Performance analysis of a two-state quantum heat engine working with a single-mode radiation field in a cavity

We present a performance analysis of a two-state heat engine model working with a single-mode radiation field in a cavity. The heat engine cycle consists of two adiabatic and two isoenergetic processes. Assuming the wall of the potential moves at a very slow speed, we determine the optimization region and the positive work condition of the heat engine model. Furthermore, we generalize the results to the performance optimization for a two-state heat engine with a one-dimensional power-law potential. Based on the generalized model with an arbitrary one-dimensional potential, we obtain the expression of efficiency as eta = 1 - E-C/E-H, with E-H (E-C) denoting the expectation value of the system Hamiltonian along the isoenergetic process at high (low) energy. This expression is an analog of the classical thermodynamical result of Carnot, eta(c) = 1 - T-C/T-H, with T-H (T-C) being the temperature along the isothermal process at high (low) temperature. We prove that under the same conditions, the efficiency eta = 1 - E-C/E-H is bounded from above the Carnot efficiency, eta(c) = 1 -T-C/T-H, and even quantum dynamics is reversible.