Performance optimization on finite-time quantum Carnot engines and refrigerators based on spin-1/2 systems driven by a squeezed reservoir

We investigate the finite-time performance of a quantum endoreversible Carnot engine cycle and its inverse operation — Carnot refrigeration cycle, employing a spin-1/2 system as the working substance. The thermal machine is alternatively driven by a hot boson bath of inverse temperature β h and a cold boson bath at inverse temperature β c (>β h). While for the engine model the hot bath is constructed to be squeezed, in the refrigeration cycle the cold bath is established to be squeezed, with squeezing parameter r. We obtain the analytical expressions for both efficiency and power in heat engines and for coefficient of performance and cooling rate in refrigerators. We find that, in the high-temperature limit, the efficiency at maximum power is bounded by the analytical value η + = 1 − sech ( 2 r ) ( 1 − η C ) , and the coefficient of performance at the maximum figure of merit is limited by ε + = sech ( 2 r ) ( 1 + ε C ) sech ( 2 r ) ( 1 + ε C ) − ε C − 1 , where η C = 1 – β h/β c and ε C = β h/(β c – β h) are the respective Carnot values of the engines and refrigerators. These analytical results are identical to those obtained from the Carnot engines based on harmonic systems, indicating that the efficiency at maximum power and coefficient at maximum figure of merit are independent of the working substance.