Cat-states in the framework of Wigner–Heisenberg algebra

Dehghani, A.; Mojaveri, B.; Shirin, S.; Saedi, Mohammad

doi:10.1016/j.aop.2015.08.031

Cited by 26 publications

(14 citation statements)

References 79 publications

(103 reference statements)

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“… . The Fock basis states are the common eigenstates of parity operator, , identity operator, , as well as number operator, and the action of the annihilation and creation operators on these states are given by The x -representation of the Fock vectors are expressed in terms of the associated Laguerre polynomials 38 as The Eqs. ( 1 ) and ( 2 ) are also known as the algebra of the para-Bose oscillator operators of order .…”

Section: Unitary Representation Of the Para-bose Oscillator Algebramentioning

confidence: 99%

The Jaynes–Cummings model of a two-level atom in a single-mode para-Bose cavity field

Fakhri

Sayyah-Fard

2021

Sci Rep

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The coherent states in the parity deformed analog of standard boson Glauber coherent states are generated, which admit a resolution of unity with a positive measure. The quantum-mechanical nature of the light field of these para-Bose states is studied, and it is found that para-Bose order plays an important role in the nonclassical behaviors including photon antibunching, sub-Poissonian statistics, signal-to-quantum noise ratio, quadrature squeezing effect, and multi-peaked number distribution. Furthermore, we consider the Jaynes-Cummings model of a two-level atom in a para-Bose cavity field with the initial states of the excited and Glauber coherent ones when the atom makes one-photon transitions, and obtain exact energy spectrum and eigenstates of the deformed model. Nonclassical properties of the time-evolved para-Bose atom-field states are exhibited through evaluating the fidelity, evolution of atomic inversion, level damping, and von Neumann entropy. It is shown that the evolution time and the para-Bose order control these properties.

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Section: Unitary Representation Of the Para-bose Oscillator Algebramentioning

confidence: 99%

The Jaynes–Cummings model of a two-level atom in a single-mode para-Bose cavity field

Fakhri

Sayyah-Fard

2021

Sci Rep

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“…We focus on the situations in which the field as an eigen-state of the λ-deformed annihilation operator is introduced48, i.e. , and its number state expansion is…”

Section: Evolution Of Atom-field Statementioning

confidence: 99%

“…Therefore, the introduced RDHA in (1) can be considered as a new deformation of the simple harmonic oscillator with significant features in quantum optics4849.…”

mentioning

confidence: 99%

Parity Deformed Jaynes-Cummings Model: “Robust Maximally Entangled States”

Dehghani¹,

Mojaveri²,

Shirin³

et al. 2016

Sci Rep

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The parity-deformations of the quantum harmonic oscillator are used to describe the generalized Jaynes-Cummings model based on the λ-analog of the Heisenberg algebra. The behavior is interestingly that of a coupled system comprising a two-level atom and a cavity field assisted by a continuous external classical field. The dynamical characters of the system is explored under the influence of the external field. In particular, we analytically study the generation of robust and maximally entangled states formed by a two-level atom trapped in a lossy cavity interacting with an external centrifugal field. We investigate the influence of deformation and detuning parameters on the degree of the quantum entanglement and the atomic population inversion. Under the condition of a linear interaction controlled by an external field, the maximally entangled states may emerge periodically along with time evolution. In the dissipation regime, the entanglement of the parity deformed JCM are preserved more with the increase of the deformation parameter, i.e. the stronger external field induces better degree of entanglement.

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“…Furthermore, it is valuable noting that because para-Bose systems reveal significant features in quantum optics, [24][25][26][27] it is also plausible to establish a connection between the quantum states of interest and para-Bose oscillators. [28,29] Considering the parity op-…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, it is valuable noting that because para‐Bose systems reveal significant features in quantum optics, [ 24–27 ] it is also plausible to establish a connection between the quantum states of interest and para‐Bose oscillators. [ 28,29 ] Considering the parity operator

\hat{R} = {(- 1)}^{\overset{n}{true}}

align with

f false(\overset{n}{true} false) = \sqrt{false(\overset{n}{true} + (p - 1) [1 - {(- 1)}^{\overset{n}{true}}] / 2 false) / \hat{n}}

, with p as the para‐Bose order, one is able to see that the f ‐deformed bosonic operators

\hat{A} = \hat{a} f false(\overset{n}{true} false)

and

{\overset{A}{true}}^{†} = f false(\overset{n}{true} false) {\overset{a}{true}}^{†}

, and the parity operator

\overset{R}{true}

satisfy the Wigner–Heisenberg algebra, which implies the algebra of the para‐Bose systems.…”

Section: Introductionmentioning

confidence: 99%

Generalized Photon Added and Subtracted f‐Deformed Displaced Fock States

Faghihi

2020

Annalen der Physik

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In this paper, by making use of the nonlinear coherent states approach, the generalized photon added and subtracted f-deformed displaced Fock states are introduced. In other words, a natural link between photon added and subtracted displaced Fock states and nonlinear coherent states associated with nonlinear oscillator algebra is obtained. It is found that various kinds of nonclassical states can be generated by adopting appropriately controlling parameters in both linear and nonlinear regimes. Moreover, examining some of the most nonclassical properties such as Mandel's Q parameter, different types of squeezing, namely, quadrature, amplitude-squared and phase entropic squeezing, and Vogel's characteristic function, the nonclassicality features of the considered quantum states of interest are studied. Furthermore, to obtain the degree of quantum coherence, the relative entropy of coherence is investigated. Indeed, the nonclassicality aspects of the states obtained have been numerically studied to understand the roles of deformation functions, photons added and subtracted, and photon number occupied in the Fock state on physical properties. It is demonstrated that the depth and the domain of the nonclassicality features of the system can properly be controlled by selecting the suitable parameters.

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Cat-states in the framework of Wigner–Heisenberg algebra

Cited by 26 publications

References 79 publications

The Jaynes–Cummings model of a two-level atom in a single-mode para-Bose cavity field

The Jaynes–Cummings model of a two-level atom in a single-mode para-Bose cavity field

Parity Deformed Jaynes-Cummings Model: “Robust Maximally Entangled States”

Generalized Photon Added and Subtracted f‐Deformed Displaced Fock States

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