Arik-Coon q-oscillator cat states on the noncommutative complex plane Cq-1 and their nonclassical properties

摘要

The normalized even and odd q-cat states corresponding to Arik-Coon q-oscillator on the noncommutative complex plane C (q-1) are constructed as the eigenstates of the lowering operator of a q-deformed su(1, 1) algebra with the left eigenvalues. We present the appropriate noncommutative measures in order to realize the resolution of the identity condition by the even and odd q-cat states. Then, we obtain the q-Bargmann-Fock realizations of the Fock representation of the q-deformed su(1, 1) algebra as well as the inner products of standard states in the q-Bargmann representations of the even and odd subspaces. Also, the Euler's formula of the q-factorial and the Gaussian integrals based on the noncommutative q-integration are obtained. Violation of the uncertainty relation, photon antibunching effect and sub-Poissonian photon statistics by the even and odd q-cat states are considered in the cases 0 < q < 1 and q > 1.