decays due to vortices annihilating and drifting to the boundary. Our results are in excellent agreement with the experimental observations. Furthermore, we probe thermal effects through phenomenological dissipation.
We study the dynamics of a single vortex and a pair of vortices in quasi two-dimensional Bose-Einstein condensates at finite temperatures. To this end, we use the stochastic Gross--Pitaevskii equation, which is the Langevin equation for the Bose--Einstein condensate. For a pair of vortices, we study the dynamics of both the vortex-vortex and vortex-antivortex pairs, which are generated by rotating the trap and moving the Gaussian obstacle potential, respectively. Due to thermal fluctuations, the constituent vortices are not symmetrically generated with respect to each other at finite temperatures. This initial asymmetry coupled with the presence of random thermal fluctuations in the system can lead to different decay rates for the component vortices of the pair, especially in the case of two corotating vortices.
We systematically study the decay of quasi-two-dimensional vortices in an oblate strongly interacting Fermi gas over a wide interaction range and observe that, as the system temperature is lowered, the vortex lifetime increases in the Bose-Einstein condensate (BEC) regime but decreases at unitarity and in the Bardeen-Cooper-Schrieffer (BCS) regime. The observations can be qualitatively captured by a phenomenological model simply involving diffusion and two-body collisional loss, in which the vortex lifetime is mostly determined by the slower process of the two. In particular, the counterintuitive vortex decay in the BCS regime can be interpreted by considering the competition between the temperature dependence of the vortex annihilation rate and that of unpaired fermions. Our results suggest a competing mechanism for the complex vortex decay dynamics in the BCS-BEC crossover for the fermionic superfluids.
We study the instability of a doubly quantized vortex topologically imprinted on 23 Na condensate, as reported in recent experiment (Shin et al 2004 Phys. Rev. Lett. 93 160406). We have performed numerical simulations using three-dimensional Gross–Pitaevskii equation with classical thermal noise. Splitting of a doubly quantized vortex turns out to be a process that is very sensitive to the presence of thermal atoms. We observe that even very small thermal fluctuations, corresponding to 10–15% of thermal atoms, cause the decay of doubly quantized vortex into two singly quantized vortices in tens of milliseconds. As in the experiment, the lifetime of doubly quantized vortex is a monotonic function of the interaction strength.