Hyperfine and optical barium ion qubits

State preparation, qubit rotation, and high fidelity readout are demonstrated for two different ${}^{137}\mathrm{Ba}{}^{+}$ qubit types. First, an optical qubit on the narrow $6S_{1/2}$ to $5D_{5/2}$ transition at 1.76 $\mu$m is implemented. Then, leveraging the techniques developed there for readout, a ground-state hyperfine qubit using the magnetically insensitive transition at 8 GHz is accomplished.

Figure 1

A representation of the energy levels in ${}^{137}\mathrm{Ba}{}^{+}$, and the transitions accessed by various lasers. The ion is cooled on the 493-nm transition with 8.037-GHz sidebands and repumped with a 650-nm laser diode. Shelving to the $D_{5/2}$ state is accomplished through coherent excitation with the 1.76-$\mu$m laser. Hyperfine structure of the $D$ states is not shown.

Figure 2

A histogram of ion brightness for two cases; where the ion has been deliberately shelved by disabling the red laser (dark) and where it has not (light). Each case has 5000 data points, and represents a cooling-laser exposure time of 10 ms. The inset shows a zoom in of the overlap region at 6 and 7 photon counts. In this region, there are 13 offending events out of a total of 10 000 runs, corresponding to a detection fidelity of $99.87\%$.

Figure 3

The optical setup for the 1.76-$\mu$m laser. The laser power is split between laser stabilization and ion state manipulation. The laser is servo locked to a Zerodur-spaced cavity using a Pound-Drever-Hall technique, where frequency modulation is introduced by a double-passed AOM (DPAOM), whose drive frequency is modulated by an in-phase–quadrature (I-Q) modulator. The laser light intended for the ion is switched and frequency shifted by a separate AOM.

Figure 4

Coherent excitation of the 1.76-$\mu$m transition. The probability of detecting the ion in the dark state is plotted against the time for which the laser is exposed to the ion. Readout is accomplished in about 20 ms by activating the cooling lasers. The Rabi frequency is observed to be about 50 kHz with a decay time of 120 $\mu \mathrm{s}$. These parameters were determined by a least-squares fit to a sine wave with a Gaussian decay envelope, which is shown by the solid line.

Figure 5

The qubit state after an 8-GHz resonant pulse. The maximum probability of a dark ion is limited by optical pumping and the shelving efficiency, while the minimum is limited by coherence of the hyperfine qubit. At longer exposure times, the maximum shelving probability is seen to decrease due to magnetic noise of the 1.76-$\mu$m transition, while the minimum probability remains $0\%$. The Rabi frequency is 15 kHz, again obtained through a fit, which is shown as a solid line.