The properties of a unique set of quantum states of the electromagnetic field are reviewed. These ‘squeezed states’ have less uncertainty in one quadrature than a coherent state. Proposed schemes for the generation and detection of squeezed states as well as potential applications are discussed.

Squeezed states of light

Seventy five years ago, three remarkable papers by Schr¨ odinger, Kennard and Darwin were published. They were devoted to the evolution of Gaussian wave packets for an oscillator, a free particle and a particle moving in uniform constant electric and magnetic fields. From the contemporary point of view, these packets can be considered as prototypes of the coherent and squeezed states, which are, in a sense, the cornerstones of modern quantum optics. Moreover, these states are frequently used in many other areas, from solid state physics to cosmology. This paper gives a review of studies performed in the field of so-called ‘nonclassical states’ (squeezed states are their simplest representatives) over the past seventy five years, both in quantum optics and in other branches of quantum physics. My starting point is to elucidate who introduced different concepts, notions and terms, when, and what were the initial motivations of the authors. Many new references have been found which enlarge the ‘standard citation package’ used by some authors, recovering many undeservedly forgotten (or unnoticed) papers and names. Since it is practically impossible to cite several thousand publications, I have tried to include mainly references to papers introducing new types of quantum states and studying their properties, omitting many publications devoted to applications and to the methods of generation and experimental schemes, which can be found in other well known reviews. I also mainly concentrate on the initial period, which terminated approximately at the border between the end of the 1980s and the beginning of the 1990s, when several fundamental experiments on the generation of squeezed states were performed and the first conferences devoted to squeezed and ‘nonclassical’ states commenced. The 1990s are described in a more ‘squeezed’ manner: I have confined myself to references to papers where some new concepts have been introduced, and to the most recent reviews or papers with extensive bibliographical lists.

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'Nonclassical' states in quantum optics: a 'squeezed' review of the first 75 years

Multiphoton quantum optics and quantum state engineering

We present a review of theoretical and experimental aspects of multiphoton quantum optics. Multiphoton processes occur and are important for many aspects of matter-radiation interactions that include the efficient ionization of atoms and molecules, and, more generally, atomic transition mechanisms; system-environment couplings and dissipative quantum dynamics; laser physics, optical parametric processes, and interferometry. A single review cannot account for all aspects of such an enormously vast subject. Here we choose to concentrate our attention on parametric processes in nonlinear media, with special emphasis on the engineering of nonclassical states of photons and atoms. We present a detailed analysis of the methods and techniques for the production of genuinely quantum multiphoton processes in nonlinear media, and the corresponding models of multiphoton effective interactions. We review existing proposals for the classification, engineering, and manipulation of nonclassical states, including Fock states, macroscopic superposition states, and multiphoton generalized coherent states. We introduce and discuss the structure of canonical multiphoton quantum optics and the associated one- and two-mode canonical multiphoton squeezed states. This framework provides a consistent multiphoton generalization of two-photon quantum optics and a consistent Hamiltonian description of multiphoton processes associated to higher-order nonlinearities. Finally, we discuss very recent advances that by combining linear and nonlinear optical devices allow to realize multiphoton entangled states of the electromnagnetic field, that are relevant for applications to efficient quantum computation, quantum teleportation, and related problems in quantum communication and information.

https://arxiv.org/pdf/quant-ph/0701050.pdf

Multiphoton Quantum Optics and Quantum State Engineering

A review is given of correlation experiments in optics which explicitly distinguish between the predictions of classical and quantum theory. In particular, the Cauchy-Schwarz and Bell's inequalities and the phenomena of photon antibunching and squeezing are discussed. The violation of classical inequalities is shown to be associated with the nonexistence of a positive Glauber-Sudarshan P function. An example is given of a dissipative system where a violation of Bell's inequality occurs.

G. Strini

Papers

On the squeezing obtainable in parametric oscillators and bistable absorption