Adiabatic and nonadiabatic evolution of electromagnetic waves propagating in time-dependent linear media

Based on the time-dependent dynamical invariants, we present a simple and elegant approach to study in both classical and quantum contexts the adiabatic and nonadiabatic evolution of the propagation of electromagnetic waves in a homogeneous time-varying linear material medium in which the permittivity, permeability and conductivity vary exponentially at a constant rate. By assuming that the permittivity and permeability vary asynchronously, the velocity of propagation of light in this time-varying medium remains constant as time goes by. Further, we show that this propagation is governed by a time-dependent generalized harmonic oscillator. We also demonstrate that both the classical and quantum adiabatic evolution of electromagnetic waves propagating in this linear medium acquire an extra geometric phase, which provides a direct connection between the classical Hannay’s angle and the quantum Berry’s phase. Finally, we evaluate various quantum properties of quantized light, such as coherent states, expectation values of the amplitude and momentum, their quantum fluctuations and the uncertainty principle