PHYSICAL NONLINEAR ASPECTS OF CLASSICAL AND QUANTUM q-OSCILLATORS

We provide an explicit construction of entangled states in a noncommutative space with nonclassical states, particularly with the squeezed states. Noncommutative systems are found to be more entangled than the usual quantum mechanical systems. The noncommutative parameter provides an additional degree of freedom in the construction by which one can raise the entanglement of the noncommutative systems to fairly higher values beyond the usual systems. Despite of having classical-like behaviour, coherent states in noncommutative space produce little amount of entanglement and therefore they possess slight nonclassicality as well, which are not true for the coherent states of ordinary harmonic oscillator.

show abstract

“…A second approach of generalising the ladder operators can be realized in terms of the f -oscillators [25] A…”

Section: Generalised Squeezed Coherent Statesmentioning

confidence: 99%

Entangled squeezed states in noncommutative spaces with minimal length uncertainty relations

Dey

Hussin

2015

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

“…They were interpreted [11] as nonlinear oscillators with a very specific type of nonlinearity, and this led to the more general concept of f -deformed oscillator [12]. Then, the notion of f -coherent states was straightforwardly introduced [12], and the generation of such nonlinear coherent states enters in the real possibilities of trapped systems [13].…”

mentioning

confidence: 99%

“…having the same d. Then, let us consider two types of deformations in more details. The q-deformation defined by [10,11] …”

mentioning

confidence: 99%

The survival of quantum coherence in deformed-states superposition

Mancini¹,

Man’ko

2001

Europhys. Lett.

View full text Add to dashboard Cite

We study the dissipative dynamics of deformed coherent states superposition. We find that such kind of superposition can be more robust against decoherence than the usual Schrödinger cat states. 42.50.Dv, 42.50.Ar, 03.65.Ca The feature of quantum mechanics which most distinguishes it from classical mechanics is the coherent superposition of distinct physical states. Many of the less intuitive aspects of the quantum theory can be traced to this feature. The famous Schrödinger cat argument [1] highlights problems of interpretation where macroscopic superposition states is allowed. In fact, such states are very fragile in the presence of dissipation, and rapidly collapse to a classical mixture exhibiting no unusual interference features [2,3]. Environment induced decoherence has been identified in recent years as one of the main ingredients in the transition from quantum to classical behavior [4,5]. Classicality emerges as a consequence of the coupling of quantum systems to an environment which, in effect, dynamically enforces super-selection rules by precluding the stable existence of the majority of states in the Hilbert space of the system. The physics of decoherence has been studied during the last few years both from the theoretical [5] and also from the experimental point of view [6]. However, the most used paradigmatic case has been the superposition of two distinguishable coherent states [7]. The latter being eigenstates of boson annihilation operator [8].On the other hand, quantum groups [9], introduced as a mathematical description of deformed Lie algebras, have given the possibility of generalizing the notion of creation and annihilation operators of the usual oscillator and to introduce deformed oscillator [10]. They were interpreted [11] as nonlinear oscillators with a very specific type of nonlinearity, and this led to the more general concept of f -deformed oscillator [12]. Then, the notion of f -coherent states was straightforwardly introduced [12], and the generation of such nonlinear coherent states enters in the real possibilities of trapped systems [13].Successively, it was quite natural to consider the superposition of such states [14], which could be named deformed cat state. Here, we are going to study their dissipative dynamics and the related coherence properties in comparison with the usual Schrödinger cat states [7]. In particular, we shall show that the deformed cat states may result much more robust against decoherence than their undeformed version.The essential point in understanding quantum coherence is the physical distinction between the coherent superposition state |ψ = i c i |ψ i ⇐⇒ ρ =

show abstract

“…Since E is an integral of motion for both the linear and nonlinear oscillators, one can easily obtain the solution to (6) …”

Section: Classical and Quantum F -Oscillators For One-mode Fieldsmentioning

confidence: 99%