Algebraic and group treatments to nonlinear displaced number states and their nonclassicality features: A new approach

Tavassoly, M. K.; Faghihi, Mohammad Javad

doi:10.1088/1674-1056/24/6/064204

Cited by 4 publications

(2 citation statements)

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“…In the latter relation, the Baker-Campbell-Hausdorff (BCH) formula, applied for disentangling the bosonic operators in relation 5, has generally no application because of the complicated commutation relation [̂,̂ †] ≠ 1, unlike the relation [â,â † ] = 1 for standard bosonic operators. This challenge is overcome by considering two new auxiliary operators as [49,50] ℬ =â…”

Section: States Of Interestmentioning

confidence: 99%

“…In the latter relation, the Baker–Campbell–Hausdorff (BCH) formula, applied for disentangling the bosonic operators in relation (5), has generally no application because of the complicated commutation relation

[\hat{scriptA}, {\overset{A}{true}}^{†}] \neq 1

, unlike the relation

[\hat{a}, {\overset{a}{true}}^{†}] = 1

for standard bosonic operators. This challenge is overcome by considering two new auxiliary operators as [ 49,50 ]

\begin{matrix} true \\ right \overset{B}{true} = \overset{a}{true} \frac{1}{scriptF false(\overset{n}{true} false)}, {\hat{scriptB}}^{†} = \frac{1}{scriptF false(\overset{n}{true} false)} {\hat{a}}^{†} \end{matrix}

As a result, the two classes of generalized displacement operators can be introduced. Thus, the two sets of generators as

{\hat{scriptA}, {\overset{B}{true}}^{†}, {\overset{B}{true}}^{†} \hat{scriptA}, \hat{I}}

and

{\hat{scriptB}, {\overset{A}{true}}^{†}, {\overset{A}{true}}^{†} \hat{scriptB}, \hat{I}}

can be established both satisfying the Weyl–Heisenberg Lie algebra, especially the following commutation relations

\begin{matrix} true \\ right [\overset{A}{true}, {\hat{scriptB}}^{†} \overset{A}{true}] & = & left \overset{A}{true}, ([] {\overset{B}{true}}^{†}, {\overset{B}{true}}^{†} \hat{scriptA}) = - {\hat{scriptB}}^{†} \end{matrix} ...

…”

Section: States Of Interestmentioning

confidence: 99%

See 1 more Smart Citation

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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Section: States Of Interestmentioning

confidence: 99%