Test of the linearity of quantum mechanics by rf spectroscopy of theBe+9ground state
Abstract
A hyperfine transition in the ground state of $^{9}\mathrm{Be}^{+}$ was used to test a nonlinear generalization of quantum mechanics recently formulated by Weinberg. We searched for a dependence of the frequency of a coherent superposition of two hyperfine states on the populations of the states. We are able to set a limit of 4\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}27}$ on the fraction of binding energy per nucleon of the $^{9}\mathrm{Be}^{+}$ nucleus that could be due to nonlinear corrections to quantum mechanics.
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A constraint on the dimension-five neutron operators of Equation (40) was derived using limits on the spatial variation of the Be+ hyperfine nuclear spin transition as a function of the angle between the spin axis and an external magnetic field.
“A constraint of the dimension five operators of Equation (40) for neutrons was recently derived in [52] using limits on the spatial variation of the hyperfine nuclear spin transition in Be+ as a function of the angle between the spin axis and an external magnetic field [64].”
From Modern Tests of Lorentz Invariance (2005) · cites this paper as [64]
Cites
Geometrical Representation of the Schrödinger Equation for Solving Maser Problems
Feynman, R. P., Vernon, F. L., & Hellwarth, R. W. (1957) · Journal of Applied Physics · doi:10.1063/1.1722572 · Cited by 1,061 · see citing works
Characterization of Frequency Stability
Barnes, J. A., Chi, A. R., Cutler, L. S., Healey, D. J., Leeson, D. B., McGunigal, T. E., Mullen, J. A., Smith, W. L., Sydnor, R. L., Vessot, R. F. C., et al. (1971) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/tim.1971.5570702 · Cited by 849 · see citing works
Białynicki‐Birula, I., & Mycielski, J. (1976) · Annals of Physics · doi:10.1016/0003-4916(76)90057-9 · Cited by 768 · see citing works
Weinberg, S. (1989) · Annals of Physics · doi:10.1016/0003-4916(89)90276-5 · Cited by 494 · see citing works
Sympathetic cooling of trapped ions: A laser-cooled two-species nonneutral ion plasma
Larson, D. J., Bergquist, J., Bollinger, J. J., Itano, W. M., & Wineland, D. J. (1986) · Physical Review Letters · doi:10.1103/physrevlett.57.70 · Cited by 375 · see citing works
Self-citationPrecision tests of quantum mechanics.
Weinberg, S. (1989) · Physical Review Letters · doi:10.1103/physrevlett.62.485 · Cited by 297 · see citing works
Shell-Structure Phase of Magnetically Confined Strongly Coupled Plasmas
Gilbert, S. L., Bollinger, J. J., & Wineland, D. J. (1988) · Physical Review Letters · doi:10.1103/physrevlett.60.2022 · Cited by 259 · see citing works
Self-citationLaser-Cooled-Atomic Frequency Standard
Bollinger, J. J., Prestage, J. D., Itano, W. M., & Wineland, D. J. (1985) · Physical Review Letters · doi:10.1103/physrevlett.54.1000 · Cited by 166 · see citing works
Self-citationStatic properties of a non-neutral 9 Be + -ion plasma
Brewer, L. R., Prestage, J. D., Bollinger, J. J., Itano, W. M., Larson, D. J., & Wineland, D. J. (1988) · Physical Review A · doi:10.1103/physreva.38.859 · Cited by 139 · see citing works
Self-citationPrecision measurement of the ground-state hyperfine constant of Mg+25
Itano, W. M., & Wineland, D. J. (1981) · Physical Review A · doi:10.1103/physreva.24.1364 · Cited by 132 · see citing works
Self-citationNeutron optical tests of nonlinear wave mechanics
Gähler, R., Klein, A. G., & Zeilinger, A. (1981) · Physical Review A · doi:10.1103/physreva.23.1611 · Cited by 117 · see citing works
Search for a Nonlinear Variant of the Schrödinger Equation by Neutron Interferometry
Shull, C. G., Atwood, D. K., Arthur, J., et al. (1980) · Physical Review Letters · doi:10.1103/physrevlett.44.765 · Cited by 103 · see citing works
Proposed neutron interferometer test of some nonlinear variants of wave mechanics
Shimony, A. (1979) · Physical Review A · doi:10.1103/physreva.20.394 · Cited by 84 · see citing works
Lamoreaux, S. K., Jacobs, J. P., Heckel, B. R., Raab, F. J., & Fortson, E. N. (1989) · Physical Review A · doi:10.1103/physreva.39.1082 · Cited by 43 · see citing works
Chupp, T. E., Oteiza, E. R., Richardson, J. M., & White, T. R. (1988) · Physical Review A · doi:10.1103/physreva.38.3998 · Cited by 41 · see citing works
Perpendicular laser cooling of a rotating ion plasma in a Penning trap
Itano, W. M., Brewer, L. R., Larson, D. J., & Wineland, D. J. (1988) · Physical Review A · doi:10.1103/physreva.38.5698 · Cited by 38 · see citing works
Self-citationCharacteristics and performance of miniature NBS passive hydrogen masers
Walls, F. L. (1987) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/tim.1987.6312748 · Cited by 13 · see citing works
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Modern Tests of Lorentz Invariance
Mattingly, D. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-5 · Cited by 1,061 · see citing works
Quantum non-Markovianity: characterization, quantification and detection
Rivas, Á., Huelga, S. F., & Plenio, M. B. (2014) · Reports on Progress in Physics · doi:10.1088/0034-4885/77/9/094001 · Cited by 1,035 · see citing works
Quantum projection noise: Population fluctuations in two-level systems
Itano, W. M., Bergquist, J. C., Bollinger, J. J., Gilligan, J. M., Heinzen, D. J., Moore, F. L., Raizen, M. G., & Wineland, D. J. (1993) · Physical Review A · doi:10.1103/physreva.47.3554 · Cited by 613 · see citing works
Self-citationWeinberg's nonlinear quantum mechanics and the Einstein-Podolsky-Rosen paradox.
Polchinski, J. (1991) · Physical Review Letters · doi:10.1103/physrevlett.66.397 · Cited by 312 · see citing works
A 303-MHz frequency standard based on trapped Be/sup +/ ions
Bollinger, J. J., Heizen, D. J., Itano, W. M., Gilbert, S. L., & Wineland, D. J. (1991) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/tim.1990.1032897 · Cited by 169 · see citing works
Self-citationItano, W. M., Bergquist, J. C., Bollinger, J. J., & Wineland, D. J. (1995) · Physica Scripta · doi:10.1088/0031-8949/1995/t59/013 · Cited by 118 · see citing works
Self-citationShiga, N., Itano, W. M., & Bollinger, J. J. (2011) · Physical Review A · doi:10.1103/physreva.84.012510 · Cited by 30 · see citing works
Self-citationBounds on cubic Lorentz-violating terms in the fermionic dispersion relation
Bertolami, O., & Rosa, J. G. (2005) · Physical Review D · doi:10.1103/physrevd.71.097901 · Cited by 22 · see citing works
- Authors
- Bollinger, J. J., Heinzen, D. J., Itano, W. M., Gilbert, S. L., & Wineland, D. J.
- Affiliations
- National Institute of Standards and Technology (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1989-09-04
- Volume
- 63
- Issue
- 10
- Pages
- 1031-1034
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2002719646
- Cited by
- 151
- References
- 17
- Citations by year
- 2026: 1 · 2025: 5 · 2024: 1 · 2023: 7 · 2022: 3 · 2021: 2 · 2020: 7 · 2018: 1 · 2017: 3 · 2016: 2 · 2015: 2 · 2014: 3 · 2013: 4 · 2012: 2
- FWCI
- 6.60
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Atomic and Molecular Physics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Nuclear physics research studies
- Keywords
- linearity of quantum mechanics, nonlinear quantum mechanics, hyperfine transitions, coherent superposition, RF spectroscopy, binding energy per nucleon, quantum foundations
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