  The monochromatic driving of a quantum system is a successful technique in
quantum simulations, well captured by an effective Hamiltonian approach, and
with applications in artificial gauge fields and topological engineering. In
this letter, we investigate the modeling of multichromatic Floquet driving for
the slow degrees of freedom. Within a well-defined range of parameters, we show
that the time coarse-grained dynamics of such a driven closed quantum system is
encapsulated in an effective Master equation for the time-averaged density
matrix, that evolves under the action of an effective Hamiltonian and tunable
Lindblad-type dissipation/quantum gain terms. As an application, we emulate the
dissipation induced by phase noise and incoherent emission/absorption processes
in the bichromatic driving of a two-level system.
