Tunneling in a uniform one-dimensional superfluid: emergence of a complex instanton

TL;DR

This paper analyzes quantum tunneling in a one-dimensional superfluid ring, deriving the exponential rate dependence on temperature and momentum transfer, and introduces a complex instanton solution describing quasiparticle dynamics.

Contribution

It provides a detailed calculation of tunneling rates in a uniform 1D superfluid, identifying a complex instanton that captures the formation and decay of quasiparticle states.

Findings

Tunneling rate depends exponentially on temperature and momentum transfer.

Low temperature suppresses tunneling significantly compared to non-uniform cases.

Introduction of a complex instanton solution for quasiparticle dynamics.

Abstract

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 $T$. We also estimate the preexponent. We find that for small superfluid velocities the $T$-dependence of the rate is given mainly by $\exp(-c_s P/ 2T)$, where $P$ is the momentum transfer, and $c_s$ is the phonon speed. At low $T$, this represents a strong suppression of the rate, compared to the non-uniform 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.