Evolution law of Wigner function in laser process

摘要

Based on the density operator's operator-sum representation recently obtained by Fan and Hu for a laser process (Opt. Commun., 2008, 281: 5571; Opt. Commun., 2009, 282: 932; Phys. Lett. B, 2008, 22: 2435), we derive the evolution law of Wigner operator, the law is concisely expressed in the normally ordered form A(α,α*,t) = T/π : exp[-2T(α e~(-(K-g)t) - α*)(αe~(-(K-g)t) - α)]:, where g and k are the cavity gain and the loss, respectively, and T = (k - g )(k + g - 2ge~(-2(K-9)t))~(-1) When t = 0, △(α, α*,t) → 1/π : exp[-2(α - α*)(α - α)] :, which is the initial Wigner operator. Using this formalism the evolution law of Wigner functions in laser process can be directly obtained.