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 η=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, η(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 η=1-E(C)/E(H) is bounded from above the Carnot efficiency, η(c)=1-T(C)/T(H), and even quantum dynamics is reversible.