  Quantum heat engines are subjected to quantum fluctuations related to their
discrete energy spectra. Such fluctuations question the reliable operation of
quantum engines in the microscopic realm. We here realize an endoreversible
quantum Otto cycle in the large quasi-spin states of Cesium impurities immersed
in an ultracold Rubidium bath. Endoreversible machines are internally
reversible and irreversible losses only occur via thermal contact. We employ
quantum control over both machine and bath to suppress internal dissipation and
regulate the direction of heat transfer that occurs via inelastic spin-exchange
collisions. We additionally use full-counting statistics of individual atoms to
monitor heat exchange between engine and bath at the level of single quanta,
and evaluate average and variance of the power output. We optimize the
performance as well as the stability of the quantum engine, achieving high
efficiency, large power output and small power output fluctuations.
