Motional heating of spatially extended ion crystals

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 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.

Quantum nanofriction in trapped ion chains with a topological defect

“…Experimentally reaching the required temperature regime close to the critical point could be achieved by preparing the system deeper in the pinned phase, where the mode frequency of the kink is high enough in order to allow for sufficient cooling while being energetically well isolated from the residual phonon spectrum [42]. In addition, studies have shown, that heating of short wavelength motional modes by dc electric field noise is strongly suppressed [44][45][46], such that effective cooling of the kink dynamics is possible. The kink in a crystal of 30 ions could be prepared at α − α A = 0.091 where the kink mode exhibits a frequency of 2π • 65.17 kHz at an axial trapping frequency of ω z = 2π • 150 kHz.…”

Dark resonance spectra of trapped ions under the influence of micromotion

“…We show how to retrieve the modulation factor of the ion using a theoretical model to fit the spectra. We also estimate an effective temperature of the ion, evidencing the presence of an additional heating mechanism due to micromotion known as RF heating (Blümel et al, 1989;Kalincev et al, 2021). Moreover, we measure the spectra of more than one ion at the same time and retrieve the modulation factor of each ion through a fit to the model for the full measurement.…”