  The isoenergetic cycle is a purely mechanical cycle comprised of adabatic and
isoenergetic processes. In the latter the system interacts with an energy bath
keeping constant the expectation value of the Hamiltonian. This cycle has been
mostly studied in systems consisting of particles confined in a power-law trap.
In this work we study the performance of the isoenergetic cycle for a system
described by the quantum Rabi model for the case of controlling the coupling
strength parameter, the resonator frequency and the two-level system frequency.
For the cases of controlling either the coupling strength parameter or the
resonator frequency, we find that it is possible to reach maximal unit
efficiency when the parameter is sufficiently increased in the first adiabatic
stage. In addition, for the first two cases the maximal work extracted is
obtained at parameter values corresponding to high efficiency which constitutes
an improvement over current proposals of this cycle.
