Memory coherence of a sympathetically cooled trapped-ion qubit

We demonstrate sympathetic cooling of a ${{}^{43}\text{C}\text{a}}^{+}$ trapped-ion “memory” qubit by a ${{}^{40}\text{C}\text{a}}^{+}$ “coolant” ion sufficiently near the ground state of motion for fault-tolerant quantum logic, while maintaining coherence of the qubit. This is an essential ingredient in trapped-ion quantum computers. The isotope shifts are sufficient to suppress decoherence and phase shifts of the memory qubit due to the cooling light which illuminates both ions. We measure the qubit coherence during ten cycles of sideband cooling, finding a coherence loss of 3.3% per cooling cycle. The natural limit of the method is $O\left({10}^{-4}\right)$ infidelity per cooling cycle.

Figure 1

Frequencies at zero magnetic field of the four hyperfine components of the $S_{1/2}\to P_{1/2}$ transition in ${{}^{43}\text{C}\text{a}}^{+}$, relative to the same transition in ${{}^{40}\text{C}\text{a}}^{+}$. The labels give $F_S:F_P$, the total angular-momentum quantum number for the $S$ $\left(P\right)$ level. ${\Delta }_I$ in Eq. (1) is taken as the smallest isotope shift in the set; the influence of the other components is included via the factor $h$.

Figure 2

Results of scanning a $24\text{−}\mu \text{s}$-Raman probe pulse over the red (rsb) and blue (bsb) sidebands of (a) the in-phase mode and (b) the out-of-phase mode, after cooling. The data show the fraction of times in 500 repetitions that no ${{}^{40}\text{C}\text{a}}^{+}$ fluorescence was observed after a detection pulse. It is fitted with sinc functions, and from the ratio of the fitted amplitudes we obtain ${\overline{n}}_{\text{in}}=0.06\left(3\right)$ and ${\overline{n}}_{\text{out}}=0.07\left(5\right)$. Vertical lines indicate the (known) frequencies of the red sidebands.

Figure 3

(Color online) (a) ${\overline{n}}_{\text{out}}$ as a function of the number of cycles $N$ of pulsed Raman sideband cooling. Each point is obtained from data similar to that shown in Fig. 2. (b) Ramsey fringe amplitude normalized to a control experiment with no sideband cooling cycles. Two data sets are shown (◼, ◆); the results are fitted with exponential decay curves. Insets: (a) two-ion fluorescence image and (b) pulse sequence. Also shown is a single point $(\star )$ from an experiment in which only the ten repump $\sigma$ pulses were applied. The amplitude of this fringe pattern relative to the control experiment is 1.08(9).

Figure 4

The population of the ${{}^{43}\text{C}\text{a}}^{+}$ $S_{1/2}^{F=4}$ level as a function of the duration of a ${{}^{40}\text{C}\text{a}}^{+}$ repump pulse inserted between two $\pi /2$ pulses on the “clock” qubit transition. The initial population of $S_{1/2}^{F=4,M_F=0}$ is $\simeq 0.15$.