Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:hep-ph/0405143 · Physical Review Letters

Testing Spatial Noncommutativity via Rydberg Atoms

Jian-zu Zhang A B

Published Jul 21, 2004• 108 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.93.043002

Related papers

Searching for effects of Spatial Noncommutativity via a Penning Trap

Jian-zu Zhang A B

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 $\hbar/4$, which is a clear signal of spatial noncommutativity. An experimental verification of this prediction by a Stern-Gerlach-type experiment is suggested.

arXiv:hep-ph/0508042•Aug 3, 2005•0 citations

Testing Spatial Noncommutativity via Magnetic Hyperfine Structure Induced by Fractional Angular Momentum of Rydberg System

Jian-zu Zhang A B, Hongping Liu, Wei Cao +1 more

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.

•Aug 21, 2012•2 citations

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

Jian-Zu Zhang, Hong-Ping Liu, Wei Cao +1 more

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.

arXiv:1205.2474•Europhysics Letters (EPL)•May 1, 2012•3 citations

Fractional Angular Momentum of an Atom on a Noncommutative Plane*

Jian Jing, Qiu-Yue Zhang, Qing xiang Wang +2 more

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 .

Communications in Theoretical Physics•Nov 1, 2019•4 citations

Angular Momentum of Supersymmetric Cold Rydberg Atoms

Jian-zu Zhang A B

Semiunitary transformation is applied to discuss supersymmetrization of cold Rydberg atoms. In the limit of vanishing kinetic energy the lowest angular momentum of the supersymmetric cold Rydberg atom is $3\ensuremath{\Elzxh}/2$. A possible experimental verification is suggested.

arXiv:0901.4832•Physical Review Letters•Jul 1, 1996•28 citations

ANALYSIS OF IMPOSSIBILITY OF TESTING SPATIAL NONCOMMUTATIVITY USING RYDBERG ATOMS IN THE VICINITY OF SADDLE-POINT IN CROSSED ELECTRIC AND MAGNETIC FIELDS

Jian-zu Zhang A B, Li-Ming He, Zhu Yun-Xia

In relation to the current controversy over the need for an experimental test of spatial noncommutativity at the normal quantum scale, the spectra of a Rydberg electron in the vicinity of the saddle-point in a suitable combination of crossed electric and magnetic fields are investigated in both cases of commutative space and noncommutative space. Its local behavior around the saddle-point is clarified. An unbounded mode is revealed. It describes the unbounded direction along which the electron will escape the vicinity of the saddle-point, which means that it is impossible to locate electronic states. This finding indicates that the possibility of testing spatial noncommutativity in the vicinity of the saddle-point is ruled out. Because this unbounded mode applies only to states near the saddle-point, not to those from the outer well, it is suggested that if any test of spatial noncommutativity can be performed by using atoms in the crossed-field, then the test must be performed using states from the outer well, not those close to the saddle-point.

International Journal of Modern Physics A•Jul 30, 2010•2 citations
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.
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.
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 relation to the current controversy over the need for an experimental test of spatial noncommutativity at the normal quantum scale, the spectra of a Rydberg electron in the vicinity of the saddle-point in a suitable combination of crossed electric and magnetic fields are investigated in both cases of commutative space and noncommutative space. Its local behavior around the saddle-point is clarified. An unbounded mode is revealed. It describes the unbounded direction along which the electron will escape the vicinity of the saddle-point, which means that it is impossible to locate electronic states. This finding indicates that the possibility of testing spatial noncommutativity in the vicinity of the saddle-point is ruled out. Because this unbounded mode applies only to states near the saddle-point, not to those from the outer well, it is suggested that if any test of spatial noncommutativity can be performed by using atoms in the crossed-field, then the test must be performed using states from the outer well, not those close to the saddle-point.