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

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. (paper)