Normally-Ordered Time Evolution Operator for Mass-Varying Harmonic Oscillator and Wigner Function of Squeezed Number State

Xubing Tang, Xuefen Xu, Fan Hong‐Yi

For investigating dynamic evolution of a mass-varying harmonic oscillator we constitute a ket-bra integration operator in coherent state representation and then perform this integral by virtue of the technique of integration within an ordered product of operators. The normally ordered time evolution operator is thus obtained. We then derive the Wigner function of u(t)|n⟩, where |n⟩ is a Fock state, which exhibits a generalized squeezing, the squeezing effect is related to the varying mass with time.

Laurent A. Beauregard

Jun Song, Hong-Yi Fan

Xiang‐Guo Meng, Zhen Wang, Hong-Yi Fan +1 more

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.

Octavio Castaños, Ramón López–Peña, Vladimir I. Man’ko

A quantum system described by a two-dimensional harmonic oscillator with a varying mass parameter plus the projection of the angular momentum in the z direction with a time-dependent mode coupling constant is considered to study the two-mode squeezing and photon generation phenomena. For some specific time dependences of the oscillator mass and an arbitrary function of time for the coupling constant exact results on the time evolution of the density matrix and the Wigner function are presented. An analytical expression of the photon distribution is obtained explicitly in terms of Hermite polynomials of two variables, and it shows the effect of oscillations characteristic of squeezing and correlation of the photon quadratures.

Seoktae Koh