Covariance, Squeezed and Coherent States: Proposal for Experimental Realization of Covariance States

Abstract

Coherent and Squeezed States are widely discussed in literature, but there exist an other class of states (Covariance), minimizing more general inequality [Schrodinger, 1930] then Heisenberg’s one. To examine this relation and classify the Covariance, Squeezed and Coherent States, we consider the quantum optical problem of the propagation of electromagnetic waves in an anisotropic waveguide. The squeezed parameter, taking place in both — squeezed and covariance states, is expressed in explicit form through the main parameters of degenerated parametric amplification in an anisotropic waveguide. The expressions for the three independent quantum fluctuations are derived. The presence of nonlinearity is essential for the Covariance that appears in the Schrodinger Uncertainty Relation. Proposal for experimental realization of Covariance States in anisotropic optical waveguides is done.