  We investigate the optimal performance of quantum Otto engine and
refrigeration cycles of a time-dependent harmonic oscillator under a trade-off
figure of merit for both adiabatic and nonadiabatic (sudden-switch) frequency
modulations. For heat engine (refrigerator), the chosen trade-off figure of
merit is an objective function defined by the product of efficiency
(coefficient of performance) and work output (cooling load), thus representing
a compromise between them. We obtain analytical expressions for the efficiency
and coefficient of performance of the harmonic Otto cycle for the optimal
performance of the thermal machine in various operational regimes.
Particularly, in the sudden-switch regime, we discuss the implications of the
nonadiabatic driving on the performance of the thermal machine under
consideration, and obtain analytic expressions for the maximum achievable
efficiency and coefficient of performance of the harmonic Otto thermal machine.
Further, by carrying out a detailed comparative analysis of the heat engine
operating under the chosen trade-off objective function with one operating at
maximum work output, we show that the trade-off objective functions have
desirable operation only for the adiabatic driving whereas for the sudden
switch operation, the choice of a trade-off objective function does not make
much difference as the performance of the engine is dominated by frictional
effects.
