Unified trade-off optimization of a three-level quantum refrigerator

We study the optimal performance of a three-level quantum refrigerator using trade-off objective function, $\Omega$ which represents compromise between energy benefits and losses thermal device. First, we optimize our by employing two-parameter optimization scheme show that first two-terms in series expansion obtained coefficient (COP) match with those some classical models refrigerator. Then, high-temperature limit, optimizing respect to one parameter while constraining other one, obtain lower upper bounds on COP for both strong as well weak (intermediate) matter-field coupling conditions. In regime, exactly already known refrigerators. Further coupling, derive new lie beyond range covered coupling. Finally, regime where cooling power function can be maximized, compare at maximum power.