Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Cyclotron frequency shifts arising from polarization forces

Abstract

The cyclotron frequency of a charged particle in a uniform magnetic field B is related to its mass m and charge q by the relationship ωc = qB/m. This simple relationship forms the basis for sensitive mass comparisons using ion cyclotron resonance mass spectroscopy, with applications ranging from the identification of biomolecules1 and the study of chemical reaction rates2 to determinations of the fine structure constant of atomic spectra3. Here we report the observation of a deviation from the cyclotron frequency relationship for polarizable particles: in high-accuracy measurements of a single CO+ ion, a dipole induced in the orbiting ion shifts the measured cyclotron frequency. We use this cyclotron frequency shift to measure non-destructively the quantum state of the CO+ ion. The effect also provides a means to determine to a few per cent the body-frame dipole moment of CO+, thus establishing a method for measuring dipole moments of molecular ions for which few comparably accurate measurements exist4,5,6. The general perturbation that we describe here affects the most precise mass comparisons attainable today7,8, with applications including direct tests of Einstein's mass–energy relationship9 and charge-parity-time reversal symmetry10, and possibly the weighing of chemical bonds7.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: An exaggerated microscopic picture of the polarization force shift of the cyclotron frequency.
Figure 2: The cyclotron frequency ratio R = ωc[N2+]/ωc[CO+].

References

  1. 1

    Marshall, A. G., Hendrickson, C. L. & Shi, S. D. Scaling MS plateaus with FTICR MS. Anal. Chem. 74, 252A–259A (2002)

    CAS  Article  Google Scholar 

  2. 2

    Heninger, M. et al. Successive reactions of iron carbonyl cations with methanol. Int. J. Mass Spectrom. Ion Process. 199, 267–285 (2000)

    CAS  Article  Google Scholar 

  3. 3

    Bradley, M. P., Porto, J. V., Rainville, S., Thompson, J. K. & Pritchard, D. E. Penning trap measurements of the masses of 133Cs, 87Rb, 85Rb, and 23Na with uncertainties ≤ 0.2 ppb. Phys. Rev. Lett. 83, 4510–4513 (1999)

    ADS  CAS  Article  Google Scholar 

  4. 4

    Havenith, M., Zwart, E., Meerts, W. L. & ter Meulen, J. J. Determination of the electric dipole moment of HN2+. J. Chem. Phys. 93, 8446–8451 (1990)

    ADS  CAS  Article  Google Scholar 

  5. 5

    Laughlin, K. B., Blake, G. A., Cohen, R. C., Hovde, D. C. & Saykally, R. J. Determination of the dipole moment of ArH+ from the rotational Zeeman effect by tunable far-infrared laser spectroscopy. Phys. Rev. Lett. 58, 996–999 (1987)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Linnartz, H., Havenith, M., Zwart, E., Meerts, W. L. & ter Meulen, J. J. Determination of the electric-dipole moment of KrH+. J. Mol. Spectrosc. 153, 710–717 (1992)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Rainville, S., Thompson, J. K. & Pritchard, D. E. An ion balance for ultra-high-precision atomic mass measurements. Science 303, 334–338 (2004)

    ADS  CAS  Article  Google Scholar 

  8. 8

    VanDyck, R. S., Zafonte, S. L. & Schwinberg, P. B. Ultra-precise mass measurements using the UW-PTMS. Hyperfine Interact. 132, 163–175 (2001)

    ADS  CAS  Article  Google Scholar 

  9. 9

    Greene, G. L., Dewey, M. S., Kessler, E. G. & Fischbach, E. Test of special relativity by a determination of the Lorentz limiting velocity — does E = mc2? Phys. Rev. D 44, R2216–R2219 (1991)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Gabrielse, G. et al. Precision mass spectroscopy of the antiproton and proton using simultaneously trapped particles. Phys. Rev. Lett. 82, 3198–3201 (1999)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Wei, H. Q., Han, R. S. & Wei, X. Q. Quantum phase of induced dipoles moving in a magnetic field. Phys. Rev. Lett. 75, 2071–2073 (1995)

    ADS  CAS  Article  Google Scholar 

  12. 12

    Bergstrom, I. et al. SMILETRAP — A Penning trap facility for precision mass measurements using highly charged ions. Nucl. Instrum. Methods Phys. Res. A 487, 618–651 (2002)

    ADS  CAS  Article  Google Scholar 

  13. 13

    Jagod, M. F. et al. Infrared spectroscopy of carbo-ions. VI. C-H stretching vibration of the acetylene ion C2H2+ and isotopic species. J. Chem. Phys. 97, 7111–7123 (1992)

    ADS  CAS  Article  Google Scholar 

  14. 14

    Dixon, T. A. & Woods, R. C. Microwave absorption spectrum of the CO+ ion. Phys. Rev. Lett. 34, 61–63 (1975)

    ADS  CAS  Article  Google Scholar 

  15. 15

    Townes, C. H. & Schawlow, A. L. Microwave Spectroscopy (Dover Pub. Inc., New York, 1975)

    Google Scholar 

  16. 16

    Martin, P. A. & Feher, M. CASSCF calculations of the multipole moments and dipole polarizability functions of the X2Σ+ and A2Π states of CO+. Chem. Phys. Lett. 232, 491–496 (1995)

    ADS  CAS  Article  Google Scholar 

  17. 17

    Beier, T. et al. New determination of the electron's mass. Phys. Rev. Lett. 88, 011603 (2002)

    ADS  Article  Google Scholar 

  18. 18

    Huber, K.P. & Herzberg G. (data prepared by Gallager, J.W. & Johnson, R. D.) “Constants of Diatomic Molecules”, NIST Chemistry WebBook, NIST Standard Reference Database Number 69 (eds Lindstrom, P.J. & Mallard, W. G.) (National Institute of Standards and Technology, Gaithersburg, MD, 2003); 〈http://webbook.nist.gov〉 (2003).

  19. 19

    Audi, G., Wapstra, A. H. & Thibault, C. The AME2003 atomic mass evaluation (II). Tables, graphs and references. Nucl. Phys. A 729, 337–676 (2003)

    ADS  Article  Google Scholar 

  20. 20

    DiFilippo, F., Natarajan, V., Boyce, K. R. & Pritchard, D. E. Accurate atomic masses for fundamental metrology. Phys. Rev. Lett. 73, 1481–1484 (1994)

    ADS  CAS  Article  Google Scholar 

  21. 21

    Bhatia, A. K. & Drachman, R. J. Polarizability of helium and the negative hydrogen ion. J. Phys. B 27, 1299–1305 (1994)

    ADS  CAS  Article  Google Scholar 

  22. 22

    Kozlov, M. G. & DeMille, D. Enhancement of the electric dipole moment of the electron in PbO. Phys. Rev. Lett. 89, 133001 (2002)

    ADS  CAS  Article  Google Scholar 

Download references

Acknowledgements

We thank E.G. Myers, G.J. Sussman, J. Wisdom and W. Ketterle for useful discussions. This work was supported by the National Science Foundation and a National Institutes of Standards and Technology Precision Measurement Grant. S.R. acknowledges support from the Fonds pour la Formation de Chercheurs et l'Aide à la Recherche.

Author information

Affiliations

Authors

Corresponding author

Correspondence to James K. Thompson.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Thompson, J., Rainville, S. & Pritchard, D. Cyclotron frequency shifts arising from polarization forces. Nature 430, 58–61 (2004). https://doi.org/10.1038/nature02682

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing