Coherent and Squeezed States: Theoretical Aspects and Some Applications

J. C. Garrison, R. Y. Chiao

This chapter reviews theoretical and experimental aspects of non-classical states of light, e.g., squeezed states and number states. The definition of squeezed states and a review of their general properties is followed by a discussion of special kinds of squeezing, e.g., squeezed coherent states, displaced squeezed states, and amplitude or phase squeezing. An overview of photon counting statistics and robustness of squeezed states is followed by a theoretical model of their generation and a description of their experimental production. The chapter ends with a brief discussion of the experimental generation of number states, including methods for generation of single-photon states on demand, which have applications to quantum information processing.

M. Satyanarayana

A. D. Jannussis, Vasileios Bartzis, E. Vlahos

Bernard Yurke

Recently a number of laboratories have demonstrated the generation of squeezed light, a new kind of light which in some of its aspects exhibits less quantum noise then coherent light. Here a description will be given of how such light is generated and detected. With the successful generation and detection of squeezed light by a number of laboratories1-5 a new degree of control over the quantum statistics of light has been achieved. Light can now be generated which, in some of its aspects, has less quantum noise than coherent light. Such light may find applications in optical communications and in sensitive and precision measurement. Here a description will be given of how squeezed light is generated and detected.6-8 The discussion will be restricted to what is called "quadrature squeezing". The electric field operator for a single mode of the electromagnetic field can be written in the form

Willi-Hans Steeb

Spiros Konstantogiannis

The purpose of this work is to introduce, in a simple, intuitive way, the coherent and squeezed states of the quantum harmonic oscillator (QHO), through a series of exercises, which are solved in detail. Starting from the application of a spatial translation to the ground state of the QHO, we introduce the spatial and momentum translations, focusing on their application to the QHO, which leads us to the displacement operator. Next, we introduce the coherent states and examine their basic aspects. We then proceed to give a simple and purely intuitive introduction to the squeezed states and we conclude by identifying the coherent states as states of minimum energy expectation value compared to the respective squeezed states. The reader is assumed to have a basic knowledge of the postulates and the mathematical formalism of quantum mechanics, including the Dirac notation and the ladder operator method of the QHO.