  We study how a quantum heat engine based on a single trapped ion performs in
finite time. The always-on thermal environment acts like the hot bath, while
the motional degree of freedom of the ion plays the role of the effective cold
bath. The hot isochoric stroke is implemented via the interaction of the ion
with its hot environment, while a projective measurement of the internal state
of the ion is performed as an equivalent to the cold isochoric stroke. The
expansion and compression strokes are implemented via suitable change in
applied magnetic field. We study in detail how the finite duration of each
stroke affects the engine performance. We show that partial thermalization can
in fact enhance the efficiency of the engine, due to the residual coherence,
whereas faster expansion and compression strokes increase the inner friction
and therefore reduce the efficiency.
