  Coherent quantum-state manipulation of trapped ions using classical laser
fields is a trademark of modern quantum technologies. In this work, we study
aspects of work statistics and irreversibility in a single trapped ion due to
sudden interaction with the impinging laser. This is clearly an
out-of-equilibrium process where work is performed through illumination of an
ion by the laser. Starting with the explicit evaluation of the first moments of
the work distribution, we proceed to a careful analysis of irreversibility as
quantified by the nonequilibrium lag. The treatment employed here is not
restricted to the Lamb-Dicke limit, which allows us to investigate the
interplay between nonlinearities and irreversibility. We show that in these
multiquantum or sideband regimes, variation of the Lamb-Dicke parameter causes
a non-monotonic behavior of the irreversibility indicator. Counterintuitively,
we find a working point where nonlinearity helps reversibility, making the
sudden quench of the Hamiltonian closer to what would have been obtained
quasistatically and isothermally.
