Time-dependent Andreev reflection

We extend the basic theory of Andreev reflection (AR) in a normal metal/superconductor junction to the situation with an arbitrary time-dependent bias voltage $V(t)$ across the junction. The central element of the theory is the fact that the Fourier transform of the AR amplitude has a causal structure. As an example, the theory is used to describe the current response to short pulses of the bias voltage, which create coherent superposition of quasiparticle states with different energies. The current oscillates in time, with the gap frequency $\mathrm{\ensuremath{\Delta}}/\ensuremath{\hbar}$, and also as a function of the pulse area $\ensuremath{\int}V(t)dt$, with the period of the single-electron flux quantum $e/h$.