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Michelson–Morley analogue for electrons using trapped ions to test Lorentz symmetry

Abstract

All evidence so far suggests that the absolute spatial orientation of an experiment never affects its outcome. This is reflected in the standard model of particle physics by requiring all particles and fields to be invariant under Lorentz transformations. The best-known tests of this important cornerstone of physics are Michelson–Morley-type experiments verifying the isotropy of the speed of light1,2,3. For matter, Hughes–Drever-type experiments4,5,6,7,8,9,10,11 test whether the kinetic energy of particles is independent of the direction of their velocity, that is, whether their dispersion relations are isotropic. To provide more guidance for physics beyond the standard model, refined experimental verifications of Lorentz symmetry are desirable. Here we search for violation of Lorentz symmetry for electrons by performing an electronic analogue of a Michelson–Morley experiment. We split an electron wave packet bound inside a calcium ion into two parts with different orientations and recombine them after a time evolution of 95 milliseconds. As the Earth rotates, the absolute spatial orientation of the two parts of the wave packet changes, and anisotropies in the electron dispersion will modify the phase of the interference signal. To remove noise, we prepare a pair of calcium ions in a superposition of two decoherence-free states, thereby rejecting magnetic field fluctuations common to both ions12. After a 23-hour measurement, we find a limit of h × 11 millihertz (h is Planck’s constant) on the energy variations, verifying the isotropy of the electron’s dispersion relation at the level of one part in 1018, a 100-fold improvement on previous work9. Alternatively, we can interpret our result as testing the rotational invariance of the Coulomb potential. Assuming that Lorentz symmetry holds for electrons and that the photon dispersion relation governs the Coulomb force, we obtain a fivefold-improved limit on anisotropies in the speed of light2,3. Our result probes Lorentz symmetry violation at levels comparable to the ratio between the electroweak and Planck energy scales13. Our experiment demonstrates the potential of quantum information techniques in the search for physics beyond the standard model.

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Figure 1: Rotation of the quantization axis of the experiment with respect to the Sun as the Earth rotates.
Figure 2: Oscillation of the decoherence-free state.
Figure 3: Outline of the experimental scheme.
Figure 4: Frequency measurements for 40Ca+.

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References

  1. Michelson, A. A. & Morley, E. W. On the relative motion of the Earth and the luminiferous ether. Am. J. Sci. 34, 333–345 (1887)

    Article  ADS  Google Scholar 

  2. Herrmann, S. et al. Rotating optical cavity experiment testing Lorentz invariance at the 10−17 level. Phys. Rev. D 80, 105011 (2009)

    Article  ADS  Google Scholar 

  3. Eisele, Nevsky, A. Yu. & Schiller, S. Laboratory test of the isotropy of light propagation at the 10−17 level. Phys. Rev. Lett. 103, 090401 (2009)

    Article  ADS  Google Scholar 

  4. Hughes, V. W., Robinson, H. G. & Beltran-Lopez, V. Upper limit for the anisotropy of inertial mass from nuclear resonance experiments. Phys. Rev. Lett. 4, 342–344 (1960)

    Article  ADS  Google Scholar 

  5. Drever, R. W. P. A search for anisotropy of inertial mass using a free precession technique. Phil. Mag. 6, 683–687 (1961)

    Article  ADS  Google Scholar 

  6. Smiciklas, M., Brown, J. M., Cheuk, L. W., Smullin, S. J. & Romalis, M. V. New test of local Lorentz invariance using a 21Ne-Rb-K comagnetometer. Phys. Rev. Lett. 107, 171604 (2011)

    Article  ADS  CAS  Google Scholar 

  7. Allmendinger, F. et al. Upper limit for the anisotropy of inertial mass from nuclear resonance experiments. Phys. Rev. Lett. 112, 110801 (2014)

    Article  ADS  CAS  Google Scholar 

  8. Peck, S. K. et al. Upper limit for the anisotropy of inertial mass from nuclear resonance experiments. Phys. Rev. A 86, 012109 (2012)

    Article  ADS  Google Scholar 

  9. Hohensee, M. A. et al. Limits on violations of Lorentz symmetry and the Einstein equivalence principle using radio-frequency spectroscopy of atomic dysprosium. Phys. Rev. Lett. 111, 050401 (2013)

    Article  ADS  CAS  Google Scholar 

  10. Altschul, B. Testing electron boost invariance with 2S–1S hydrogen spectroscopy. Phys. Rev. D 81, 041701(R) (2010)

    Article  ADS  Google Scholar 

  11. Matveev, A. et al. Precision measurement of the hydrogen 1S–2S frequency via a 920-km fiber link. Phys. Rev. Lett. 110, 230801 (2013)

    Article  ADS  Google Scholar 

  12. Roos, C. F., Chwalla, M., Kim, K., Riebe, M. & Blatt, R. ‘Designer atoms’ for quantum metrology. Nature 443, 316–319 (2006)

    Article  ADS  CAS  Google Scholar 

  13. Kostelecký, V. A. & Potting, R. CPT, strings, and meson factories. Phys. Rev. D 51, 3923–3935 (1995)

    Article  ADS  Google Scholar 

  14. Kostelecký, V. A. & Samuel, S. Spontaneous breaking of Lorentz symmetry in string theory. Phys. Rev. D 39, 683–685 (1989)

    Article  ADS  Google Scholar 

  15. Hořava, P. Quantum gravity at a Lifshitz point. Phys. Rev. D 79, 084008 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  16. Pospelov, M. & Shang, Y. Lorentz violation in Horava-Lifshitz-type theories. Phys. Rev. D 85, 105001 (2012)

    Article  ADS  Google Scholar 

  17. Nibbelink, S. G. & Pospelov, M. Lorentz violation in supersymmetric field theories. Phys. Rev. Lett. 94, 081601 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  18. Liberati, S. & Mattingly, D. Lorentz breaking effective field theory models for matter and gravity: theory and observational constraints. Preprint at http://arxiv.org/abs/1208.1071 (2012)

  19. Colladay, D. & Kostelecký, V. A. CPT violation and the standard model. Phys. Rev. D 55, 6760–6774 (1997)

    Article  ADS  CAS  Google Scholar 

  20. Colladay, D. & Kostelecký, V. A. Lorentz-violating extension of the standard model. Phys. Rev. D 58, 116002 (1998)

    Article  ADS  Google Scholar 

  21. Russell, N. & Kostelecký, V. A. Data tables for Lorentz and CPT violation. Rev. Mod. Phys. B 83, 11–31 (2011)

    Article  ADS  Google Scholar 

  22. Müller, H., Herrmann, S., Saenz, A., Peters, A. & Lämmerzahl, C. Optical cavity tests of Lorentz invariance for the electrons. Phys. Rev. D 68, 116006 (2003)

    Article  ADS  Google Scholar 

  23. Müller, H. Testing Lorentz invariance by the use of vacuum and matter filled cavity resonators. Phys. Rev. D 71, 045004 (2005)

    Article  ADS  Google Scholar 

  24. Kostelecký, V. A. & Lane, C. Constraints on Lorentz violation from clock-comparison experiments. Phys. Rev. D 60, 116010 (1999)

    Article  ADS  Google Scholar 

  25. Chwalla, M. et al. Precision spectroscopy with two correlated atoms. Appl. Phys. B 89, 483–488 (2007)

    Article  ADS  CAS  Google Scholar 

  26. Chou, C. W., Hume, D. B., Rosenband, T. & Wineland, D. J. Optical clocks and relativity. Science 329, 1630–1633 (2010)

    Article  ADS  CAS  Google Scholar 

  27. Madej, A. A., Dubé, P., Zhou, Z., Bernard, J. E. & Gertsvolf, M. 88Sr+ 445-THz single-ion reference at the 10−17 level via control and cancellation of systematic uncertainties and its measurement against the SI second. Phys. Rev. Lett. 109, 203002 (2012)

    Article  ADS  Google Scholar 

  28. Iskrenova-Tchoukova, E. & Safronova, M. S. Theoretical study of lifetimes and polarizabilities in Ba+. Phys. Rev. A 78, 012508 (2008)

    Article  ADS  Google Scholar 

  29. Safronova, M. S. et al. Highly-charged ions for atomic clocks, quantum information, and search for α-variation. Phys. Rev. Lett. 113, 030801 (2014)

    Article  ADS  CAS  Google Scholar 

  30. Wolf, P., Chapelet, F., Bize, S. & Clairon, A. Cold atom clock test of Lorentz invariance in the matter sector. Phys. Rev. Lett. 96, 060801 (2006)

    Article  ADS  Google Scholar 

  31. Kostelecký, V. A. & Mewes, M. Signals for Lorentz violation in electrodynamics. Phys. Rev. D 66, 056005 (2002)

    Article  ADS  Google Scholar 

  32. Bailey, Q. & Kostelecký, V. A. Lorentz-violating electrostatics and magnetostatics. Phys. Rev. D 70, 076006 (2004)

    Article  ADS  Google Scholar 

  33. Häffner, H. et al. Robust entanglement. Appl. Phys. B 81, 151–153 (2005)

    Article  ADS  Google Scholar 

  34. Yu, N., Zhao, X., Dehmelt, H. & Nagournet, W. Stark shift of a single barium ion and potential application to zero-point confinement in a rf trap. Phys. Rev. A 50, 2738–2741 (1994)

    Article  ADS  CAS  Google Scholar 

  35. Safronova, M. S. & Johnson, W. R. All-order methods for relativistic atomic structure calculations. Adv. At. Mol. Opt. Phys. 55, 191–233 (2008)

    Article  ADS  CAS  Google Scholar 

  36. Tupitsyn, I. I. et al. Magnetic-dipole transition probabilities in B-like and Be-like ions. Phys. Rev. A 72, 062503 (2005)

    Article  ADS  Google Scholar 

  37. Tupitsyn, I. I. et al. Relativistic calculations of the charge-transfer probabilities and cross sections for low-energy collisions of H-like ions with bare nuclei. Phys. Rev. A 82, 042701 (2010)

    Article  ADS  Google Scholar 

  38. Kramida, A. Ralchenko, Yu., Reader, J. & NIST ASD Team. NIST Atomic Spectra Database (version 5.1)http://physics.nist.gov/asd (NIST, 2013)

  39. Kreuter, A. et al. Experimental and theoretical study of the 3d2D–level lifetimes of 40Ca+. Phys. Rev. A 71, 032504 (2005)

    Article  ADS  Google Scholar 

  40. Jiang, D., Arora, B. & Safronova, M. S. Electric quadrupole moments of metastable states of Ca+, Sr+, and Ba+. Phys. Rev. A 78, 022514 (2008)

    Article  ADS  Google Scholar 

  41. Altschul, B. Limits on Lorentz Violation from synchrotron and inverse Compton sources. Phys. Rev. Lett. 96, 201101 (2006)

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

This work was supported by the NSF CAREER programme grant no. PHY 0955650 and NSF grants no. PHY 1212442 and no. PHY 1404156, and was performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. We thank H. Müller for critical reading of the manuscript.

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Authors and Affiliations

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Contributions

H.H., M.A.H. and T.P. had the idea for the experiment. T.P. and M.R. carried out the measurements. S.G.P., I.I.T. and M.S.S. calculated the sensitivity of the energy to Lorentz violation. T.P., M.A.H. and H.H. wrote the main part of the manuscript. S.G.P., I.I.T. and M.S.S. wrote the Methods section on calculating the energy shift. All authors contributed to the discussions of the results and manuscript.

Corresponding authors

Correspondence to T. Pruttivarasin or H. Häffner.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Cancellation of the contributions from the magnetic field gradient.

The frequency measurements of the states and for a Ramsey duration of 100 ms are shown in the top green (fL) and bottom blue (fR) data sets, respectively. We offset both data sets for visualization purposes. The contribution from the magnetic field gradient is subtracted out in the average frequency , which is shown as red data points.

Extended Data Table 1 Lowest-order DF, DF+RPA, CI+SD and all-order results for the 〈3d 2DJ|p2|3d 2DJ〉 and 〈3d 2DJ||T(2)||3d 2DJ〉 matrix elements in Ca+ in atomic units
Extended Data Table 2 Amplitudes of various frequency components for expressed in terms of in the SCCEF

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Pruttivarasin, T., Ramm, M., Porsev, S. et al. Michelson–Morley analogue for electrons using trapped ions to test Lorentz symmetry. Nature 517, 592–595 (2015). https://doi.org/10.1038/nature14091

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