ANALYTICAL SOLUTION TO THE MASTER EQUATION FOR A QUANTIZED CAVITY MODE

We solve analytically the master equation for a quantized cavity mode, finding the time-dependent reduced density operator. The formalism ap plies to both amplifiers and attenuator, permitting the results to be converted between them by introducing a temperature that can be negati ve. We obtain a quasi-probability distribution function similar to tha t obtained by Glauber [R. J. Glauber, ed., Quantum Optics (Academic, N ew York, 1969)] from our reduced density matrix and equate his paramet ers with the coefficients appearing in the master equation. We illustr ate the formalism by calculating variances, expectation values, and ph oton statistics for the damped simple harmonic oscillator and the line ar amplifier.