Generalized mean-field or master equation for nonlinear cavities with transverse effects

C.L. Tsangaris

Franco Fagnola, Carlos M. Mora

We study the nonlinear quantum master equation describing a laser under the mean field approximation. The quantum system is formed by a single mode optical cavity and two level atoms, which interact with reservoirs. Namely, we establish the existence and uniqueness of the regular solution to the nonlinear operator equation under consideration, as well as we get a probabilistic representation for this solution in terms of a mean field stochastic Schrödinger equation. To this end, we find a regular solution for the nonautonomous linear quantum master equation in Gorini–Kossakowski–Sudarshan–Lindblad form, and we prove the uniqueness of the solution to the nonautonomous linear adjoint quantum master equation in Gorini–Kossakowski–Sudarshan–Lindblad form. Moreover, we obtain rigorously the Maxwell–Bloch equations from the mean field laser equation.

Rebecca R. McGowan, William C. Schieve

The field in the micromaser cavity, the atoms which both pump and probe the micromaser, and the detectors that determine the outgoing states of the atoms are treated as a single system in order to derive a nonlinear master equation for the field in the micromaser cavity which takes the effect of undetected atoms into account. Analytic solutions for this master equation are found for both phase-insensitive and phase-sensitive detection. These solutions can be used to explicitly show the back-action effects that measurement has on the spectrum of the micromaser. In addition, these solutions are used to find analytic expressions for the mean number of successive detector clicks of the same kind as well as atom-atom and photon-photon correlation functions. In this way, the analytic solutions are linked to experimentally accessible data.

Jack Boyce

Paul Mandel, Miltos Georgiou, Thomas Erneux

We derive reduced field equations describing two cases of optical cavities driven by an external coherent field, taking into account the influence of transverse effects. For the passive-cavity case, we focus on the transistor characteristic and the onset of optical bistability. We prove that, depending on the sign of the detuning, different equations are needed. A global description of the field is possible in terms of a generalized Ginzburg-Landau equation, unless the detuning is finite and positive. That case requires a modal expansion. Furthermore, the good-cavity limit is regular, implying the same differentiation according to the sign of the detuning. For the active-cavity case, the same dependence on the sign of the detuning is found. A global description is obtained only for negative detunings. The good-cavity limit is described by a unique equation for all detunings.

Nikolai N Rozanov