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 $\eta =1-\frac{E_C}{E_H}$, 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, ${\eta }_c=1-\frac{T_C}{T_H}$, 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 $\eta =1-\frac{E_C}{E_H}$ is bounded from above the Carnot efficiency, ${\eta }_c=1-\frac{T_C}{T_H}$, and even quantum dynamics is reversible.

• Received 22 April 2011

DOI:https://doi.org/10.1103/PhysRevE.84.041127