Quantum phase slips (QPS) are the primary excitations in one-dimensional superfluids and superconductors at low temperatures. They have been well characterized in most condensed-matter systems, and signatures of their existence have been recently observed in superfluids based on quantum gases too. In this review, we briefly summarize the main results obtained on the investigation of phase slips from superconductors to quantum gases. In particular, we focus our attention on recent experimental results of the dissipation in one-dimensional Bose superfluids flowing along a shallow periodic potential, which show signatures of QPS.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.
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 $\mathrm{exp}(\ensuremath{-}{c}_{s}P∕2T)$, where
P is the momentum transfer and
cs 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.
We report results of a classical simulation of thermal phase slips, and the associated relaxation of supercurrent, in a ring-shaped one-dimensional superfluid. We find that the classical relaxation rate vanishes in the uniform limit. This leaves the quantum relaxation, with momentum transfer to phonons, the only mechanism of supercurrent decay in the uniform system. In the presence of a smooth periodic potential, classical decay becomes possible, and we identify a family of moving critical droplets that can mediate it.
A theory accounting for the dynamical aspects of the superfluid response of one dimensional (1D) quantum fluids is reported. In long 1D systems, the onset of superfluidity is related to the dynamical suppression of quantum phase slips at low temperatures. The effect of this suppression as a function of frequency and temperature is discussed within the framework of the experimentally relevant momentum response function. Applications of these results to the understanding of the superfluid properties of helium confined in 1D pores with nanometer diameter, dislocations in solid 4He, and ultracold atomic gases are also briefly discussed.
We consider a 3D homogeneous superfluid at low temperature
T with 2 types of excitations, gapless phonons with a linear dispersion relation at low wavenumber, and gapped quasiparticles with a quadratic dispersion relation around extrema. We calculate the scattering amplitude of a phonon on a quasiparticle to leading order in
T for all subsonic quasiparticle velocities, with a
S-matrix formalism between exact asymptotic states dressed by virtual phonons. We then characterize the erratic motion of the quasiparticle in the superfluid due to its unceasing collisions with thermal phonons through mean force
F(k), longitudinal and transverse
k-dependent momentum diffusion coefficients, and spatial diffusion coefficient. At the minimum location
k0 of the dispersion relation, where the velocity vanishes,
F(k) varies linearly with velocity with an isotropic friction coefficient; if
k0=0, the momentum diffusion is also isotropic and
F(k0)=0; if
k0>0, it is not, and
F(k0) is nonzero but subleading with respect to friction by one order in
T. The velocity time correlation function, whose integral is the spatial diffusion coefficient, decays with the mean velocity damping rate if
k0=0; if
k0>0, it has a second exponential component, with an amplitude and a damping rate lower by a factor
∝T (it is the velocity direction thermalization rate). We also characterize force and momentum diffusion close to the stability domain sonic edge. Our general expressions are expected to be exact to leading order in
T. We illustrate them in the BCS approximation, for a fermionic quasiparticle (an unpaired fermion) in a superfluid of spin 1/2 fermions, realisable with cold atoms in flat bottom traps. We also refute the statement of Lerch, Bartosch and Kopietz (2008), that there would be no fermionic quasiparticle in such a superfluid.
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
p is small, we find that the nucleation rate per unit length increases algebraically with
p as $\ensuremath{\Gamma}/L\ensuremath{\propto}{p}^{2K\ensuremath{-}2}$, 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 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.