1202.5104 (V. Chithiika Ruby et al.)

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

V. Chithiika Ruby, M. Senthilvelan

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 an 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 $A_3$ 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.

View original: http://arxiv.org/abs/1202.5104