LAUSR

Abstract The q -coherent states associated with the noncommutative complex plane C q 2 for the Biedenharn–Macfarlane q -oscillator are constructed by using a q -generalization of the Glauber’s unitary displacement operator. The q -deformed counterpart of the eigenvalue equation of undeformed harmonic oscillator coherent states is obtained. Some properties of the q -coherent states are considered. It is shown that super-Poissonian statistics and saturation of the uncertainty relation occur simultaneously with the nonclassical behaviors including antibunching effects with nonnegative values less than unity and the negative values, for the second-order intensity q -correlation function in the case of q > 1 . Furthermore, the nonclassical sub-Poissonian statistics is demonstrated simultaneously with bunching and antibunching effects such that in some regions of the coherence parameter the uncertainty inequality is satisfied, and violated elsewhere. We show that another nonclassical effect, the so-called strong squeezing effect, is exhibited by both quadrature variances in the latter issue.