Interpreting quantum states of electromagnetic field in time-dependent linear media

Abstract

Recently, Pedrosa and Rosas [Phys. Rev. Lett. 103, 010402 (2009)] investigated the quantum states of an electromagnetic field in time-dependent linear media using a Hermitian linear invariant. The wave function obtained by them is represented in terms of an arbitrary weight function $g({\ensuremath{\lambda}}_{l})$. Since the type of wave function varies depending on the choice of $g({\ensuremath{\lambda}}_{l})$ in their problem, it may be a difficult task to construct a coherent state that resembles the classical state from their theory. We suggest, on the basis of a non-Hermitian linear invariant, another quantum state that is a kind of coherent state. The expectation value of canonical variables in this alternate state follows an exact classical trajectory. For a simple case in which the time dependence of the parameters $\ensuremath{\epsilon}(t)$, $\ensuremath{\mu}(t)$, and $\ensuremath{\sigma}(t)$ disappears, we showed that the quantum energy expectation value in the alternate quantum state recovers exactly to the classical energy in the limit $\ensuremath{\hbar}\ensuremath{\rightarrow}0$. This alternate state leads to the correspondence between the quantum and the classical behaviors of physical observables in a high-energy limit.