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We investigate the non-equilibrium behavior of BCS superconductors subjectedto slow ramps of their internal interaction strength. We identify threedynamical regimes as a function of ramp duration. For short ramp times, thesesystems become non-superconducting; however, fermions with opposite momentaremain paired albeit with reduced amplitudes, and the associated pair amplitudedistribution is non-thermal. In this first regime, the disappearance ofsuperconductivity is due to the loss of phase coherence between pairs. Bycontrast, for intermediate ramp times, superconductivity survives but themagnitude of the order parameter is reduced and presents long-livedoscillations. Finally, for long ramp times, phase coherence is almost fullyretained during the slow interaction quench, and the steady-state ischaracterized by a thermal-like pair amplitude distribution. Using thisapproach, one can therefore dynamically tune the coherence between pairs inorder to control the magnitude of the superconducting order parameter and evenengineer a non-equilibrium state made of pre-formed pairs.

Slow interaction quench in BCS superconductors: emergence of pre-formed pairs