Theory of excess noise of a quantum dot in the presence of a microwave field

The power spectrum of excess noise of a quantum dot coupled to two leads and irradiated by a microwave field of frequency $\Omega$ is derived exactly by directly solving the Heisenberg equation. We found that for $\Gamma <ħ\Omega ,$ where $\Gamma$ is the linewidth of the intradot energy level, the power spectrum can be nonzero even if the averaged current is zero. This property originates from photon-assisted tunneling and is very different from the shot noise in steady state. For $\Gamma \gg ħ\Omega ,$ our results are consistent with the recent experiment by Schoelkopf et al. and previous theory.