A quantum theory of nonlinear excitations in a matter-photon system is developed by generalizing the conventional two-level-atom model of a matter in several directions, on the assumption that the overlapping of atomic wave functions on different atomic sites is negligible.The model matter Hamiltonian is shown to be expressible in a generalized form' of the Heisenberg model Hamiltonian with anisotropic long-range exchange interactions with spin operators replaced by quasi-Pauli operators.From approxirpate formal solutions of a set of nonlinear equations satisfied by the quasi-Pauli operators ~nd photon operators, brief discussion is given on nonlinear Frenkel excitons and nonlinear exciton-photon coupled modes.An attempt is made to formulate a theory of higher-order nonlinear physical properties of the matter-photon system by including interactions of magnetic as •well as electric dipoles of atoms with photons.A brief discussion is also given on the coherence properties. of the matter-photon system which are characterized by the simultaneo~s existence of •a photon coherent state and an atomic-polarization coherent state.*> Throughout this paper, we will often use a simplified .notation l, rather than l 1, whenever appropriate, to avoid the use of complicated symbols.Also, the complex conjugate of a quantity• A is denoted by A*.
The rate of
m-photon transitions in matter, induced by an incident light field, depends on the field's
mth order coherence function. Consequently, the coherence properties of the light field may be shaped to increase the rate of multi-photon transitions. Here, we determine the optimal state of a weak fixed-intensity, narrow-band incident light field, with a restricted maximal photon number, that optimally drives
m-photon transitions in the case of a short-lived atomic multilevel system. We show that, in this case, no quantum properties of the light field need to be exploited, but that classical mixtures of coherent states are optimal.
The modification of the quantum properties of coherence of photons through their interaction with matter lies at the heart of the quantum theory of light. Indeed, the absorption and emission of photons by atoms can lead to different kinds of light with characteristic quantum statistical properties. As such, different types of light are typically associated with distinct sources. Here, we report on the observation of the modification of quantum coherence of multiphoton systems in free space. This surprising effect is produced by the scattering of thermal multiphoton wavepackets upon propagation. The modification of the excitation mode of a photonic system and its associated quantum fluctuations result in the formation of different light fields with distinct quantum coherence properties. Remarkably, we show that these processes of scattering can lead to multiphoton systems with subshot-noise quantum properties. Our observations are validated through the nonclassical formulation of the emblematic van Cittert–Zernike theorem. We believe that the possibility of producing quantum systems with modified properties of coherence, through linear propagation, can have dramatic implications for diverse quantum technologies.