Dark-soliton-like excitations in the Yang-Gaudin gas of attractively interacting fermions

Abstract

Yrast states are the lowest energy states at given non-zero momentum and provide a natural extension of the concept of dark solitons to strongly-interacting one-dimensional quantum gases. Here we study the yrast states of the balanced spin-$\frac{1}{2}$ Fermi gas with attractive delta-function interactions in one dimension with the exactly solvable Yang-Gaudin model. The corresponding Bethe-ansatz equations are solved for finite particle number and in the thermodynamic limit. Properties corresponding to the soliton-like nature of the yrast excitations are calculated including the missing particle number, phase step, and inertial and physical masses. The inertial to physical mass ratio, which is related to the frequency of oscillations in a trapped gas, is found to be unity in the limits of strong and weak attraction and falls to $\approx 0.78$ in the crossover regime. This result is contrasted by one-dimensional mean field theory, which predicts a divergent mass ratio in the weakly attractive limit. By means of an exact mapping our results also predict the existence and properties of dark-soliton-like excitations in the super Tonks-Girardeau gas. The prospects for experimental observations are briefly discussed.

31 pages, 9 figures. Versions 4 and 5 are identical (up to the addition of this comment), and incorporate a corrigendum to the published NJP article, now also available on the NJP website. The correction affected the last paragraph of section 2.2 and Fig. 2. None of the main results or conclusions of the paper are affected

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• Magnetic impurity in a one-dimensional few-fermion system
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• Exactly solvable model for a solitonic vortex in a compressible superfluid
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• Emergence of dark soliton signatures in a one-dimensional unpolarized attractive Fermi gas on a ring
• Excitation Spectra of one-dimensional spin-1/2 Fermi gas with an attraction
• Effective theory for strongly attractive one-dimensional fermions
• 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