Shapiro steps of superfluid Fermi gases in a ring trap across the BCS--BEC crossover

Abstract

We investigate the transport properties of a superfluid Fermi gas confined in a ring trap with a moving potential barrier across the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) crossover. Employing time-dependent Bogoliubov--de Gennes (BdG) equations, we simulate the dynamics of a Josephson junction biased by both DC and AC currents. Over a wide range of interaction strengths, we observe clear low-order Shapiro-step plateaus in the barrier-velocity--chemical-potential-diffenrence, within the phase-coherent regime, where the time-averaged chemical potential difference is quantized in units of $\hbar\omega/2$. This factor of $1/2$ reflects our convention of defining the chemical potential per single fermion in the BdG framework. Microscopic analysis reveals that these fundamental steps originate from synchronized phase slips mediated by periodic soliton generation at the barrier. Our findings clarify the role of interaction regimes in the nonequilibrium phase dynamics of ring-trapped fermionic superfluids and provide microscopic insights relevant to future studies of atomtronic systems with nontrivial topology.