Communication: The origin of many-particle signals in nonlinear optical spectroscopy of non-interacting particles

Nonlinear spectroscopy signals detected by fluorescence from dilute samples of N non-interacting molecules are usually adequately described by simply multiplying the single molecule response by N. We show that signals that scale with higher powers of N are generated by the joint detection of several particles. This can be accomplished by phase sensitive detection such as phase cycling, photo-acoustic modulation, or by Hanbury-Brown Twiss photon coincidence. Such measurements can dissect the ensemble according to the number of excited particles.