Nonclassical Properties of Intelligent SU(1,1) States for Two Modes

Abstract

Intelligent states are those states which equalize an uncertainty relation. The ordinary coherent states¹ equalize the usual uncertainty relation between the canonical position and momentum variables while exhibiting the noise of the vacuum in each. On the other hand, a squeezed state may also equalize the uncertainty relation while exhibiting less noise than the vacuum in one of the variables with a corresponding enhancement of noise in the other variable². Other kinds of intelligent states have been constructed on the basis of Lie algebras associated with important symmetry or dynamical groups such as SU(2)³ and SU(1,1)⁴. It turns out that for a single mode field, the su(1,1) Lie algebra is related to the square of the field amplitude and the corresponding SU(1,1) squeezing is the squeezing of the quadratures of the squared field⁵. The intelligent states associated with this algebra have been shown to possess a number of nonclassical properties such as squeezing and oscillations of the photocount probabilities^6,7. Also a method for generating such states⁷ has been proposed.