Generalized Heisenberg Algebras: periodicity and finite representation

Belfakir, Abdessamad; Hassouni, Y.

doi:10.1088/1402-4896/ab5fa5

Cited by 4 publications

(1 citation statement)

References 22 publications

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“…Furthermore, it has been shown that the GHA can be applied for physical systems involving known spectrum such as the square well potential [49], the Morse potential [50,51] and the Pöschl-Teller potential [11,52].…”

Section: Generalities On Ghamentioning

confidence: 99%

Robustness of deformed catlike states under dissipative decoherence

Belfakir,

Belhaj,

Hassouni

2020

Preprint

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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 deformation parameters, we reveal that the nonclassical properties of catlike states under dissipative interaction can be more retarded and preserved in the time.

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Section: Generalities On Ghamentioning

confidence: 99%

Robustness of deformed catlike states under dissipative decoherence

Belfakir,

Belhaj,

Hassouni

2020

Preprint

Self Cite

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Time evolution and anti-bunching effect of diatomic molecules coherent states

Belfakir

Curado²,

Hassouni

2020

Annals of Physics

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Quantum optimal control of molecular coherent states

Belfakir,

Belhaj,

Hassouni

et al. 2024

Phys. Scr.

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In this paper, we address the optimal control problem in molecular systems, focusing on transitions within coherent states characterised by complex coefficients. Employing Hölder's inequality, we establish a mathematical relationship between the energy requirement and the distance separating the initial and the target coherent states. A key part of our study is the application of this framework to the $\text{H}_2\text{O}$ molecule, specifically examining the local OH bond. Here, we demonstrate how energy requirements for the state transitions are influenced by the distance between these states. Furthermore, we investigate the effects of a heat bath coupled to the system, by analysing its impact on transferring the molecular system to different final coherent states. These coherent states are defined as \textit{almost} eigenvectors of the Generalised Heisenberg Algebra (GHA) annihilation operator. By using the Perolomov approach, another type of coherent states for the Morse potential associated with the GHA can be constructed. By leveraging the GHA structure, we revisit and analyse Morse coherent states previously established for certain diatomic molecules, offering a deeper insight into the dynamics of state transitions under various conditions.

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Generalized Heisenberg Algebras: periodicity and finite representation

Cited by 4 publications

References 22 publications

Robustness of deformed catlike states under dissipative decoherence

Robustness of deformed catlike states under dissipative decoherence

Time evolution and anti-bunching effect of diatomic molecules coherent states

Quantum optimal control of molecular coherent states

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