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Physical review. D/Physical review. D.

Noncommutative deformed cat states under decoherence

K. Berrada, Hichem Eleuch

Published Jul 29, 2019• 39 citations
Publisher

Abstract

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.

DOI
10.1103/physrevd.100.016020

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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, qqq deformation that describes a large class of deformed harmonic oscillators and LLL 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.
The generation of coherent superposition of distinct physical systems and the construction of robust entangled states under decoherence are the most experimental challenges of quantum technologies. In this work, we investigate the behaviors of catlike states of a deformed harmonic oscillator under dissipative decoherence. Varying the deformation parameters, we obtain catlike states having more resistance against decoherence than catlike states of the ordinary harmonic oscillator. Furthermore, we study nonclassical properties and entanglement of different catlike states subjects to decoherence caused by a dissipative interaction with a large environment. Depending on different parameters of the deformation, we reveal that the nonclassical properties of catlike states under dissipative interaction can be more retarded and preserved in the time.
We propose a new kind of Schrödinger cat state introduced as a superposition of spin coherent states in the framework of noncommutative spaces. We analyze the nonclassical features for these noncommutative deformed states in terms of the main physical parameters. The physical importance of deformed states is that they provide a convenient description of a large set of laser systems. As an application, we develop the Jaynes–Cummings model by considering the interaction among atoms and cat state fields associated to deformed spin algebras. In this context, we show the dynamical behavior of the nonlocal correlation and nonclassical properties in these quantum systems.
Decoherence of q−q-q−Deformed Photon Added Coherent State
In this study, we explore the behavior of photon added coherent states in a deformed harmonic oscillator subjected to dissipative decoherence. We use q−q-q−deformation as our nonlinear function to model our system. By adjusting the deformation parameter, we show that q−q-q−deformed photon added coherent state (DPACS) exhibit greater nonclassicality and resilience to decoherence compared to those of a standard harmonic oscillator. Additionally, we investigate the nonclassical properties and entanglement of DPACS under decoherence induced by interaction with a dissipative photon-loss environment.
We study several classical-like properties of qqq-deformed nonlinear coherent states as well as nonclassical behaviors of qqq-deformed version of the Schr\"odinger cat states in noncommutative space. Coherent states in qqq-deformed space are found to be minimum uncertainty states together with the squeezed photon distributions unlike the ordinary systems, where the photon distributions are always Poissonian. Several advantages of utilizing cat states in noncommutative space over the standard quantum mechanical spaces have been reported here. For instance, the qqq-deformed parameter has been utilized to improve the squeezing of the quadrature beyond the ordinary case. Most importantly, the parameter provides an extra degree of freedom by which we achieve both quadrature squeezed and number squeezed cat states at the same time in a single system, which is impossible to achieve from ordinary cat states.
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.
Nonclassicality is an interesting property of light having applications in many different contexts of quantum optics, quantum information and computation. Nonclassical states produce substantial amount of reduced noise in optical communications. Furthermore, they often behave as sources of entangled quantum states, which are the most elementary requirement for quantum teleportation. We study various nonclassical properties of coherent states and Schrödinger cat states in a setting of noncommutative space resulting from the generalized uncertainty relation, first, in a complete analytical fashion and, later, by computing their entanglement entropies, which in turn provide supporting arguments behind our analytical results. By using standard theoretical frameworks, they are shown to produce considerably improved squeezing and nonclassicality and, hence, significantly higher amount of entanglement in comparison to the usual quantum mechanical models. Both the nonclassicality and the entanglement can be enhanced further by increasing the noncommutativity of the underlying space. In addition, we find as a by-product some rare explicit minimum uncertainty quadrature and number squeezed states, i.e., ideal squeezed states.