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arXiv:cond-mat/9704094 · Physical Review Letters

Quantum Nucleation of Phase Slips in a 1D Model of a Superfluid

José A. Freire, Daniel P. Arovas, Herbert Levine

Published Dec 22, 1997• 19 citations
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Abstract

We use a 1D model of a superfluid based on the Gross-Pitaevskii Lagrangian to illustrate a general numerical method designed to find quantum tunneling rates in extended bosonic systems. Specifically, we study flow past an obstacle and directly solve the imaginary time dynamics to find the ``bounce'' solution connected with the decay of the metastable laminar state via phase slip nucleation. The action for the tunneling configuration goes to zero at the threshold (in superfluid velocity) for classical production of these slips. Applications to other processes are briefly discussed.

DOI
10.1103/physrevlett.79.5054

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We use a 1D model of a superfluid based on the Gross-Pitaevskii Lagrangian to illustrate a general numerical method designed to find quantum tunneling rates in extended bosonic systems. Specifically, we study flow past an obstacle and directly solve the imaginary time dynamics to find the ``bounce'' solution connected with the decay of the metastable laminar state via phase slip nucleation. The action for the tunneling configuration goes to zero at the threshold (in superfluid velocity) for classical production of these slips. Applications to other processes are briefly discussed.
We study the decay of superflow of a one-dimensional (1D) superfluid in the presence of a periodic potential. In 1D, superflow at zero temperature can decay via quantum nucleation of phase slips even when the flow velocity is much smaller than the critical velocity predicted by mean-field theories. Applying the instanton method to the O(2) quantum rotor model, we calculate the nucleation rate of quantum phase slips $\ensuremath{\Gamma}$. When the flow momentum ppp is small, we find that the nucleation rate per unit length increases algebraically with ppp as $\ensuremath{\Gamma}/L\ensuremath{\propto}{p}^{2K\ensuremath{-}2}$, where LLL is the system size and KKK is the Tomonaga-Luttinger parameter. Based on the relation between the nucleation rate and the quantum superfluid-insulator transition, we present a unified explanation on the scaling formulas of the nucleation rate for periodic, disorder, and single-barrier potentials. Using the time-evolving block decimation method, we compute the exact quantum dynamics of the superflow decay in the 1D Bose-Hubbard model at unit filling. From the numerical analyses, we show that the scaling formula is valid for the case of the Bose-Hubbard model, which can quantitatively describe Bose gases in optical lattices.
Slips of the superfluid wave-function phase occur when the flow velocity through an aperture exceeds a critical threshold vc{\mathit{v}}_{\mathit{c}}vc​. We propose a phase slip mechanism in which a microscopic vortex half ring is nucleated at the wall of the aperture. Its subsequent trajectory is described. The properties of the vortex close to the wall are inferred from the Gross-Pitaevskii equation and yield, at T\ensuremath{\sim}0.1 K, a vortex radius at nucleation of 14 \AA{} and a critical velocity of 21 m/s, in agreement with experiment.
The quantum nucleation of phase slips in neutral superfluids confined in a thin torus is investigated by means of the collective coordinate method. We have devised, with numerical justification, a certain collective coordinate to describe the quantum nucleation process of a phase slip. Considering the quantum fluctuation around the local minimum of the action, we calculate the effective mass of the phase slip. Due to the coherence of the condensate throughout the torus, the effective mass is proportional to the circumference L of the torus, and the decay rate has a strong exponential L-dependence.
We present an analytical derivation for the quantum decay rate of the superflow through a weak link in a one-dimensional Bose-Einstein-condensate. The effective action for the phase difference across the link reduces to that of a massive particle with damping subject to a periodic potential. We find an algebraic flow-pressure relation, characteristic for quantum nucleation of phase slips in the link and show how short-wave length fluctuations renormalizing the interaction between the Bosons remove the quantum phase transition expected in this class of systems.
Quantum phase slips are the primary excitations in one-dimensional superfluids and superconductors at low temperatures but their existence in ultracold quantum gases has not been demonstrated yet. We now study experimentally the nucleation rate of phase slips in one-dimensional superfluids realized with ultracold quantum gases, flowing along a periodic potential. We observe a crossover between a regime of temperature-dependent dissipation at small velocity and interaction and a second regime of velocity-dependent dissipation at larger velocity and interaction. This behavior is consistent with the predicted crossover from thermally-assisted quantum phase slips to purely quantum phase slips.
The ground state of Bose-Einstein condensates with attractive particle interactions is metastable. One of the decay mechanisms of the condensate is a collapse by macroscopic quantum tunneling, which can be described by the bounce trajectory as a solution of the time-dependent Gross-Pitaevskii equation in imaginary time. For condensates with an electromagnetically induced gravity-like interaction, the bounce trajectory is computed with an extended variational approach using coupled Gaussian functions and is simulated numerically exact within the mean-field approach on a spacetime lattice. It is shown that the variational computations converge very rapidly to the numerically exact result with increasing number of Gaussians. The tunneling rate of the condensate is obtained from the classical action and additional parameters of the bounce trajectory. The converged variational and numerically exact results drastically improve by several orders of magnitude the decay rates obtained previously with a simple variational approach using a single Gaussian-type orbital for the condensate wave function.