In the previous chapters, we have seen that quantum-optical correlations can produce effects that have no classical explanation. In particular, the matter excitations can depend strongly on the specific form of the quantum fluctuations, i.e., the quantum statistics of the light source. For example, Fock-state sources can produce quantum Rabi flopping with discrete frequencies while coherent-state sources generate a sequence of collapses and revivals in atomic excitations. Hence, not only the intensity or the classical amplitude of the field is relevant but also the quantum statistics of the exciting light influences the matter response. Even if we take sources with identical intensities, the resulting atomic excitations are fully periodic for a Fock-state excitation while a coherentstate excitation produces a chaotic Bloch-vector trajectory with multiple collapses and revivals.

In this chapter, we use this fundamental observation as the basis to develop the concept of quantum-optical spectroscopy. We show in Chapter 30 that this method yields a particularly intriguing scheme to characterize and control the quantum dynamics in solids. Since one cannot imagine how to exactly compute the many-body wave function or the density matrix, we also study how principal quantum-optical effects can be described with the help of the cluster-expansion scheme.

Quantum-optical spectroscopy

Historically, the continued refinement of optical spectroscopy and its use to manipulate the states of matter has followed a very distinct path where one simultaneously tries to control and characterize light with increased accuracy.