Three-level systems as amplifiers and attenuators: a thermodynamic analysis.

Thermodynamics of a three-level maser was studied in the pioneering work of Scovil-Schulz-DuBois [Phys. Rev. Lett. 2, 262 (1959)10.1103/PhysRevLett.2.262]. In this Letter we consider the same three-level model, but we give a full thermodynamic analysis based on Hamiltonian and dissipative Lindblad superoperators. The first law of thermodynamics is obtained using a recently developed alternative [Phys. Rev. A 74, 063823 (2006)10.1103/PhysRevA.74.063823] to Alicki's definitions for heat flux and power [J. Phys. A 12, L103 (1979)10.1088/0305-4470/12/5/007]. Using a novel variation on Spohn's entropy production function [J. Math. Phys. (N.Y.) 19, 1227 (1978)10.1063/1.523789], we obtain Carnot's efficiency inequality and the Scovil-Schulz-DuBois maser efficiency formula when the three-level system is operated as a heat engine (amplifier). Finally, we show that the three-level system has two other modes of operation--a refrigerator mode and a squanderer mode--both of which attenuate the electric field.