Coherent states for the “isotonic oscillator”

Yitzhak Weissman, Joshua Jortner

A. Banerjee

Wenbo Li, Kexuan Li, Ye Li +5 more

Symmetry in spectrum space of isotonic oscillators is studied, and a distinct fi gure is given by appropriate parametric substitution. An analytic expression of normalized eigenfunction is obtained. It is proven that linear oscillator is a degeneration of isotonic oscillator. It is revealed that an isotonic oscillator is a two_photon parametric model. Coherent state of that model is given, and that coherent state includes odd_coherent state and even_coherent state constru cted by Glauber coherent states in a natural way.

V. Chithiika Ruby, Paulsamy Muruganandam, Murugaian Senthilvelan

In this paper, we investigate revival and super revivals of nonlinear coherent states while generating these states through the interaction of coherent states of a generalized isotonic oscillator with the nonlinear media during time evolution. We construct the f-deformed generalized isotonic oscillator which is a non-isochronous partner of the generalized isotonic oscillator. We connect these two nonlinear oscillators through deformed ladder operators. The generalized isotonic oscillator possesses linear energy spectrum whereas f-deformed generalized isotonic oscillator exhibits nonlinear energy spectrum. The presence of the cubic nonlinearity in the f-deformed oscillator motivates us to study revivals, super and fractional revivals of coherent states which are nonlinearly evolved. We also investigate time-dependent expectation values of uncertainties in certain canonically conjugate variables and demonstrate that at revival and super revival times the uncertainty relation attains its minimum value.

Rainer Dick

Ji‐Suo Wang, Tang-Kun Liu, Mingsheng Zhan

We used the numerical method to study nonclassical properties of the even and odd generalized coherent states and superposition states of generalized coherent states for an isotonic oscillator. The following was shown. (1) The quantum statistical properties of the even and odd generalized coherent states are very different from those of the usual even and odd coherent states, and the N th-order ( N = 2 m + 1, m = 0,1,2,...) squeezing and sub-Poisson distribution appear alternately for both the even and odd generalized coherent states in some ranges of z = |β| 2 . The weaker the isotonic oscillator potential, the narrower the ranges. (2) The superposition states of generalized coherent states may exhibit the N th-order squeezing effect too, and this kind of higher-order squeezing effect appears periodically.