  The work performed by a classical electromagnetic field on a quantum dipole
is well known in quantum optics. The absorbed power linearly depends on the
time derivative of the average dipole moment, in that case. The following
problem, however, still lacks an answer: can the most elementary
electromagnetic pulse, consisting of a single-photon state, perform work on a
quantum dipole? As a matter of fact, the average quantum dipole moment exactly
vanishes in such a scenario. In this paper, we present a method that positively
answers to this question, by combining techniques from the fields of quantum
machines and open quantum systems. Quantum work here is defined as the unitary
contribution to the energy variation of the quantum dipole. We show that this
quantum work corresponds to the energy spent by the photon pulse to dynamically
Stark shift the dipole. The non-unitary contribution to the dipole energy is
defined here as a generalized quantum heat. We show that this generalized
quantum heat is the energy corresponding to out-of-equilibrium photon
absorption and emission. Finally, we reveal connexions between the quantum work
and the generalized quantum heat transferred by a single photon and those by a
low-intensity coherent field.

Quantum Physics