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

Area of Science:

• Atomic Physics
• Quantum Metrology
• Spectroscopy

Background:

• Trapped-ion optical atomic clocks are sensitive to systematic errors.
• Background-gas collisions can introduce frequency shifts and uncertainties.
• Achieving uncertainties below 10^-18 requires precise error mitigation.

Purpose of the Study:

• To develop a framework for calculating frequency shifts and uncertainties in trapped-ion clocks due to background-gas collisions.
• To apply this framework to an ²⁷Al⁺ clock and achieve a total fractional systematic uncertainty below 10^-18.
• To investigate the impact of collisional heating on the clock's performance.

Main Methods:

• Development of a theoretical framework for collision-induced frequency shifts.
• Application to an ²⁷Al⁺ optical atomic clock.
• Experimental validation using mixed-species ion pair reordering rates to determine background-gas pressure.
• In situ measurement of background-gas pressure.

Main Results:

• A framework for calculating background-gas collision effects was established.
• For an ²⁷Al⁺ clock with 38(19) nPa H₂, collisional heating creates a non-thermal motional state distribution.
• The background-gas collision (BGC) shift was calculated to be -0.6(2.4) × 10^-19.
• The framework was experimentally validated, achieving a total fractional systematic uncertainty below 10^-18.

Conclusions:

• The developed framework accurately quantifies background-gas collision effects in trapped-ion clocks.
• Collisional heating effects, while present, are suppressed in the spectroscopy signal.
• The ²⁷Al⁺ clock demonstrates potential for ultra-high precision timekeeping below 10^-18 uncertainty.