Quantum statistics of a three-level maser

Abstract: Lasers and masers have numerous uses in today’s society. Improving our understanding of the underlying physics and its application is thus of great importance. In this paper, the physics of a three-level maser when treated as a heat-engine was investigated: certain levels were coupled to thermal-reservoirs, effectively allowing for pumping without an external bias. The thermodynamical treatment for a three-level maser stems from the Scovil & Schulz-Dubois maser, who first discussed and theorized this model. This treatment allows for investigation of the laws of thermodynamics when applied to a system of quantum-mechanical nature, as well as the intricacy of the underlying physics. Under the assumption that the system is governed by Lindblad’s master equation, one solved the differential equation, numerically, with two methods: Euler’s-, and Runge-Kutta’s method. Comparing the two methods, yielded in the use of Runge-Kutta’s method for further simulations. For a set of initial-conditions, one found Rabi-oscillations between the atomic ground state, and the corresponding first excited state, when initially starting the system. Moreover, the entropy of the cavity increased in time, as expected. The Rabi-oscillations affected the time-derivative of S. Lastly, an initial-condition constructed by a Glauber-state was simulated; the mean field of ˆa oscillates in time, which is expected since one effectively treats the system as a classical harmonic oscillator.