Physical significance of correlated and squeezed states

Abstract

and During last two decades the so called squeezed states were the subject of increasing flow of papers in various fields of quantum physics. It seems rather difficult to cite the first paper, since the history of these states goes back In ref.[13] the concept of correlated states was introduced. These states correspond to the minimal possible value of the lefthand side of the RobertsonSchr6dinger uncertainty relation [14,15] O-p O"q ( 1 -r 2 ) > h2 /4 .Here trp and trq are variances of the momentum and coordinate operators: ~q = (~2) _ (~)2 , while r is the dimensionless correlation coefficient:In the special case of r : 0 (1) turns into the more familiar Heisenberg-Weyl 'uncertainty relation. The explicit form of the correlated state wave function in the coordinate representation is as follows,

Properties of squeezed-state excitations

“…The distributions for nonclassical light have frequently oscillatory character [17,18,19]. For correlated light [20], this has been found in [21] and this phenomenon takes place for generalized correlated states [22] as well.…”

Correlated states and nuclear reactions: An experimental test with low energy beams

“…In fact, the explicit form of the CCS wave function (1) is quite similar to the solution of Schrödinger equation for the parametric oscillator case, as described by a timedependent Hamiltonian [16,17].…”

“…At the same time, a further generalization was introduced, the CCSs, which equalize the SRI so that they must be considered as the minimum uncertainty states in the Schrödinger-Robertson sense. They were analytically constructed and their eigenfunctions evaluated by Dodonov, Klimov, and Man'ko [16] (β is a complex number) as…”

Transmission of Correlated Gaussian Packets Through a Delta-Potential

“…We dedicate this paper to the memory of Allan Solomon. We both met him for the first time in 1990 in Moscow during the XVIII International Colloquium on Group Theoretical Methods in Physics, where one of the authors spoke about the physical meaning of correlated states [17]. Since then we had a pleasure to meet Allan at many scientific and private events in different countries and continents, enjoying his brilliant talks and stories.…”