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arXiv:1205.2474 · Europhysics Letters (EPL)

Testing spatial noncommutativity via magnetic hyperfine structure induced by fractional angular momentum of Rydberg system

Jian-Zu Zhang, Hong-Ping Liu, Wei Cao, Ke-Lin Gao

Published May 1, 2012• 3 citations
arXivHTMLPDF

Abstract

An approach to solve the critical problem of testing quantum effects of spatial noncommutativity is proposed. Magnetic hyperfine structures in a Rydberg system induced by fractional angular momentum originated from spatial noncommutativity are discussed. The orders of the corresponding magnetic hyperfine splitting of the spectrum ∼10 −7 –10 − 8 eV lie within the limits of accuracy of current experimental measurements. Experimental tests of physics beyond the standard model are the focus of broad interest. We note that the present approach is reasonably achievable with current technology. The proof is based on very general arguments involving only the deformed Heisenberg-Weyl algebra and the fundamental property of angular momentum. Its experimental verification would constitute an advance in understanding of fundamental significance, and would be a key step towards a decisive test of spatial noncommutativity.

DOI
10.1209/0295-5075/98/40002

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An approach to solve the critical problem of testing quantum effects of spatial noncommutativity is proposed. Magnetic hyperfine structures in a Rydberg system induced by fractional angular momentum originated from spatial noncommutativity are discussed. The orders of the corresponding magnetic hyperfine splitting of the spectrum ∼10 −7 –10 − 8 eV lie within the limits of accuracy of current experimental measurements. Experimental tests of physics beyond the standard model are the focus of broad interest. We note that the present approach is reasonably achievable with current technology. The proof is based on very general arguments involving only the deformed Heisenberg-Weyl algebra and the fundamental property of angular momentum. Its experimental verification would constitute an advance in understanding of fundamental significance, and would be a key step towards a decisive test of spatial noncommutativity.
An approach to solve the critical problem of testing quantum effects of spatial noncommutativity is proposed. Magnetic hyperfine structures in a Rydberg system induced by fractional angular momentum originated from spatial noncommutativity are discussed. The orders of the corresponding magnetic hyperfine splitting of the spectrum ~10−7–10− 8 eV lie within the limits of accuracy of current experimental measurements. Experimental tests of physics beyond the standard model are the focus of broad interest. We note that the present approach is reasonably achievable with current technology. The proof is based on very general arguments involving only the deformed Heisenberg-Weyl algebra and the fundamental property of angular momentum. Its experimental verification would constitute an advance in understanding of fundamental significance, and would be a key step towards a decisive test of spatial noncommutativity.
The possibility of testing spatial noncommutativity via Rydberg atoms is explored. An atomic di-pole of a cold Rydberg atom is arranged in appropriate electric and magnetic fields, so that the motion of the dipole is constrained to be planar and rotationally symmetric. Spatial noncommutativity leads the canonical angular momentum to possess fractional values. In the limit of vanishing kinetic energy, the dominate value of the lowest canonical angular momentum takes variant Planck's over h/2. Furthermore, in the limit of eliminating the magnetic field, the dominate value of the lowest canonical angular momentum changes from variant Planck's over h/2 to variant Planck's over h/4. This result is a clear signal of spatial noncommutativity. An experimental verification of this prediction is suggested.
The possibility of testing spatial noncommutativity via a Penning trap is explored. The case of both space-space and momentum-momentum noncommuting is considered. Spatial noncommutativity leads to the spectrum of the orbital angular momentum of a Penning trap possessing fractional values, and in the limits of vanishing kinetic energy and subsequent vanishing magnetic field, this system has non-trivial dynamics. The dominant value of the lowest orbital angular momentum is ℏ/4\hbar/4ℏ/4, which is a clear signal of spatial noncommutativity. An experimental verification of this prediction by a Stern-Gerlach-type experiment is suggested.
Abstract The mechanism of obtaining the fractional angular momentum by employing a trapped atom which possesses a permanent magnetic dipole moment in the background of two electric fields is reconsidered by using an alternative method. Then, we generalize this model to a noncommutative plane. We show that there are two different mechanisms, which include cooling down the atom to the negligibly small kinetic energy and modulating the density of electric charges to the critical value to get the fractional angular momentum theoretically .
In noncommutative spaces to maintain Bose–Einstein statistics for identical particles at the non-perturbation level described by deformed annihilation-creation operators when the state vector space of identical bosons is constructed by generalizing one-particle quantum mechanics it is explored that the consistent ansatz of commutation relations of phase space variables should simultaneously include space–space non-commutativity and momentum–momentum non-commutativity, and a new type of boson commutation relations at the deformed level is obtained. Consistent perturbation expansions of deformed annihilation-creation operators are obtained. The influence of the new boson commutation relations on dynamics is discussed. The non-perturbation and perturbation property of the orbital angular momentum of two-dimensional system are investigated. Its spectrum possesses fractional eigen values and fractional intervals.
A quantum model for calculating the combined Stark and Zeeman effects of simultaneously applied electric and magnetic fields is presented. Our focus here is on atoms with hyperfine structure, such as Cesium. Matrix representations of the Stark, Zeeman, and hyperfine interaction operators are constructed using angular momentum theory and spherical tensor algebra. Matrix elements are evaluated in order to determine the energy-level dependence on the applied fields and reveal intriguing state dynamics in both parallel and orthogonal electric and magnetic fields. The fundamental physics is relevant for an advanced undergraduate or graduate quantum mechanics course.