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.
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Marshall, A. G., Hendrickson, C. L. & Shi, S. D. Scaling MS plateaus with FTICR MS. Anal. Chem. 74, 252A–259A (2002)
Heninger, M. et al. Successive reactions of iron carbonyl cations with methanol. Int. J. Mass Spectrom. Ion Process. 199, 267–285 (2000)
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)
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)
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)
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)
Rainville, S., Thompson, J. K. & Pritchard, D. E. An ion balance for ultra-high-precision atomic mass measurements. Science 303, 334–338 (2004)
VanDyck, R. S., Zafonte, S. L. & Schwinberg, P. B. Ultra-precise mass measurements using the UW-PTMS. Hyperfine Interact. 132, 163–175 (2001)
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)
Gabrielse, G. et al. Precision mass spectroscopy of the antiproton and proton using simultaneously trapped particles. Phys. Rev. Lett. 82, 3198–3201 (1999)
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)
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)
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)
Dixon, T. A. & Woods, R. C. Microwave absorption spectrum of the CO+ ion. Phys. Rev. Lett. 34, 61–63 (1975)
Townes, C. H. & Schawlow, A. L. Microwave Spectroscopy (Dover Pub. Inc., New York, 1975)
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)
Beier, T. et al. New determination of the electron's mass. Phys. Rev. Lett. 88, 011603 (2002)
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).
Audi, G., Wapstra, A. H. & Thibault, C. The AME2003 atomic mass evaluation (II). Tables, graphs and references. Nucl. Phys. A 729, 337–676 (2003)
DiFilippo, F., Natarajan, V., Boyce, K. R. & Pritchard, D. E. Accurate atomic masses for fundamental metrology. Phys. Rev. Lett. 73, 1481–1484 (1994)
Bhatia, A. K. & Drachman, R. J. Polarizability of helium and the negative hydrogen ion. J. Phys. B 27, 1299–1305 (1994)
Kozlov, M. G. & DeMille, D. Enhancement of the electric dipole moment of the electron in PbO. Phys. Rev. Lett. 89, 133001 (2002)
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.
The authors declare that they have no competing financial interests.
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Thompson, J., Rainville, S. & Pritchard, D. Cyclotron frequency shifts arising from polarization forces. Nature 430, 58–61 (2004). https://doi.org/10.1038/nature02682
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