Probing noncommutative theories with quantum optical experiments

Dey, Sanjib; Bhat, Abdul Hamid; Momeni, Davood; Faizal, Mir; Ali, Ahmed Farag; Dey, Tarun Kumar; Rehman, Atikur

doi:10.1016/j.nuclphysb.2017.09.024

Cited by 34 publications

(42 citation statements)

References 59 publications

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“…The tiny gravitational corrections beyond the √ T scaling should be compared to effects due to space-time noncommutativity [47][48][49] (see App. B), and a conceivable limitation of the achievable accuracy due to a gravitationally induced collapse of the wave function (Penrose conjecture, see Refs.…”

Section: Discussionmentioning

confidence: 99%

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Gravitational effects in g -factor measurements and high-precision spectroscopy: Limits of Einstein's equivalence principle

Jentschura

2018

Phys. Rev. A

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We study the interplay of general relativity, the equivalence principle, and high-precision experiments involving atomic transitions and g factor measurements. In particular, we derive a generalized Dirac Hamiltonian, which describes both the gravitational coupling for weak fields, as well as the electromagnetic coupling, e.g., to a central Coulomb field. An approximate form of this Hamiltonian is used to derive the leading gravitational corrections to transition frequencies and g factors. The position-dependence of atomic transitions is shown to be compatible with the equivalence principle, up to a very good approximation. The compatibility of g factor measurements requires a deeper, subtle analysis, in order to eventually restore the compliance of g factor measurements with the equivalence principle. Finally, we analyze small, but important limitations of Einstein's equivalence principle due to quantum effects, within high-precision experiments. We also study the relation of these effects to a conceivable gravitationally induced collapse of a quantum mechanical wave function (Penrose conjecture), and space-time noncommutativity, and find that the competing effects should not preclude the measurability of the higher-order gravitational corrections. In the course of the discussion, a renormalized form of the Penrose conjecture is proposed and confronted with experiment. Surprisingly large higher-order gravitational effects are obtained for transitions in diatomic molecules.

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Section: Discussionmentioning

confidence: 99%

“…The term V [0] is absorbed in the scaling factor √ T which multiplies the mass term in H kin , as given in Eqs. (47) and (49). The expectation value of the leading correction V [1] vanishes on any atomic energy eigenstate, due to parity.…”

Section: Gravitation and Size Of The Atommentioning

confidence: 98%

Gravitational effects in g -factor measurements and high-precision spectroscopy: Limits of Einstein's equivalence principle

Jentschura

2018

Phys. Rev. A

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“…The so-called natural realization [25,26,27,29] of the κ-Minkowski spacetime is defined by (20) It does not belong to the family of realizations parametrized by u, but it can nevertheless be related to the left covariant realization…”

Section: Relation Between Natural and Left Covariant Realizationsmentioning

confidence: 99%

“…As before we make the choice a µ = ( 1 κ , 0, 0, 0). From (73), (74) and (75) or (16) and (20) it follows that…”

Section: Left Covariant Realization and κ-Poincaré Algebramentioning

confidence: 99%

“…Some proposals have been advanced based on the cumulative effect of the energy-dependent velocity of photons traveling in quantum spacetime across cosmological distances, that could cause a measurable delay in the arrival time of gamma-ray bursts from distant galaxies [17]. Other proposals for the detection of quantum-gravity effects rely on ground-based experiments like Holometer in Fermilab [18] and various quantum optics experiments [19,20].…”

Section: Introductionmentioning

confidence: 99%

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κ -deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra, and dispersion relations

Meljanac

Mignemi

et al. 2019

Phys. Rev. D

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We consider κ-deformed relativistic quantum phase space and possible implementations of the Lorentz algebra. There are two ways of performing such implementations. One is a simple extension where the Poincaré algebra is unaltered, while the other is a general extension where the Poincaré algebra is deformed. As an example we fix the Jordanian twist and the corresponding realization of noncommutative coordinates, coproduct of momenta and addition of momenta. An extension with a one-parameter family of realizations of the Lorentz generators, dilatation and momenta closing the Poincaré-Weyl algebra is considered. The corresponding physical interpretation depends on the way the Lorentz algebra is implemented in phase space. We show how the spectrum of the relativistic hydrogen atom depends on the realization of the generators of the Poincaré-Weyl algebra. * Daniel.Meljanac@irb.hr † meljanac@irb.hr ‡ smignemi@unica.it § rina.strajn@unidu.hr

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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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Probing noncommutative theories with quantum optical experiments

Cited by 34 publications

References 59 publications

Gravitational effects in g -factor measurements and high-precision spectroscopy: Limits of Einstein's equivalence principle

Gravitational effects in g -factor measurements and high-precision spectroscopy: Limits of Einstein's equivalence principle

κ -deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra, and dispersion relations

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

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