Emergence of dark soliton signatures in a one-dimensional unpolarized attractive Fermi gas on a ring

The two-component Fermi gas with contact attractive interactions between different spin components can be described by the Yang-Gaudin model. Applying the Bethe ansatz approach, one finds analytical formulae for the system eigenstates that are uniquely parametrized by the solutions of the corresponding Bethe equations. Recent numerical studies of the so-called yrast eigenstates, i.e. lowest energy eigenstates at a given non-zero total momentum, in the Yang-Gaudin model show that their spectrum resembles yrast dispersion relation of the Lieb-Liniger model which in turn matches the dark soliton dispersion relation obtained within the nonlinear Schr\"{o}dinger equation. It was shown that such conjecture in the case of the Lieb-Liniger model was not accidental and that dark soliton features emerged in the course of measurement of positions of particles, when the system was initially prepared in an yrast eigenstate. Here, we demonstrate that, starting with yrast eigenstates in the Yang-Gaudin model, the key soliton signatures are revealed by the measurement of pairs of fermions. We study soliton signatures in a wide range of the interaction strength.