Moving solitons in a one-dimensional fermionic superfluid

Abstract

A fully analytical theory of a traveling soliton in a one-dimensional fermionic superfluid is developed within the framework of time-dependent self-consistent Bogoliubov-de Gennes equations, which are solved exactly in the Andreev approximation. The soliton manifests itself in a kink-like profile of the superconducting order parameter and hosts a pair of Andreev bound states in its core. They adjust to soliton's motion and play an important role in its stabilization. A phase jump across the soliton and its energy decrease with soliton's velocity and vanish at the critical velocity, corresponding to the Landau criterion, where the soliton starts emitting quasiparticles and becomes unstable. The "inertial" and "gravitational" masses of the soliton are calculated and the former is shown to be orders of magnitude larger than the latter. This results in a slow motion of the soliton in a harmonic trap, reminiscent to the observed behavior of a soliton-like texture in related experiments in cold fermion gases [T. Yefsah et al., Nature 499, 426, (2013)]. Furthermore, we calculate the full non-linear dispersion relation of the soliton and solve the classical equations of motion in a trap. The strong non-linearity at high velocities gives rise to anharmonic oscillatory motion of the soliton. A careful analysis of this anharmonicity may provide a means to experimentally measure the non-linear soliton spectrum in superfluids.

12 pages and 5 figures. Minor changes. Updated references. Published version

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• Traveling Majorana solitons in a one-dimensional spin-orbit coupled Fermi superfluid
• Dark-soliton-like excitations in the Yang-Gaudin gas of attractively interacting fermions
• Kinetic theory of dark solitons with tunable friction
• Snake instability of dark solitons across the BEC-BCS crossover: an effective field theory perspective
• Soliton core filling in superfluid Fermi gases with spin-imbalance
• Collective modes of a soliton train in a Fermi superfluid
• Bogoliubov-de Gennes Soliton Dynamics in Unconventional Fermi Superfluids
• Signatures of the BCS-BEC crossover in the yrast spectra of Fermi quantum rings
• Nambu-Jona Lasinio and Nonlinear Sigma Models in Condensed Matter Systems
• Dynamical generation of solitons in one-dimensional Fermi superfluids with and without spin-orbit coupling
• Protocol to engineer Fulde-Ferrell-Larkin-Ovchinnikov states in a cold Fermi gas
• Two types of dark solitons in a spin-orbit-coupled Fermi gas
• Solitons in One Dimensional Systems at BCS-BEC Crossover
• Coexistence of topological and nontopological Fermi-superfluid phases
• Soliton Diffusion as a Signature of Hawking Radiation in Bose-Einstein Condensates
• Solitons in a class of interacting scalar field theories without $SO(2)$ invariance
• Solitons in lattice field theories via tight-binding supersymmetry
• Drag-induced dynamical formation of dark solitons in Bose mixture on a ring
• Swallow-tail dispersions of moving solitons in a two-dimensional fermionic superfluid