Quantum Logic Spectroscopy with Ions in Thermal Motion

A mixed-species geometric phase gate has been proposed for implementing quantum logic spectroscopy on trapped ions, which combines probe and information transfer from the spectroscopy to the logic ion in a single pulse. We experimentally realize this method, show how it can be applied as a technique for identifying transitions in currently intractable atoms or molecules, demonstrate its reduced temperature sensitivity, and observe quantum-enhanced frequency sensitivity when it is applied to multi-ion chains. Potential applications include improved readout of trapped-ion clocks and simplified error syndrome measurements for quantum error correction.

Popular Summary

Atoms and molecules feature a variety of transitions that can be driven with light. Spectroscopy maps out what frequencies of light are absorbed or emitted for each transition, but for a single atom or molecule, these signals are often too weak to directly detect. This motivated the development of quantum logic spectroscopy (QLS), where an ion is trapped alongside a helper ion. Information is transferred from the spectroscopy ion to the helper through the repulsion of like charges. The helper ion can repeatedly absorb and emit light, thereby amplifying the signal. Traditional QLS requires that the ions’ shared motion is initially frozen. Inspired by techniques developed for quantum computation with ions, we demonstrate an approach to QLS that tolerates some initial ion motion and allows for enhanced spectroscopic sensitivity by entangling multiple ions, rather than observing them individually.

In our version of QLS, entanglement can be used to enhance sensitivity, scaling as the square root of the number of ions under study. We apply it to one or two beryllium ions combined with one or two magnesium ions to demonstrate increased robustness to ion motion and other experimental imperfections, as well as consistency with the expected enhanced sensitivity.

Our approach can be extended in several ways. For example, it can be used in an “atomic combination clock” where two or more species of ions contribute to the timekeeping. Since this technique originates from quantum logic, it may also be straightforwardly modified to detect errors in the context of quantum computation and spectroscopy.

Figure 1

Spin populations for the LI-SI pair (SI, blue; LI, orange). Fits are displayed in matching colors with solid (dashed) curves for fits to SI (LI) data. (a) Rabi spectroscopy with the SI’s spin state initialized to $|{\uparrow }_{\mathrm{SI}}⟩$. (b) Rabi spectroscopy with the SI’s spin state initialized to $|{\downarrow }_{\mathrm{SI}}⟩$. (c) Ramsey spectroscopy with a contrast of 0.89(1) (LI populations) and a phase shift of $\mathrm{\Delta }\varphi =0.01(1)$ between LI and SI sinusoids. (d) Rabi and (e) Ramsey spectroscopy with Doppler cooling only; fits to Ramsey data give a contrast 0.57(2) (LI populations) and a phase shift $\mathrm{\Delta }\varphi =0.21(4)$ between LI and SI sinusoids. Rabi spectroscopy with (f) ${\mathrm{\Omega }}_{\mathrm{SI}}={\mathrm{\Omega }}_{\mathrm{MS}}/2$ and (g) ${\mathrm{\Omega }}_{\mathrm{SI}}=2{\mathrm{\Omega }}_{\mathrm{MS}}$. In all figures, error bars (one sigma) are calculated assuming only quantum projection noise [35]. Each data point represents the average outcome of 200 repetitions of the experiment [100 for (e)].

Figure 2

Spin populations for the four-ion chain LI-SI-SI-LI (SI, blue; LI, orange), initially prepared in the spin state $|{\uparrow }_{\mathrm{LI}}{\uparrow }_{\mathrm{SI}}{\uparrow }_{\mathrm{SI}}{\uparrow }_{\mathrm{LI}}⟩$, performing Ramsey spectroscopy with free evolution time $T_R=500\mu \mathrm{s}$. The data show the same Ramsey-fringe oscillation frequency as the LI-SI data with $T_R=1\mathrm{ms}$, consistent with Heisenberg scaling. We fit sinusoids to the LI-LI and SI-SI data [displayed in matching colors with solid (dashed) curves for fits to SI (LI) data] and extract a contrast of 75(2)% for the LI data and a phase shift between the LI-LI and SI-SI data of $\mathrm{\Delta }\varphi =0.03(3)$. In this experiment, $t_{\mathrm{MS}}\approx 64\mu \mathrm{s}$. Error bars (1 sigma) are calculated assuming quantum projection noise only. Each data point represents the average outcome of 200 repetitions of the experiment.