Evolution law of Wigner function in laser process

LU Dao-ming

Liyun Hu, Hong-Yi Fan

Junhua Chen, Hong-Yi Fan

Rui He, Junhua Chen, Hong-Yi Fan

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 $\Delta (\alpha ,\alpha ^* ,t) = \tfrac{T} {\pi }:\exp [ - 2T(a^\dag e^{ - (\kappa - g)t} - \alpha ^* )(ae^{ - (\kappa - g)t} - \alpha )] $ :, where g and κ are the cavity gain and the loss, respectively, and T ≡ (κ − g)(κ + g − 2ge−2(κ−g)t )−1:, When $t = 0,\Delta (\alpha ,\alpha ^* ,t) \to \tfrac{1} {\pi }:\exp [ - 2(a^\dag - \alpha ^* )(a - \alpha )] $ ;, which is the initial Wigner operator. Using this formalism the evolution law of Wigner functions in laser process can be directly obtained.

Fu-Yi You, Junhua Chen, Hong-Yi Fan

We analyze the laser process with three different initial states using the entangled state representation, obtain the evolution law of the mean photon number, the entropy, the specific entropy, the second degree of coherence and the Wigner functions, and find out the common characteristics of these three processes.

Nian-Quan Jiang, Hong-Yi Fan, Liyun Hu

Based on the Kraus operator of laser theory which we derived in [2] and by virtue of the technique of integration within ordered product of operators we exactly calculate the evolving result of a chaotic field, governed by the master equation describing the laser process, we find that the initial density operator evolves into a new chaotic field, with where g and κ represent the cavity gain and loss of the laser, respectively. When g = 0, the system reduces to an amplitude dissipative channel, and f' becomes −ln [(e−f − 1) e2κt + 1]. The law of photon number decay in this process is evaluated, and the corresponding Wigner function's evolution is also demonstrated.