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arXiv:cond-mat/9911301

Transport in a One-Dimensional Superfluid: Quantum Nucleation of Phase Slips

Hans Peter Büchler, V. B. Geshkenbeǐn, G. Blatter

Published Nov 19, 1999• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.cond-mat/9911301

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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.
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.
We study the decay of superflow via thermally activated phase slips in one-dimensional Bose gases in a shallow optical lattice. By using the Kramers formula, we numerically calculate the nucleation rate of a thermally activated phase slip for various values of the filling factor and flow velocity in the absence of a harmonic trapping potential. Within the local density approximation, we derive a formula connecting the phase-slip nucleation rate with the damping rate of a dipole oscillation of the Bose gas in the presence of a harmonic trap. We use the derived formula to directly compare our theory with the recent experiment done by the LENS group [L. Tanzi et al., Sci. Rep. 6, 25965 (2016)]. From the comparison, the observed damping of dipole oscillations in a weakly correlated and small velocity regime is attributed dominantly to thermally activated phase slips rather than quantum phase slips.
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. 03.75.Fi, 05.30.Jp, 64.60.Qb, 67.40.Fd, 67.40.Hf Typeset using REVTEX 1 The circulation of superflow in a macroscopic torus container is quantized. However, it has been pointed out that the quantized circulation can decay via the thermal nucleation of phase slips in the case of very narrow torus, or extremely thin superconducting wires [1–4]. If the temperature is low enough, it is probable that the nucleation due to the macroscopic
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 study superflow decay via quantum phase slips in trapped one-dimensional (1D) quantum gases through dipole oscillations induced by sudden displacement of the trapping potential. We find the relation between the damping rate of the dipole oscillation G and the phase-slip nucleation rate Γ as G∝Γ/v, where v is the flow velocity. This relation allows us to show that damping of 1D Bose gases in optical lattices, which has been extensively studied in experiment, is due to quantum phase slips. It is also found that the damping rate versus the flow velocity obeys the scaling formula for an impurity potential even in the absence of an explicit impurity. We suggest that the damping rate at a finite temperature exhibits a universal crossover behavior upon changing the flow velocity.
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.