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arXiv:cond-mat/0502343

Classical stability of supercurrent in one dimension: a numerical study

Sergei Khlebnikov

Published Feb 14, 2005• 0 citations
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Abstract

We report results of a classical simulation of thermal phase slips, and the associated relaxation of supercurrent, in a ring-shaped one-dimensional superfluid. We find that the classical relaxation rate vanishes in the uniform limit. This leaves the quantum relaxation, with momentum transfer to phonons, the only mechanism of supercurrent decay in the uniform system. In the presence of a smooth periodic potential, classical decay becomes possible, and we identify a family of moving critical droplets that can mediate it.

DOI
10.48550/arxiv.cond-mat/0502343

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We report results of a classical simulation of thermal phase slips, and the associated relaxation of supercurrent, in a ring-shaped one-dimensional superfluid. We find that the classical relaxation rate vanishes in the uniform limit. This leaves the quantum relaxation, with momentum transfer to phonons, the only mechanism of supercurrent decay in the uniform system. In the presence of a smooth periodic potential, classical decay becomes possible, and we identify a family of moving critical droplets that can mediate it.
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In a uniform ring-shaped one-dimensional superfluid, quantum fluctuations that unwind the order parameter need to transfer momentum to quasiparticles (phonons). We present a detailed calculation of the leading exponential factor governing the rate of such phonon-assisted tunneling in a weakly coupled Bose gas at a low temperature TTT. We also estimate the preexponent. We find that for small superfluid velocities the TTT dependence of the rate is given mainly by $\mathrm{exp}(\ensuremath{-}{c}_{s}P∕2T)$, where PPP is the momentum transfer and cs{c}_{s}cs​ is the phonon speed. At low TTT, this represents a strong suppression of the rate compared to the nonuniform case. As a part of our calculation, we identify a complex instanton whose analytical continuation to suitable real-time segments is real and describes formation and decay of coherent quasiparticle states with nonzero total momenta.
We study the supercurrent decay of a Bose-Einstein condensate in a ring trap combined with a repulsive barrier potential. In recent experiments, Kumar et al. [Phys. Rev. A 95, 021602(R) (2017)] have measured the dependence of the decay rate on the temperature and the barrier strength. However, the origin of the decay observed in the experiment remains unclear. We calculate the rate of supercurrent decay due to thermally activated phase slips (TAPS) by using the Kramers formula based on the Gross-Pitaevskii mean-field theory. The resulting decay rate is astronomically small compared to that measured in the experiment, thus excluding the possibility of TAPS as the decay mechanism. Alternatively, we argue that three-body losses can be relevant to the observed decay and predict that one can observe supercurrent decay via TAPS by decreasing the number of atoms.
Quantum phase slips (QPS) in narrow superfluid channels generate momentum by unwinding the supercurrent. In a uniform Bose gas, this momentum needs to be absorbed by quasiparticles (phonons). We show that this requirement results in an additional exponential suppression of the QPS rate (compared to the rate of QPS induced by a sharply localized perturbation). In BCS-paired fluids, momentum can be transferred to fermionic quasiparticles, and we find an interesting interplay between quasiparticle scattering on QPS and on disorder.
We analyze the stability and decay of supercurrents of strongly interacting bosons on optical lattices. At the mean-field level, the system undergoes an irreversible dynamic phase transition, whereby the current decays beyond a critical phase gradient that depends on the interaction strength. At commensurate filling the transition line smoothly interpolates between the classical modulational instability of weakly interacting bosons and the equilibrium Mott transition at zero current. Below the mean-field instability, the current can decay due to quantum and thermal phase slips. We derive asymptotic expressions of the decay rate near the critical current. In a three-dimensional optical lattice this leads to very weak broadening of the transition. In one and two dimensions the broadening leads to significant current decay well below the mean-field critical current. We show that the temperature scale below which quantum phase slips dominate the decay of supercurrents is easily within experimental reach.