Motional heating of spatially extended ion 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 ṅ ≈ 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 ṅ = 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 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

Combined atomic clock with blackbody-radiation-shift-induced instability below 10-19under natural environment conditions

We develop a method of synthetic frequency generation to construct an atomic clock with blackbody radiation (BBR) shift uncertainties below 10-19 at environmental conditions with a very low level of temperature control. The proposed method can be implemented for atoms and ions, which have two different clock transitions with frequencies ν1 and ν2 allowing to form a synthetic reference frequency νsyn = (ν1 - ϵν2)/(1 - ϵ), which is absent in the spectrum of the involved atoms or ions. Calibration coefficient ϵ can be chosen such that the temperature dependence of the BBR shift for the synthetic frequency νsyn has a local extremum at an arbitrary operating temperature T0. This leads to a weak sensitivity of BBR shift with respect to the temperature variations near operating temperature T0. As a specific example, the Yb+ ion is studied in detail, where the utilized optical clock transitions are of electric quadrupole (S → D) and octupole (S → F) type. In this case, temperature variations of ±7 K lead to BBR shift uncertainties of less than 10-19, showing the possibility to construct ultra-precise combined atomic clocks (including portable ones) without the use of cryogenic techniques