Input-output theory with time-reversal

Abstract

We incorporate unitary transformations to the photon wave packet propagating between cascaded quantum systems in input-output theory. This is a basis for quantum state transfer between different quantum systems (quantum transduction), from system 1 to system 2. We present a transformation, U , that time reverses, frequency translates, and stretches the photon wave packet. U can be tuned such that a wave packet emitted by system 1 is absorbed by system 2. We find concomitant modifications to the standard input-output theory that can best be understood in terms of a change to the state's time argument, ρ(t) = ρ1( t) ⊗ ρ2(t), where t is a fictitious time for system 1, which runs backwards, as determined by U .