An observation of quadratic algebra, dual family of nonlinear coherent states and their non-classical properties, in the generalized isotonic oscillator

Abstract

In this paper, we construct nonlinear coherent states for the generalized isotonic oscillator and study their non-classical properties in detail. By transforming the deformed ladder operators suitably, which generate the quadratic algebra, we obtain Heisenberg algebra. From the algebra, we define two non-unitary and one unitary displacement type operators. While the action of one of the non-unitary type operators reproduces the original nonlinear coherent states, the other one fails to produce a new set of nonlinear coherent states (dual pair). We show that these dual states are not normalizable. For the nonlinear coherent states, we evaluate the parameter A3 and examine the non-classical nature of the states through quadratic and amplitude-squared squeezing effect. Further, we derive analytical formula for the P-function, Q-function, and the Wigner function for the nonlinear coherent states. All of them confirm the non-classicality of the nonlinear coherent states. In addition to the above, we obtain the harmonic oscillator type coherent states from the unitary displacement operator.