Table of contents

A two-mode photon operator satisfying the canonical boson commutation relations is used to define two-mode coherent states for the Weyl, SU(2) and SU(1,1) groups. In all these cases squeezing is determined by an appropriate correlation, which the authors evaluate. The generalisation to multi-mode, many-photon states is indicated.

The authors have shown that excitonic polaritons are two-mode intrinsically squeezed states of certain bosons A_{contained in} . They give the wavevector (frequency) dependence of the squeezing factor. They predict the fluctuations in time of the polariton wave probability density distribution and they calculate the time interval during which squeezing occurs. For experimental detection of polariton squeezing they extend a proposal of B Yurke, see Phys. Rev. Lett., vol.60, p.2476, eqn.6 (1988) by showing that via frequency tuning the vanishing of the particle-polariton scattering cross section can be achieved. They illustrate some results for the case of CdS.

Three characteristic functions are reviewed along with the quantum theory of linear systems and used to derive the P-representation, Wigner distribution and quasi-probability density of coherent states and squeezed states. The quasiprobability density is interpreted as the outcome of measurements utilising a beamsplitter with homodyne detection. The quasiprobability density concept is generalised and its interpretation in terms of a measurement is presented. The measurement utilises a beam splitter with one of its inputs in a squeezed state followed by two homodyne detectors.

The two basic interaction Hamiltonians for the quantum optical problems, namely the so-called minimal coupling one (p.A) and the multipolar one (d.E) are studied in the dipole approximation. The rigorous and exactly solvable model of an oscillator interacting with the electromagnetic field is employed. The Power-Zienau transformation is discussed. It is concluded that both Hamiltonians lead to the same S-matrix. The existence of an example like the one studied in this paper can be treated as support for the formal proofs given in the literature, which show that both Hamiltonians lead to the same predictions in the case of the more realistic description of the interaction of atoms with photons.

A concept 'probability-density functional' combined with the path integral technique is shown to provide a new framework for quantum photodetection theory. It replaces the conventional picture of unitary evolution of the total density operator followed by von Neumann's projection postulate for the case in which the effects of nonunitary state reduction and continuous measurements must be taken into account. This paper shows that an expression of the probability-density functional which incorporates both these effects provides complete quantum-statistical information about photoelectron statistics. Simple procedures are given for calculating the ensemble average and generating the functional of a quantity distributed in time.

In this tutorial article the authors provide a discussion of squeezed states of light from an elementary point of view. An outline of the topics considered is provided in the contents list below. Following the presentation of topics 1-3, which are of a general nature, they discuss two kinds of nonclassical light: quadrature-squeezed light (topics 4-6) and photon-number-squeezed light (topics 7-9). In the last part of the article they provide a listing of early nonclassical light experiments and consider a number of applications (and potential applications) of squeezed light. Finally, they provide a survey of the available general literature.