Accurate microwave control and real-time diagnostics of neutral-atom qubits

We demonstrate accurate single-qubit control in an ensemble of atomic qubits trapped in an optical lattice. The qubits are driven with microwave radiation, and their dynamics tracked by optical probe polarimetry. Real-time diagnostics is crucial to minimize systematic errors and optimize the performance of single-qubit gates, leading to fidelities of 0.99 for single-qubit $\pi$ rotations. We show that increased robustness to large, deliberately introduced errors can be achieved through the use of composite rotations. However, during normal operation the combination of very small intrinsic errors and additional decoherence during the longer pulse sequences precludes any significant performance gain in our current experiment.

Figure 1

(Color online) (a) Experimental setup, showing the optical lattice and the configuration used for optical probe polarimetry. (b) Birefringent phase shift $\phi$ seen by the probe (solid line), and the probe-induced differential light shift $\Delta U$ of the qubit states (dashed line), as a function of the probe detuning from the $6S_{1∕2}(F=4)\to 6P_{1∕2}(F^{\prime }=4)$ transition of the $D_1$ line.

Figure 2

(Color online) Polarimetry signal $S\left(t\right)$ measured during qubit Rabi oscillation, for atoms in free fall (top) and atoms trapped in the optical lattice (bottom). The dark line is experimental data, and the underlying light line is the result of a fit of the form given in Eq. (5). Insets show a close-up of data points (filled circles) and fit for a representative time interval.

Figure 3

Polarimetry signal $S\left(t\right)$ during qubit Rabi oscillation (top) and a rotary-$2\pi$ spin-echo sequence (bottom). An artificially large inhomogeneity in the microwave detuning has been added to demonstrate the robustness of the rotary-$2\pi$ echo.

Figure 4

(Color online) (a) Polarimetry signals $S\left(t\right)$ measured during rotary-$2\pi$ spin-echo sequences. The probe power is reduced by a factor of $\sim 40$ from top to bottom, to demonstrate the longer coherence times and lower signal levels available at lower rates of probe photon scattering. (b) Coherence time ${\tau }_d$ vs probe photon scattering time ${\tau }_s$.

Figure 5

(Color online) (a) Trajectories on the Bloch sphere during the three parts of a composite CORPSE $\pi$-pulse, in the presence of a detuning $\Delta =0.3\chi$. (b) Evolution of the logical-∣1⟩ population during the pulse.

Figure 6

(Color online) Fidelity of a plain and three types of composite $\pi$-pulses, as a function of deliberately applied errors in either the average detuning ${\Delta }_0$ or average resonant Rabi frequency ${\chi }_0$. The pulse sequences are (a) CORPSE, (b) SCROFULOUS, and (c) BB1. Filled and open circles are experimentally measured fidelities for the composite pulses and plain pulses, respectively. Solid lines are theoretical fidelities found by solving the optical Bloch equations, using independently determined inhomogeneities and coherence times.

Figure 7

(a) Polarimetry signals $S\left(t\right)$ measured during a rotary-$2\pi$ spin-echo sequence (top) and a sequence of CORPSE $\pi$-pulses. The nearly identical decay times demonstrate that the CORPSE pulse successfully compensates for detuning errors, with little or no cost incurred from the increased sensitivity to angle errors. (b) Population of the logical-∣1⟩ state after an integral number of CORPSE $\pi$-pulses. Solid circles are experimental data extracted from the signal in (a). Open circles are theoretical values found by solving the optical Bloch equations, using independently determined inhomogeneities and coherence times.