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arXiv:1608.05047 · Physical Review Letters

Sympathetic Ground State Cooling and Time-Dilation Shifts in an Al 27 + Optical Clock

Jwo-Sy Chen, Samuel M. Brewer, C. W. Chou, D. J. Wineland, David R. Leibrandt, David B. Hume

Published Jan 30, 2017• 102 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.118.053002

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Journal of Physics B Atomic Molecular and Optical Physics•Jan 5, 2018•17 citations
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.
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.
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.
Raman sideband cooling of 25^{25}25Mg+^++ -27^{27}27Al+^++ ions pair and observation of quantum logic spectra
We perform quantum logic spectroscopy (QLS) on 27^{27}27Al+^++ ion 1^11S0_00​ - 3^33P1_11​ transition, which is an important step toward the QLS based 27^{27}27Al+^++ ion optical clock. As a precondition of QLS, both the stretch (STR) mode and the common (COM) mode of the 27^{27}27Al+^++ and 25^{25}25Mg+^++ ions pair are cooled to the vibrational ground state by Raman sideband cooling. The mean phonon number is measured to be 0.10(1) for the STR mode and 0.01(1) for the COM mode, respectively. The heating rate is evaluated to be 13(3) phonons/s for the STR mode and 5.5(1) phonons/s for the COM mode.
We describe an optical atomic clock based on quantum-logic spectroscopy of the ^{1}S_{0}↔^{3}P_{0} transition in ^{27}Al^{+} with a systematic uncertainty of 9.4×10^{-19} and a frequency stability of 1.2×10^{-15}/sqrt[τ]. A ^{25}Mg^{+} ion is simultaneously trapped with the ^{27}Al^{+} ion and used for sympathetic cooling and state readout. Improvements in a new trap have led to reduced secular motion heating, compared to previous ^{27}Al^{+} clocks, enabling clock operation with ion secular motion near the three-dimensional ground state. Operating the clock with a lower trap drive frequency has reduced excess micromotion compared to previous ^{27}Al^{+} clocks. Both of these improvements have led to a reduced time-dilation shift uncertainty. Other systematic uncertainties including those due to blackbody radiation and the second-order Zeeman effect have also been reduced.
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.
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.