Non-classical properties for SU(1, 1) pair coherent states

Abstract A new type of pair quantum states is introduced. Which can be considered as pair Barut-Girardello coherent states. It is an eigenstate of the operators K − ab = K − a K − b and K 3 a − K 3 b . We construct these eigenstates and generation scheme is proposed in terms of two mode state described in terms of su(1, 1) Lie algebra , We employ the second-order correlation function to discuss some non-classical properties,and violations of Cauchy-Schwarz inequalities. The phenomenon of squeezing is examined , squeezing is clear and Q-functions support that. Finally the phase distribution in the framework of an appropriate Pegg and Barnett formalism is considered and discussed.