  We study the thermodynamic performance of the finite-time non-regenerative
Stirling cycle used as a quantum heat engine. We consider specifically the case
in which the working substance (WS) is a two-level system. The Stirling cycle
is made of two isochoric transformations separated by a compression and an
expansion stroke during which the working substance is in contact with a
thermal reservoir. To describe these two strokes we derive a non-Markovian
master equation which allows to study the dynamics of a driven open quantum
system with arbitrary fast driving. We found that the finite-time dynamics and
thermodynamics of the cycle depend non-trivially on the different time scales
at play. In particular, driving the WS at a time scale comparable to the
resonance time of the bath enhances the performance of the cycle and allows for
an efficiency higher than the efficiency of the slow adiabatic cycle, but still
below the Carnot bound. Interestingly, performance of the cycle is dependent on
the compression and expansion speeds asymmetrically. This suggests new freedom
in optimizing quantum heat engines. We further show that the maximum output
power and the maximum efficiency can be achieved almost simultaneously,
although the net extractable work declines by speeding up the drive.
