Thermodynamic analysis of quantum light purification
Erez Boukobza, David J. Tannor · Physical Review A · 2008
We studied the thermodynamics of quantum light amplification in Phys. Rev. A 74, 063822 (2006). In this work we extend our analysis to include quantum light attenuation, as well as saturated amplification. We show that, for a given excitation of the two reservoirs, different field states converge to the same final stationary state. We provide a full analytic solution of the $3\ensuremath{\bigotimes}n$ matter-light density matrix at steady state. The final steady state has three remarkable properties: (i) it is in fact an equilibrium state, (ii) it is an independent (single tensor product) matter-field state (as seen by the vanishing thermodynamic fluxes), and (iii) the final field state assumes a bithermal distribution (as seen by a wide Gaussian $Q$ function centered around the origin). By partially tracing over the field, we obtain the Scovil--Schulz-DuBois atomic inversion formula [Phys. Rev. Lett. 2, 262 (1959)] analytically. We compare the quantum model with its semiclassical analog. Unlike the amplification scenario discussed in Phys. Rev. A 74, 063822 (2006), the quantum and the semiclassical models differ dramatically under the conditions discussed in this paper.