Systematic uncertainty due to background-gas collisions in trapped-ion optical clocks

Abstract

We describe a framework for calculating the frequency shift and uncertainty of trapped-ion optical atomic clocks caused by background-gas collisions, and apply this framework to an ${}^{27}$Al${}^{+}$ clock to enable a total fractional systematic uncertainty below $10^{-18}$. For this clock, with 38(19) nPa of room temperature H${}_2$ background gas, we find that collisional heating generates a non-thermal distribution of motional states with a mean time-dilation shift of order $10^{-16}$ at the end of a 150 ms probe, which is not detected by sideband thermometry energy measurements. However, the contribution of collisional heating to the spectroscopy signal is highly suppressed and we calculate the BGC shift to be $-0.6(2.4)\times 10^{-19}$, where the shift is due to collisional heating time-dilation and the uncertainty is dominated by the worst case $\pm \pi /2$ bound used for collisional phase shift of the ${}^{27}$Al${}^{+}$ superposition state. We experimentally validate the framework and determine the background-gas pressure in situ using measurements of the rate of collisions that cause reordering of mixed-species ion pairs.

arXiv comment13 pages, 7 figures, 3 tables

References in corpus (28)

• Experimental issues in coherent quantum-state manipulation of trapped atomic ions
• Frequency Comparison of Two High-Accuracy Al+ Optical Clocks
• Atomic clock performance beyond the geodetic limit
• An ${}^{27}$Al${}^{+}$ quantum-logic clock with systematic uncertainty below $10^{-18}$
• Single-Ion Atomic Clock with $3\times 10^{-18}$ Systematic Uncertainty
• 1.5 $\mu$m lasers with sub 10 mHz linewidth
• Direct observation of dynamical quantum phase transitions in an interacting many-body system
• Progress in Atomic Fountains at LNE-SYRTE
• Power-Law Distributions for a Trapped Ion Interacting with a Classical Buffer Gas
• Cryogenic Trapped-Ion System for Large Scale Quantum Simulation
• Improved accuracy of the NPL-CsF2 primary frequency standard: evaluation of distributed cavity phase and microwave lensing frequency shifts
• Precision calculation of blackbody radiation shifts for optical frequency metrology
• Dynamics of a ground-state cooled ion colliding with ultra-cold atoms
• Sympathetic ground state cooling and time-dilation shifts in an ${}^{27}{\text{Al}}^{+}$ optical clock
• Sympathetic Cooling of Mixed Species Two-Ion Crystals for Precision Spectroscopy
• A transportable 40Ca+ single-ion clock with $7.7\times 10^{-17}$ systematic uncertainty
• Decoherence of a single-ion qubit immersed in a spin-polarized atomic bath
• Auto-Balanced Ramsey Spectroscopy
• Scattering of Cold Atom Coherences by Hot Atoms: Frequency Shifts from Background Gas Collisions
• Neutral gas sympathetic cooling of an ion in a Paul trap
• Quantum coherence between two atoms beyond Q=10^15
• Kinetics of a single trapped ion in an ultracold buffer gas
• Development of a new UHV/XHV pressure standard (cold atom vacuum standard)
• Probing beyond the laser coherence time in optical clock comparisons
• A Single-Ion Trap with Minimized Ion-Environment Interactions
• Blue-sky bifurcation of ion energies and the limits of neutral-gas sympathetic cooling of trapped ions
• The collisional frequency shift of a trapped-ion optical clock
• Doppler and collisional frequency shifts in trapped-atom clocks

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