3-LEVEL QUANTUM AMPLIFIER AS A HEAT ENGINE - A STUDY IN FINITE-TIME THERMODYNAMICS

The finite-rate performance of a quantum heat engine, constructed from a three-level amplifier, is analyzed. Consistent definitions of therm odynamical quantities in terms of quantum observables are postulated. The performance is analyzed in steady state, where the operation of th e amplifier only influences the surroundings. Quantum master equations describe the irreversible dynamics induced by the coupling of the wor king medium to the reservoirs. It is shown that the standard assumptio n of field-independent dissipation is inconsistent with thermodynamics . Field-dependent relaxation equations, based upon the semigroup appro ach, and consistent with thermodynamics, are formulated. These equatio ns are valid if the time scale of the external field is slow compared to that associated with the bath fluctuations. The steady-state values of the thermodynamical quantities are evaluated. The power is found t o have maxima as a function of important controls, such as the field a mplitude, frequency, and the coupling with the baths. The existence an d locations of these maxima differ from those obtained in the standard treatment, where the dissipation is field independent. The irreversib le nature of engine operation is due to the finite rate of heat transf er and a genuine ''quantum-friction'' loss term due to dephasing.