  We propose a quantum Stirling heat engine with an ensemble of harmonic
oscillators as the working medium. We show that the efficiency of the harmonic
oscillator quantum Stirling heat engine (HO-QSHE) at a given frequency can be
maximized at a specific ratio of the temperatures of the thermal reservoirs. In
the low temperature or equivalently high frequency limit of the harmonic
oscillators, the efficiency of the HO-QSHE approaches the Carnot efficiency.
Further, we analyse quantum Stirling heat engine with an ensemble of particle
in box quantum systems as the working medium. Here both work and efficiency can
be maximized at a specific ratio of temperatures of the thermal reservoirs.
These studies will enable us to operate the quantum Stirling heat engines at
its optimal performance. The theoretical study of the HO-QSHE would provide
impetus for its experimental realisation, as most real systems can be
approximated as harmonic oscillators for small displacements near equilibrium.
