Introduction to Quantum Electronics and Nonlinear Optics

H. M. Moya-Cessa, Francisco Soto

L. Allen, Joseph H. Eberly

"Coherent and lucid…a valuable summary of a subject to which [the authors] have made significant contributions by their own research." - Contemporary PhysicsOffering an admirably clear account of the basic principles behind all quantum optical resonance phenomena, and hailed as a valuable contribution to the literature of nonlinear optics, this distinguished work provides graduate students and research physicists probing fields such as laser physics, quantum optics, nonlinear optics, quantum electronics, and resonance optics an ideal introduction to the study of the interaction of electroma

Mark S. Hillery

An introduction to the quantum theory of nonlinear optics This article is provides an introduction to the quantum theory of optics in nonlinear dielectric media. We begin with a short summary of the classical theory of nonlinear optics, that is nonlinear optics done with classical fields. We then discuss the canonical formalism for fields and its quantization. This is applied to quantizing the electromagnetic field in free space. The definition of a nonclassical state of the electromagnetic field is presented, and several examples are examined. This is followed by a brief introduction to entanglement in the context of field modes. The next task is the quantization of the electromagnetic field in an inhomogeneous, linear dielectric medium. Before going on to field quantization in nonlinear media, we discuss a number of commonly employed phenomenological models for quantum nonlinear optical processes. We then quantize the field in both nondispersive and dispersive nonlinear media. Flaws in the most commonly used methods of accomplishing this task are pointed out and discussed. Once the quantization has been completed, it is used to study a multimode theory of parametric down conversion and the propagation of quantum solitons.

L. Allen

O. Morsch, Markus K. Oberthaler

Matter waves inside periodic potentials are well known from solid-state physics, where electrons interacting with a crystal lattice are considered. Atomic Bose-Einstein condensates inside light-induced periodic potentials (optical lattices) share many features with electrons in solids, but also with light waves in nonlinear materials and other nonlinear systems. Generally, atom-atom interactions in Bose-Einstein condensates lead to rich and interesting nonlinear effects. Furthermore, the experimental control over the parameters of the periodic potential and the condensate make it possible to enter regimes inaccessible in other systems. In this review, an introduction to the physics of ultracold bosonic atoms in optical lattices is given and an overview of the theoretical and experimental advances to date.

T. Coudreau, Claude Fabre, Serge Reynaud