Thermodynamic analysis of quantum light amplification

Abstract

Thermodynamics of a three-level maser was studied in the pioneering work of Scovil and SchulzDuBois [Phys. Rev. Lett. 2, 262 (1959)]. In this work we consider the same three-level model, but treat both the matter and light quantum mechanically. Specifically, we analyze an extended (three-level) dissipative Jaynes-Cummings model (ED-JCM) within the framework of a quantum heat engine, using novel formulas for heat flux and power in bipartite systems introduced in our previous work [E. Boukobza and D. J. Tannor, PRA (in press)]. Amplification of the selected cavity mode occurs even in this simple model, as seen by a positive steady state power. However, initial field coherence is lost, as seen by the decaying off-diagonal field density matrix elements, and by the Husimi-Kano Q function. We show that after an initial transient time the field's entropy rises linearly during the operation of the engine, which we attribute to the dissipative nature of the evolution and not to matter-field entanglement. We show that the second law of thermodynamics is satisfied in two formulations (Clausius, Carnot) and that the efficiency of the ED-JCM heat engine agrees with that defined intuitively by Scovil and Schulz-DuBois. Finally, we compare the steady state heat flux and power of the fully quantum model with the semiclassical counterpart of the ED-JCM, and derive the engine efficiency formula of Scovil and Schulz-DuBois analytically from fundamental thermodynamic fluxes.

Energy flux operator, current conservation and the formal Fourier's law

“…Of special interest are hybrid structures, e.g. normal metal-superconductor junctions with applications in thermometry and refrigeration [17], and atom-radiation field systems, serving as a prototype for studying thermodynamics of quantum systems [18,19].…”

Thermodynamic output of single-atom quantum optical amplifiers and their phase-space fingerprint

“…A detailed thermodynamic balance shows that the non-linear amplifier is thermodynamically equivalent to the linear amplifier discussed in Ref. [1]. However, by calculating the Wigner quasi-probability distribution for various initial field states, we show that unique quantum features in optical phase space, absent from the linear amplifier, are maintained for extended times.…”

“…A pioneering formalism of quantum heat engines with a quantized reservoir is presented in [18]. This formalism was applied to the processes of quantum light amplification and attenuation, and compared with its semiclassical analogue (using Alicki's formalism or an alternative semiclassical formalism) in [1,19,20].…”

“…This amplifier is the two-photon analogue of the linear amplifier discussed in [1]. Related work studied the two-photon, non-linear JaynesCummings (JCM) Hamiltonian [29], where the unitary propagator was analytically derived.…”

“…In Sec. III we thermodynamically analyze the non-linear amplifier at steady state, based on the thermodynamical bipartite formalism presented in [20] and [18]. We show that from a steady state thermodynamic efficiency stand point, a non-linear amplifier is equivalent to a linear quantum optical amplifier.…”