Optimized finite-time performance of endoreversible quantum Carnot machine working with a squeezed bath

We consider a quantum endoreversible Carnot engine cycle and its inverse operation–Carnot refrigeration cycle, working between a hot bath of inverse temperature [Formula: see text] and a cold bath at inverse temperature [Formula: see text]. For the engine model, the hot bath is constructed to be squeezed, whereas for the refrigeration cycle, the cold bath is set to be squeezed. In the high-temperature limit, we analyze efficiency at maximum power and coefficient of performance at maximum figure of merit, revealing the effects of the times allocated to two thermal-contact and two adiabatic processes on the machine performance. We show that, when the total time spent along the two adiabatic processes is negligible, the efficiency at maximum power reaches its upper bound, which can be analytically expressed in terms of squeezing parameter [Formula: see text]: [Formula: see text], with the Carnot efficiency [Formula: see text] and the coefficient of performance at maximum figure of merit is bounded from the upper side by the analytical function: [Formula: see text], where [Formula: see text].