Quantum Optics: Journal of the European Optical Society Part B

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.

A theoretical review of the use of optical solitons in fibres for high speed communication is presented with emphasis on recent progress in soliton control. An optical soliton is a pulse of light in a fibre produced by a balance of group velocity dispersion and cubic non-linearity. Twenty years after its discovery, optical solitons are rapidly attracting interest from technical as well as scientific communities thanks to progress in coherent light source, fibre amplifier and other photonic devices and surprising agreement of the theoretical predictions with experimental observations.

Phase properties of binomial and negative binomial states are studied within the Pegg-Barnett hermitian phase formalism.

A method is developed for constructing a (- pi , pi ) arc distribution function of one-dimensional coherent state superpositions on a circle from the (- infinity , infinity ) weight function. Changing the parameters of a Gaussian weight function superposition states with different amplitude-squeezed and number-phase uncertainty properties can be prepared.

The Barut-Girardello states (the eigenstates of the SU(1, 1) lowering generator K_- are considered in the harmonic oscillator Hilbert space. They are found to have sub-Poissonian photon statistics. By using these states, the diagonal P-representation of the density operator is constructed, and it is shown to be well behaved for non-classical photon states.

It is shown that the Bayesian methods in statistics can be used to solve problems in continuous photodetection with dramatically reduced effort compared with the traditional superoperator approach.

A theoretical review of the use of optical solitons in fibres for high speed communication is presented with emphasis on recent progress in soliton control. An optical soliton is a pulse of light in a fibre produced by a balance of group velocity dispersion and cubic non-linearity. Twenty years after its discovery, optical solitons are rapidly attracting interest from technical as well as scientific communities thanks to progress in coherent light source, fibre amplifier and other photonic devices and surprising agreement of the theoretical predictions with experimental observations.

A combination of less frequent criticism with positive investigations has resulted in the substitution of group theoretic considerations by a simpler quantum mechanical model, has taken into account homodyne and heterodyne detection schemes, and proceeded by an analysis of phase data processing. Limiting procedures in s-phase formalisms have been provided concentrating on the Wigner function for number and ideal phase. The Wigner function for number and realistic phase has been expressed by closed formulae along with the antinormal phase distributions.

A scheme for deriving a field kinetic equation for the problems of macroscopic quantum optics has been formulated. The general master equation obtained for the s-ordered quasi-probability, and Glauber-Sudarshan P-function in particular, has been concretized for the case of three-photon parametric processes in a multi-level medium. Thus the three-photon parametric phenomena have been examined without exploiting the traditional effective Hamiltonian. Discussed here is the problem of formation of field statistics depending on the type of excitation medium with two-level lasing levels that reduce to the Lamb-Scully or Haken models. The form of the kinetic equation obtained is shown to depend on the types of atomic transitions.

The ideas of localizability of elementary particles introduced by Newton and Wigner (1949) are expressed in the language of imprimitivities as formulated by Mackey and Wightman. This naturally brings in the induced representations of the Euclidean and Poincare groups. The authors specialize the discussion to the case of the photon and show in detail that an imprimitivity for the Euclidean group is not consistent with representations of the Poincare group relevant to the photon.

Some past and some possible future experiments that make use of the photon pairs generated in the process of parametric down-conversion are reviewed and briefly analysed. The experiments demonstrate that the average position in time of an optical photon can be determined with accuracy better than one period, and that two-photon coincidence measurements can carry useful information about the phase of the electro-magnetic field. Several different experiments for exhibiting violations of Einstein locality with down-converted photon pairs are discussed.