Speeding up thermalization in quantum thermal engines

We consider a two-stroke
ergotropy engine operating between two temperatures. The two heat
baths are taken to be spin baths at different
temperatures. The working fluid is
composed of a double quantum dot system. Such a working fluid
undergoes two strokes, namely: (a) a thermalization stroke by coupling
one qubit to the hot bath and the other qubit to the cold bath and (b)
a work stroke composed of an optimal two-qubit unitary. The power of
the engine per stroke is defined as the work extracted per cycle
divided by the time for the stroke. Since the time to implement the
optimal unitary operator is usually very fast, the power per stroke of
such engines typically is dominated by the thermalization times. We
show that this power can be improved by using quantum control
techniques in order to speed up thermalization. We employ a generalized
Krotov algorithm to improve thermalization. We calculate the work, the power and the
commensurate loss in efficiency of the engine.