Nonclassical properties of the q-coherent and q-cat states of the Biedenharn-Macfarlane q oscillator with q > 1

This paper has been motivated by a recent paper by Dey [Phys. Rev. D 91, 044024 (2015)] on the known Arik-Coon q oscillator. We construct q coherent, even and odd q-cat states in Fock representation for the Biedenharn-Macfarlane q oscillator with q > 1 and study their nonclassical properties. The q-coherent states minimize the Heisenberg uncertainty relation between the generalized position and momentum operators as well as the x and y components of a q-deformed su(1,1) algebra in the Schwinger boson representation. The latter is also minimized by the even and odd q-cat states. We show that, contrary to the undeformed harmonic oscillator, the squeezing effect in both position and momentum operators can be exhibited by odd q-cat states. It is also violated by even q-cat states. Furthermore, it is shown that the antibunching effect and sub-Poissonian or super-Poissonian statistics can simultaneously appear by each of the even or odd q-cat states. Finally, a unitary Fock representation of the q-deformed su(1,1) algebra is obtained by the q-deformed Bargmann-Fock realization.