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 light. For matter, Hughes-Drever-type experiments 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 ions. 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 10(18), a 100-fold improvement on previous work. 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 light. Our result probes Lorentz symmetry violation at levels comparable to the ratio between the electroweak and Planck energy scales. Our experiment demonstrates the potential of quantum information techniques in the search for physics beyond the standard model.

Effects of Lorentz-symmetry violation on the spectra of rare-earth ions in a crystal field

“…Er 3+ is a particularly interesting case, as the optical coherence of the J = 15/2 → J = 13/2 transition is particularly long-lived at 4.4 ms for 0.001% doping concentration Er 3+ :Y 2 SiO 5 [25]. An experiment that is sensitive to a 1 mHz orientation-dependent modulation of the Z 1 → Y 1 optical transition in Er 3+ :Y 2 SiO 5 could measure spatial components of the electronic c µν tensor as small as 10 −19 , improving upon existing limits by an order of magnitude [7,8]. An experiment measuring orientation-dependent modulations of the THz-scale energy difference between the |c and |e states (see Tab.…”

“…More recently, a still more sensitive measurement of the electron c µν coefficients was obtained by engineering the quantum state of a pair of trapped Ca + ions [8], extending precision tests of electronic LLI past the electroweak (relative to the Planck mass) scale. Both of these experiments operate at or near the interrogation-time-of-flight or atom (ion) shot-noise limit.…”

Highly charged ions for atomic clocks and search for variation of the fine structure constant

“…Highly charged ions (HCI) can be used for building a new generation of very accurate optical clocks [1,2]. This may have many technical applications but also clock transitions in HCI can be used to study fundamental problems of modern physics such as variation of fundamental constants [3], local Lorentz invariance violation [4,5], search for dark matter [6], etc. Having extremely high accuracy of the clocks is crucial for these studies.…”

Highly charged ions for atomic clocks and search for variation of the fine structure constant

“…This may have many technical applications but also clock transitions in HCI can be used to study fundamental problems of modern physics such as variation of fundamental constants [3], local Lorentz invariance violation [4,5], search for dark matter [6], etc. Having extremely high accuracy of the clocks is crucial for these studies.…”