Abstract
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 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 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 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.
Highlights
Single-ion spectroscopy has lead to accurate optical atomic clock operation and enabled searches for new physics with high sensitivity over the past decades [1]
These are both of fundamental nature to trapping ions in rf-traps, e.g. frequency shifts induced by excess micromotion (EMM) or additional electric field gradients from neighbouring ions, and of a technical nature, e.g. reaching the required homogeneity of spectroscopy beam intensities, electric and magnetic fields over a larger region
We have experimentally studied heating effects from electric field noise on the motion of trapped ions, originating from both dc and rf electric fields
Summary
Single-ion spectroscopy has lead to accurate optical atomic clock operation and enabled searches for new physics with high sensitivity over the past decades [1]. New challenges arise from extending the crystal size and dimension These are both of fundamental nature to trapping ions in rf-traps, e.g. frequency shifts induced by excess micromotion (EMM) or additional electric field gradients from neighbouring ions, and of a technical nature, e.g. reaching the required homogeneity of spectroscopy beam intensities, electric and magnetic fields over a larger region. Many of these effects have been investigated in linear ion chains, where micromotion can be well controlled and uncertainties on frequency shifts are expected to be at the 10−19 level [20, 23]. We calculate the time dilation shifts and the influence from the Debye-Waller effect on each individual ion for spectroscopy applications of extended crystals
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