Josephson effect throughout the BCS-BEC crossover

We study the stationary Josephson effect for neutral fermions across the BCS-BEC (Bose-Einstein condensate) crossover, by solving numerically the Bogoliubov-de Gennes equations at zero temperature. The Josephson current is found to be considerably enhanced for all barriers at about unitarity. For vanishing barrier, the Josephson critical current approaches the Landau limiting value which, depending on the coupling, is determined by either pair-breaking or sound-mode excitations. In the coupling range from the BCS limit to unitarity, a procedure is proposed to extract the pairing gap from the Landau limiting current.