| Summary: | This tutorial outlines the theory of nonlinear spectroscopy with quantum light, and in particular with entangled photons. To this end, we briefly review molecular quantum electrodynamics, and discuss the approximations involved. Then we outline the perturbation theory underlying nonlinear spectroscopy. In contrast to the conventional semiclassical theory, our derivation starts from Glauber's photon counting formalism, and naturally includes the semiclassical theory as a special case. Finally, we review previous work, which we sort into work depending on the unusual features of quantum noise, and work relying upon quantum correlations in entangled photons. This work naturally draws from both quantum optics and chemical physics. Even though it is impossible to provide a comprehensive overview of both fields in one tutorial, this text aims to be self-contained. We refer to specialised reviews, where we cannot provide details. We do not attempt to provide an exhaustive review of all the literature, but rather focus on specific examples intended to elucidate the underlying physics, and merely cite the remaining publications.
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