Quantum phase slips in one-dimensional superfluids in a periodic potential

TL;DR

This paper investigates quantum phase slip-induced superflow decay in one-dimensional superfluids within periodic potentials, deriving scaling laws and validating them through numerical simulations of the Bose-Hubbard model.

Contribution

It provides a unified theoretical framework for quantum phase slip nucleation rates across different potentials and confirms the scaling laws using numerical simulations.

Findings

Nucleation rate scales as p^{2K-2} at small momenta.

Scaling laws are validated in the Bose-Hubbard model.

Quantum decay mechanisms are quantitatively described.

Abstract

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 $\Gamma$. When the flow momentum $p$ is small, we find that the nucleation rate per unit length increases algebraically with $p$ as $\Gamma/L \propto p^{2K-2}$, where $L$ is the system size and $K$ 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 formulae 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.