  The question of whether quantum coherence is a resource beneficial or
detrimental to the performance of quantum heat engines has been thoroughly
studied but remains undecided. To isolate the contribution of coherence, we
analyze the performance of a purely coherence-driven quantum heat engine, a
device that does not include any heat flow during the thermodynamic cycle. The
engine is powered by the coherence of a multiqubit system, where each qubit is
charged via interaction with a coherence bath using the Jaynes-Cummings model.
We demonstrate that optimal coherence charging and hence extractable work is
achieved when the coherence bath has an intermediate degree of coherence. In
our model, the extractable work is maximized when four copies of the charged
qubits are used. Meanwhile, the efficiency of the engine, given by the
extractable work per input coherence flow, is optimized by avoiding the
coherence being stored in the system-bath correlations that is inaccessible to
work. We numerically find that the highest efficiency is obtained for slightly
lower temperatures and weaker system-bath coupling than those for optimal
coherence charging.
