  We study photon-assisted transport in a single-level quantum dot system under
a periodically oscillating field. Photon-assisted current noises in the
presence of the Coulomb interaction are calculated based on a gauge-invariant
formulation of time-dependent transport. We derive the vertex corrections
within the self-consistent Hartree-Fock approximation in terms the
Floquet-Green's functions (Floquet-GFs), and examine the effects of the Coulomb
interaction on the photon-assisted current noises. Moreover, we introduce a
concept of an effective temperature to characterize nonequilibrium properties
under the influence of the AC field. The vertex corrections are suppressed by
the rise of the effective temperature, whereas characteristic resonant
structures appear in the frequency spectra of the vertex corrections. The
present result provides a useful viewpoint for understanding photon-assisted
transport in interacting electron systems.
