This work has been motivated through the paper [42] by S. Dey on the nonclassical properties of the deformed harmonic oscillators. We study the dynamics of the nonclassical properties and nonlocal correlation for deformed coherent states superposition (DCSS) subjects to decoherence effect due to a dissipative interaction in deformed spaces. We consider two types of deformations,
q deformation that describes a large class of deformed harmonic oscillators and
L deformation that enters in the real possibilities of trapped ion systems. We find that such a kind of superposition, that gives rise to a richer phase space structure, the nonclassicality, squeezing, and entanglement can survive and they are robust against decoherence. The present results show that DCSS have less optical noise under dissipative dynamics in comparison with the usual Schr\"odinger cat states and may open new perspectives for the experimental observation of macro realism in quantum mechanics.
We study the dynamics of a catlike superposition of f-deformed coherent states under dissipative decoherence. For this purpose, we investigate two important categories of f-deformed coherent states: Gazeau–Klauder and displacement-type coherent states. In addition, we consider two deformation functions; one of them describes a harmonic oscillator in an infinite well and another corresponds to a harmonic oscillator in a quantum well with finite depth. The decoherence effects appeared through a dissipative interaction of the environment with the catlike states. In this study, we first show that the Gazeau–Klauder coherent state is more resistant under the decoherence process, in contrast to the displacement-type one, and second, that the potential range of the infinite well and the depth of potential possess a remarkable role in the decoherence process.