Abstract: A quantum Stirling cycle with a single quantum mechanical particle confined in a one-dimensional box trap is made of two isoenergetic branches corresponding to isothermal processes and two constant-well widen branches corresponding to isovolumic regenerating processes. The quantum thermodynamic model of a quantum Stirling engine with two-energy-level is established. The evolution of quantum states is investigated. The quantum characteristics of the cycle are analyzed by solving the Schrödinger equation. Based on the assumption that there exists a heat leakage between two energy baths, the expressions of the maximum work output W* and the maximum efficiency η for the two-eigenstate system are derived. The relationship between the work output W* versus the efficiency η is obtained by numerical calculation. It is a willow-shaped curve in harmony with that of a classical Stirling cycle. The region between the maximum work and the maximum efficiency is the optimization criteria of a quantum Stirling engine. The analysis will be helpful to further understand the optimal thermodynamic performance of a quantum Stirling engine. The results obtained here provides a new theoretical basis for the model evaluation and the optimal design of a quantum Stirling engine.

Key words: quantum engine;Stirling cycle;work output;efficiency