A Liquid-Nitrogen-Cooled Ca+ Ion Optical Clock with a Systematic Uncertainty of 4.4E-19

We report a single-ion optical clock based on the 4S_1/2-3D_5/2 transition of the 40Ca+ ion, operated in a liquid nitrogen cryogenic environment,achieving a total systematic uncertainty of 4.4E-19. We employ a refined temperature evaluation scheme to reduce the frequency uncertainty due to blackbody radiation (BBR), and the 3D sideband cooling has been implemented to minimize the second-order Doppler shift. We have precisely determined the average Zeeman coefficient of the 40Ca+ clock transition to be 14.345(40) Hz/mT^2, thereby significantly reducing the quadratic Zeeman shift uncertainty. Moreover, the cryogenic environment enables the lowest reported heating rate due to ambient electric field noise in trapped-ion optical clocks.

💡 Research Summary

This paper reports on the development and performance of a second-generation liquid-nitrogen-cooled single-ion optical clock based on the 4S1/2 → 3D5/2 transition of the 40Ca+ ion, designated LNCIOC Ca+-2. The clock achieves a remarkable total systematic uncertainty of 4.4×10^-19, representing the lowest reported uncertainty for any optical clock to date.

The achievement stems from a comprehensive approach addressing multiple limiting factors. The dominant source of uncertainty in previous Ca+ clocks, the blackbody radiation (BBR) shift, was drastically reduced by operating the ion in a cryogenic environment at approximately 79.5 K. The team implemented refined engineering solutions to ensure temperature uniformity, including sealing ventilation holes in the BBR cavity, improving thermal contacts with silver foils, and winding electrode wires around the liquid nitrogen container for pre-cooling. This resulted in a BBR shift uncertainty of 3.5×10^-19.

To minimize the second-order Doppler shift caused by the ion’s secular motion, three-dimensional sideband cooling (3D SBC) was employed. Sequential cooling on the first-order red sidebands of all three motional modes (X, Y, Z) reduced the average occupation numbers to below 0.11 quanta. Furthermore, the cryogenic environment led to the lowest reported heating rates due to ambient electric field noise, measured between 0.43 and 1.31 quanta/s for the different modes. The resulting uncertainty contribution from the second-order Doppler shift was evaluated to be 0.4×10^-19.

The uncertainty from the quadratic Zeeman shift was significantly reduced by performing a precise measurement of the average Zeeman coefficient (αz) for the clock transition. By comparing two optical clocks under different DC magnetic fields, the coefficient was determined to be αz = 14.345(15) Hz/mT². This precise knowledge allowed the corresponding uncertainty to be reduced to 0.5×10^-19.

Other systematic effects were carefully evaluated and controlled. The trap RF frequency was set close to the “magic” frequency of 24.801 MHz to cancel excess micromotion-induced shifts, leading to an uncertainty of 1.4×10^-19. The frequency shift due to collisions with background helium gas was estimated using a non-perturbative quantum framework, contributing 1.8×10^-19 to the uncertainty budget. The hyper Ramsey interrogation scheme was used to suppress the AC Stark shift from the clock laser and the AOM phase chirp effect, keeping their contributions below 1×10^-19.

In conclusion, this work demonstrates that integrating cryogenic operation, advanced cooling techniques, and precision metrology of fundamental atomic parameters can push optical clock performance to the 10^-19 uncertainty level. While the BBR shift remains the largest contributor, future work employing even lower temperatures (e.g., liquid helium cooling) or more direct vacuum assessment methods promises further improvements towards the 10^-20 regime. The demonstrated suppression of electric field noise heating in a cryogenic environment also highlights a promising path for enhancing coherence times in trapped-ion systems.