  The Jaynes--Cummings system is one of the most fundamental models of how
light and matter interact. When driving the system with a coherent state (e.g.
laser light), it is often assumed that whether the light couples through the
cavity or atom plays an important role in determining the dynamics of the
system and its emitted field. Here, we prove that the dynamics are identical in
either case except for the offset of a trivial coherent state. In particular,
our formalism allows for both steady-state and the treatment of any arbitrary
multimode coherent state driving the system. Finally, the offset coherent state
can be interferometrically canceled by appropriately homodyning the emitted
light, which is especially important for nanocavity quantum electrodynamics
where driving the atom is much more difficult than driving the cavity.
