Squeezed number state and squeezed thermal state: decoherence analysis and nonclassical properties in the laser process

Abstract

We investigate how the squeezed thermal state (STS) and squeezed number state (SNS) evolve undergoing decoherence in the laser process. Remarkably, the initial SNS, an example of a pure state, evolves into a mixed state, which turns out to be a Laguerre polynomial of combination of creation and annihilation operators within normal ordering; however, the STS, a mixed state, still keeps squeezed and thermal. At long times, these fields lose their nonclassical nature and decay to a highly classical thermal field. The normally ordered density operators of such states in the laser channel lead to deriving the analytical time-evolution expressions of the Wigner functions (WFs). Their nonclassicality is investigated in reference to the time-evolution WFs, which indicates that both of the WFs decay to the same thermal WF as a result of decoherence when the decay time t or the cavity loss κ of the laser is large enough.