Photon Transitions in Arbitrary Time-Varying Metamaterials

We present a general theory for calculating photon transitions in arbitrarily time-varying metamaterials. This theory circumvents the difficulties of conventional approaches in solving such a general problem by exploiting the eigenstates of time-dependent number operators. We demonstrate here the temporal evolution of these operators and the related transition probabilities for the cases of logistic and linear permittivity profiles. The theory is potentially extensible to arbitrary space-time modulations and may hence lead to multiple novel quantum effects and applications.