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

摘要

In this paper, we construct nonlinear coherent states for the generalizedisotonic oscillator and study their non-classical properties in-detail. Bytransforming the deformed ladder operators suitably, which generate thequadratic algebra, we obtain Heisenberg algebra. From the algebra we define twonon-unitary and an unitary displacement type operators. While the action of oneof the non-unitary type operators reproduces the original nonlinear coherentstates, 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 thenonlinear coherent states, we evaluate the parameter $A_3$ and examine thenon-classical nature of the states through quadratic and amplitude-squaredsqueezing effect. Further, we derive analytical formula for the $P$-function,$Q$-function and the Wigner function for the nonlinear coherent states. All ofthem confirm the non-classicality of the nonlinear coherent states. In additionto the above, we obtain the harmonic oscillator type coherent states from theunitary displacement operator.