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Chinese Physics B

Sympathetic electromagnetically induced transparency ground state cooling of a 40Ca+–27Al+ pair in an 27Al+ clock

Chenglong Sun, Kaifeng Cui, Sijia Chao, Yuan-Fei Wei, Jinbo Yuan, Jian Cao, Hualin Shu, Xue-Ren Huang

Published Nov 17, 2022• 2 citations
Publisher

Abstract

We report on electromagnetically induced transparency cooling of 40Ca+ to sympathetically cool the three-dimensional secular modes of motion in a 40Ca+–27Al+ two-ion pair near the ground state. We observe simultaneous ground state cooling across all radial modes and axial modes of a 40Ca+–27Al+ ion pair, occupying a broader cooling range in frequency space over 3 MHz. The cooling time is observed to be less than 1 ms. The mean phonon number and heating rates of all motional modes are measured. This study is not only an important step for reducing the secular motion time-dilation shift uncertainty and uptime ratio of 27Al+ optical clock, but also essential for high-fidelity quantum simulations and quantum information processors using trapped ions.

DOI
10.1088/1674-1056/aca39d

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We report on electromagnetically induced transparency cooling of 40Ca+ to sympathetically cool the three-dimensional secular modes of motion in a 40Ca+–27Al+ two-ion pair near the ground state. We observe simultaneous ground state cooling across all radial modes and axial modes of a 40Ca+–27Al+ ion pair, occupying a broader cooling range in frequency space over 3 MHz. The cooling time is observed to be less than 1 ms. The mean phonon number and heating rates of all motional modes are measured. This study is not only an important step for reducing the secular motion time-dilation shift uncertainty and uptime ratio of 27Al+ optical clock, but also essential for high-fidelity quantum simulations and quantum information processors using trapped ions.
A two-ion pair in a linear Paul trap is extensively used in the research of the simplest quantum-logic system; however, there are few quantitative and comprehensive studies on the motional mode coupling of two-ion systems yet. This study proposes a method to investigate the motional mode coupling of sympathetically cooled two-ion crystals by quantifying three-dimensional (3D) secular spectra of trapped ions using molecular dynamics simulations. The 3D resonance peaks of the 40Ca+–27Al+ pair obtained by using this method were in good agreement with the 3D in- and out-of-phase modes predicted by the mode coupling theory for two ions in equilibrium and the frequency matching errors were lower than 2%. The obtained and predicted amplitudes of these modes were also qualitatively similar. It was observed that the strength of the sympathetic interaction of the 40Ca+–27Al+ pair was primarily determined by its axial in-phase coupling. In addition, the frequencies and amplitudes of the ion pair’s resonance modes (in all dimensions) were sensitive to the relative masses of the ion pair, and a decrease in the mass mismatch enhanced the sympathetic cooling rates. The sympathetic interactions of the 40Ca+–27Al+ pair were slightly weaker than those of the 24Mg+–27Al+ pair, but significantly stronger than those of 9Be+–27Al+. However, the Doppler cooling limit temperature of 40Ca+ is comparable to that of 9Be+ but lower than approximately half of that of 24Mg+. Furthermore, laser cooling systems for 40Ca+ are more reliable than those for 24Mg+ and 9Be+. Therefore, 40Ca+ is probably the best laser-cooled ion for sympathetic cooling and quantum-logic operations of 27Al+ and has particularly more notable comprehensive advantages in the development of high reliability, compact, and transportable 27Al+ optical clocks. This methodology may be extended to multi-ion systems, and it will greatly aid efforts to control the dynamic behaviors of sympathetic cooling as well as the development of low-heating-rate quantum logic clocks.
We report on Raman sideband cooling of ^{25}Mg^{+} to sympathetically cool the secular modes of motion in a ^{25}Mg^{+}-^{27}Al^{+} two-ion pair to near the three-dimensional (3D) ground state. The evolution of the Fock-state distribution during the cooling process is studied using a rate-equation simulation, and various heating sources that limit the efficiency of 3D sideband cooling in our system are discussed. We characterize the residual energy and heating rates of all of the secular modes of motion and estimate a secular motion time-dilation shift of -(1.9±0.1)×10^{-18} for an ^{27}Al^{+} clock at a typical clock probe duration of 150 ms. This is a 50-fold reduction in the secular motion time-dilation shift uncertainty in comparison with previous ^{27}Al^{+} clocks.
Single-ion optical clocks have shown systematic frequency uncertainties below 10 − 18 , but typically require more than one week of averaging to achieve a corresponding statistical uncertainty. This time can be reduced with longer probe times, but comes at the cost of a higher time-dilation shift due to motional heating of the ions in the trap. We show that sympathetic ground-state cooling using electromagnetically induced transparency of an Al + clock ion via a cotrapped Ca + ion during clock interrogation suppresses the heating of the ions. Al + can be kept close to the motional ground state, independent from the chosen interrogation time, at a relative time-dilation shift of ( − 1.69 ± 0.20 ) × 10 − 18 . The Ca + cooling light introduces an additional light shift on the Al + clock transition of ( − 9.3 ± 1.1 ) × 10 − 18 . We project that the uncertainty of this light shift can be further reduced by nearly an order of magnitude. This sympathetic cooling enables seconds of interrogation time with 10 − 19 motional and cooling laser-induced uncertainties for Al + and can be employed in other ion clocks as well.
We report on Raman sideband cooling of 25 Mg þ to sympathetically cool the secular modes of motion in a 25 Mg þ -27 Al þ two-ion pair to near the three-dimensional (3D) ground state.The evolution of the Fock-state distribution during the cooling process is studied using a rate-equation simulation, and various heating sources that limit the efficiency of 3D sideband cooling in our system are discussed.We characterize the residual energy and heating rates of all of the secular modes of motion and estimate a secular motion time-dilation shift of -ð1.9 Æ 0.1Þ × 10 -18 for an 27 Al þ clock at a typical clock probe duration of 150 ms.This is a 50-fold reduction in the secular motion time-dilation shift uncertainty in comparison with previous 27 Al þ clocks.
Abstract We achieve the sympathetic sideband cooling of a 40 Ca + – 27 Al + pair. Both axial modes of the two-ion chain are cooled simultaneously to near the ground state of the motion. The center of mass mode is cooled to an average phonon number of 0.052(9), and the breathing mode is cooled to 0.035(6). The heating rates of both a single 40 Ca + and the 40 Ca + – 27 Al + pair are measured and compared. This work is a fundamental step toward the implementation of a 40 Ca + – 27 Al + quantum logic clock.
Electromagnetically-induced-transparency (EIT) cooling is a ground-state cooling technique for trapped particles. EIT offers a broader cooling range in frequency space compared to more established methods. In this work, we experimentally investigate EIT cooling in strings of trapped atomic ions. In strings of up to 18 ions, we demonstrate simultaneous ground-state cooling of all radial modes in under 1 ms. This is a particularly important capability in view of emerging quantum simulation experiments with large numbers of trapped ions. Our analysis of the EIT cooling dynamics is based on a technique enabling single-shot measurements of phonon numbers, by rapid adiabatic passage on a vibrational sideband of a narrow transition.