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

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.

arXiv comment15 pages, 3 figures; to be published in Phys. Rev. A

References in corpus (14)

• Sonic analog of gravitational black holes in Bose-Einstein condensates
• Quantum suppression of superconductivity in ultrathin nanowires
• Electroweak Baryon Number Non-Conservation in the Early Universe and in High Energy Collisions
• Quantum Phase Slips in Superconducting Nanowires
• Gibbons-Hawking Effect in the Sonic de Sitter Space-Time of an Expanding Bose-Einstein-Condensed Gas
• Probing semiclassical analogue gravity in Bose--Einstein condensates with widely tunable interactions
• Comment on Vortex Mass and Quantum Tunneling of Vortices
• Supercurrent Stability in a Quasi-1D Weakly Interacting Bose Gas
• Multiply-connected Bose-Einstein condensed alkali gases: Current-carrying states and their decay
• Supercurrent States in 1D Finite-Size Rings
• Microscopic Analysis of the Non-Dissipative Force on a Line Vortex in a Superconductor: Berry's Phase, Momentum Flows and the Magnus Force
• Quasiparticle scattering by quantum phase slips in one-dimensional superfluids
• Fermions, Anomaly and Unitarity in High-Energy Electroweak Scattering
• Numerical Study of Periodic Instanton Configurations in Two-dimensional Abelian Higgs Theory

Cited by in corpus (4)

• Oscillations and decay of superfluid currents in a one-dimensional Bose gas on a ring
• Dynamical theory of superfluidity in one dimension
• Quantum phase slips in the presence of finite-range disorder
• Quantum phase slips in a confined geometry