Quantum Stirling heat engine based on Two-qubit Quantum Rabi Model with Spin-Spin Coupling

Abstract: Enhancing the efficiency of quantum heat engines (QHEs) is crucial for advancing fundamental research and quantum technology.We here we explore a quantum Stirling cycle using a twoqubit quantum Rabi model with spin-spin coupling as a working medium. We propose parameter optimization strategies to maximize the efficiency of the heat engine, as there are multiple ways for the effective coupling constant to move toward its critical value. In the normal phase of the system, the efficiency can be improved by increasing the temperature ratio of hot-to-cold reservoirs and enhancing spin-mode coupling strength. However, increasing spin-spin coupling strength inhibits the improvement of the efficiency. As the system goes to its critical point, QHE efficiency under low-temperature conditions tends to the Carnot limit. In the superradiant phase, the efficiency approaches the Carnot limit more closely as the cold reservoir's temperature decreases given a constant temperature ratio. Conversely, when the cold reservoir's temperature rises, the efficiency increases due to a higher ratio of spin-mode coupling strength to mode frequency. If the spinspin coupling strength is constant, increasing the hot-to-cold reservoir temperature ratio requires a corresponding increase in spin-mode coupling strength to achieve the Carnot efficiency. Our work deepens the understanding of QHE performance under various conditions and provides operative methods for optimizing the efficiency of QHE.