  We investigate the nonequilibrium dynamics of competing coexisting
superconducting (SC) and charge-density wave (CDW) orders in an attractive
Hubbard model. A time-periodic laser field $\vec{A}(t)$ lifts the SC-CDW
degeneracy, since the CDW couples linearly to the field ($\vec{A}$), whereas SC
couples in second order ($\vec{A}^2$) due to gauge invariance. This leads to a
striking resonance: When the photon energy is red-detuned compared to the
equilibrium single-particle energy gap, CDW is enhanced and SC is suppressed,
while this behavior is reversed for blue detuning. Both orders oscillate with
an emergent slow frequency, which is controlled by the small amplitude of a
third induced order, namely $\eta$ pairing, given by the commutator of the two
primary orders. The induced $\eta$ pairing is shown to control the enhancement
and suppression of the dominant orders. Finally, we demonstrate that
light-induced superconductivity is possible starting from a predominantly CDW
initial state.
