Coherent states in Quantum Optics: An oriented overview

TL;DR

The paper presents a unified framework for coherent states in a wide sense, linking linear, non-linear, and generalized CS to quantum optics through the PHIN and AN classifications. It surveys prototypical families (Glauber-Sudarshan, SU$(2)$ spin CS, SU$(1,1)$ CS, Susskind-Glogower, and DFB constructions) and details their statistical properties, phase-space interpretations, and displacement-based constructions. A key contribution is the AN CS quantization scheme, which maps phase-space functions to operators via a resolution of identity, enabling semi-classical portraits and alternative ladder operators. The work provides a conceptual foundation for non-standard quantizations of the Maxwell field, with implications for photon-counting statistics and potential experimental realizations of non-classical coherent states. Overall, it extends the toolbox of coherent states for quantum optics and clarifies how generalized CS can inform both theory and interpretation of optical measurements.

Abstract

In this survey, various generalisations of Glauber-Sudarshan coherent states are described in a unified way, with their statistical properties and their possible role in non-standard quantisations of the classical electromagnetic field. Some statistical photon-counting aspects of Perelomov SU(2) and SU(1,1) coherent states are emphasized.