Comment on 'Nonlinear fluctuations and dissipation in matter revealed by quantum light'

In a recent paper [Phys.~Rev.~A {\bf 91}, 053844 (2015)], Mukamel and Dorfman compare spectroscopies performed with classical vs.~quantum light, and conclude that \textit{nonlinear} quantum-spectroscopy signals cannot be obtained from averaging their classical-spectroscopy counterparts over the Glauber--Sudarshan quasiprobability distribution of the quantum field. In this Comment, we show that this interpretation is correct only if one assumes that a classical signal is given by a classical approximation for the field. While such an assumption can be useful for comparing theoretical results, it is never realized in laser spectroscopy experiments that typically use coherent states. Thus, instead of using classical signals, the connection between coherent states and quantum states of light must be considered. We rigorously show that quantum spectroscopy can always be projected from the experimentally realized coherent-state spectroscopy regardless how nonlinear the system response is.
Comment: 4 pages