  We study a quantum Otto cycle in which the strokes are performed in finite
time. The cycle involves energy measurements at the end of each stroke to allow
for the respective determination of work. We then optimize for the work and
efficiency of the cycle by varying the time spent in the different strokes and
find that the optimal value of the ratio of time spent on each stroke goes
through sudden changes as the parameters of this cycle vary continuously. The
position of these discontinuities depends on the optimized quantity under
consideration such as the net work output or the efficiency.
