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

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 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.