No abstract

In attempts to unify the four known fundamental forces in a single quantum-consistent theory, it is suggested that Lorentz symmetry may be broken at the Planck scale. Here we search for Lorentz violation at the low-energy limit by comparing orthogonally oriented atomic orbitals in a Michelson-Morley-type experiment. We apply a robust radiofrequency composite pulse sequence in the 2F7/2 manifold of an Yb+ ion, extending the coherence time from 200 μs to more than 1 s. In this manner, we fully exploit the high intrinsic susceptibility of the 2F7/2 state and take advantage of its exceptionally long lifetime. We match the stability of the previous best Lorentz symmetry test nearly an order of magnitude faster and improve the constraints on the symmetry breaking coefficients to the 10−21 level. These results represent the most stringent test of this type of Lorentz violation. The demonstrated method can be further extended to ion Coulomb crystals.

We study heating of motional modes of a single ion and of extended ion crystals trapped in a linear radio frequency (rf) Paul trap with a precision of Δ n ̄ ̇ ≈ 0.1 phonons s−1. Single-ion axial and radial heating rates are consistent and electric field noise has been stable over the course of four years. At a secular frequency of ω sec = 2π × 620 kHz, we measure n ̄ ̇ = 0.56 ( 6 ) phonons s−1 per ion for the center-of-mass (com) mode of linear chains of up to 11 ions and observe no significant heating of the out-of-phase (oop) modes. By displacing the ions away from the nodal line, inducing excess micromotion, rf noise heats the com mode quadratically as a function of radial displacement r by n ̄ ̇ ( r ) / r 2 = 0.89 ( 4 ) phonons s−1 μm−2 per ion, while the oop modes are protected from rf-noise induced heating in linear chains. By changing the quality factor of the resonant rf circuit from Q = 542 to Q = 204, we observe an increase of rf noise by a factor of up to 3. We show that the rf-noise induced heating of motional modes of extended crystals also depends on the symmetry of the crystal and of the mode itself. As an example, we consider several 2D and 3D crystal configurations. Heating rates of up to 500 ph s−1 are observed for individual modes, giving rise to a total kinetic energy increase and thus a fractional time dilation shift of up to −0.3 × 10−18 s−1 of the total system. In addition, we detail how the excitation probability of the individual ions is reduced and decoherence is increased due to the Debye–Waller effect.

Gravity is not understood at a quantum mechanical level. In an attempt to formulate a single quantum-consistent theory of the four known fundamental forces, it is suggested that spontaneous breaking of Lorentz symmetry might occur at the Planck scale 1,2 . In the low-energy limit, such a Lorentz violation would give rise to small shifts of energy levels with non-spherical atomic orbitals 3 . These could be observed with precision spectroscopy of atoms in a Michelson-Morley type experiment using Earth's rotation [4][5][6] . In this work we perform such an experiment in the long-lived electronic 2 F 7/2 manifold of the Yb + ion. We exploit the high intrinsic susceptibility of this state to Lorentz violation 7 and apply an elaborate radio-frequency spin-echoed Ramsey sequence 8 to investigate the isotropy of space-time with a single trapped ion. A robust composite pulse sequence allows us to extend the coherence time to more than 1 s and accurately compare the orthogonally oriented sublevels of the Zeeman manifold. With a three times higher sensitivity to Lorentz violation compared to the best test to date 6 , we improve the constraints on all the measured Lorentz symmetry breaking coefficients and set their bounds at the 10 −21 level. These results represent the most stringent test of this type of Lorentz violation in the electron-photon sector. The method is readily extendable to multiple ions in Coulomb crystals, enabling improved tests of Lorentz symmetry in the near future.