Atom–Photon Cluster in Nonlinear and Quantum Optics

Models of radiative quantum systems were constructed as analogs of multiphoton and Raman resonances of classical field quanta on an atomic system with the participation of cavity mode quanta. A distinctive feature of the models is the description of an atomic ensemble and quanta using either the generators of polynomial algebra or the two-mode Jordan–Schwinger representation of the su(2) algebra, so that one can talk about an atom–photon and/or photon clusters. The arising algebras are mathematically unsolvable, in contrast to the Heisenberg–Weyl algebra. This makes it possible to implement and observe fundamental effects of coherent nonlinear optics, such as photon echo, optical nutation, and superradiance, in ensembles of the described clusters.