Triplet q-cat states of the Biedenharn–Macfarlane q-oscillator with q &gt; 1

Fakhri, H.; Sayyah-Fard, M.

doi:10.1007/s11128-019-2507-z

Cited by 7 publications

(2 citation statements)

References 55 publications

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“…An intimate connection between the gravitation and the existence of the fundamental length scale was proposed in [109]. The minimal length has found to exist in string theory [110], loop quantum gravity [111], path integral quantum gravity [112], special relativity [113], doubly special relativity [114], coherent states [22][23][24][25][26][27][28][115][116][117][118][119][120][121][122],, etc. Furthermore, some thought experiments [109] in the spirit of black hole physics suggest that any theory of quantum gravity must be equipped with a minimum length scale [123], due to the fact that the energy required to probe any region of space below the Plank length is greater than the energy required to create a mini black hole in that region of space.…”

Section: A Noncommutative Quantum Mechanicsmentioning

confidence: 99%

A Squeezed Review on Coherent States and Nonclassicality for Non-Hermitian Systems with Minimal Length

Dey

Fring

Hussin

2018

Springer Proceedings in Physics

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It was at the dawn of the historical developments of quantum mechanics when Schrödinger, Kennard and Darwin proposed an interesting type of Gaussian wave packets, which do not spread out while evolving in time. Originally, these wave packets are the prototypes of the renowned discovery, which are familiar as "coherent states" today. Coherent states are inevitable in the study of almost all areas of modern science, and the rate of progress of the subject is astonishing nowadays. Nonclassical states constitute one of the distinguished branches of coherent states having applications in various subjects including quantum information processing, quantum optics, quantum superselection principles and mathematical physics. On the other hand, the compelling advancements of non-Hermitian systems and related areas have been appealing, which became popular with the seminal paper by Bender and Boettcher in 1998. The subject of non-Hermitian Hamiltonian systems possessing real eigenvalues are exploding day by day and combining with almost all other subjects rapidly, in particular, in the areas of quantum optics, lasers and condensed matter systems, where one finds ample successful experiments for the proposed theory. For this reason, the study of coherent states for non-Hermitian systems have been very important. In this article, we review the recent developments of coherent and nonclassical states for such systems and discuss their applications and usefulness in different contexts of physics. In addition, since the systems considered here originate from the broader context of the study of minimal uncertainty relations, our review is also of interest to the mathematical physics community. CONTENTS* dey@iisermohali.ac.in; sanjibdey4@gmail.com † a.fring@city.ac.uk ‡ veronique.hussin@umontreal.ca A. Squeezed states 11 B. Schrödinger cat states 12 C. Photon-added coherent states 13 VI. Applications 13 VII. Concluding remarks 13 References 14 arXiv:1801.01139v1 [quant-ph] 3 Jan 2018 III. NON-HERMTIAN SYSTEMS IN MINIMAL LENGTH SCENARIOHaving introduced the general features of coherent states and nonclassicality, in this section, let us discuss a system on which our article is based on, i.e. some non-Hermitian models based on quantum mechanics in NC space and, then, we discuss how these models can be applied to physical systems like coherent states. A. Noncommutative quantum mechanicsThe original proposal of space-time noncommutativity is very old and was introduced in the pioneering days of quan-

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Section: A Noncommutative Quantum Mechanicsmentioning

confidence: 99%

A Squeezed Review on Coherent States and Nonclassicality for Non-Hermitian Systems with Minimal Length

Dey

Fring

Hussin

2018

Springer Proceedings in Physics

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“…Thus, the knowledge of the eigenvalues of any quantum mechanical Hamiltonian will ensure the explicit form of the function f (n). The method is usually familiar as the nonlinear generalization [10][11][12] and the endeavor has been accepted widely; see, for instance [27][28][29][30][31][32][33]. However, a direct replacement of the generalized ladder operators (2) in (1) does not necessarily yield the generalized PSSVS, rather, the resulting states is some other state whose name is not known to us.…”

Section: Generalized Photon-subtracted Squeezed Vacuummentioning

confidence: 99%

Generalized photon-subtracted squeezed vacuum states

Dey,

Nair

2020

Preprint

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We construct a generalized version of the photon-subtracted squeezed vacuum states (PSSVS), which can be utilized to construct the same for nonlinear, deformed and any usual quantum mechanical models beyond the harmonic oscillator. We apply our general framework to trigonometric Pöschl-Teller potential and show that our method works accurately and produces a proper nonclassical state. We analyze the nonclassicality of the state using three different approaches, namely, quadrature squeezing, photon number squeezing and Wigner function and indicate how the standard definitions of those three techniques can be generalized and utilized to examine the nonclassicality of any generalized quantum optical states including the PSSVS. We observe that the generalized PSSVS are always more nonclassical than those arising from the harmonic oscillator. Moreover, within some quantification schemes, we find that the nonclassicality of the PSSVS increases almost proportionally with the number of photons subtracted from the generalized squeezed vacuum state. Thus, generalized PSSVS may provide an additional freedom with which one can regulate the nonclassicality and obtain an appropriate nonclassical state as per requirement.

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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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Triplet q-cat states of the Biedenharn–Macfarlane q-oscillator with q > 1

Cited by 7 publications

References 55 publications

A Squeezed Review on Coherent States and Nonclassicality for Non-Hermitian Systems with Minimal Length

A Squeezed Review on Coherent States and Nonclassicality for Non-Hermitian Systems with Minimal Length

Generalized photon-subtracted squeezed vacuum states

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

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