High-fidelity entanglement of ${}^{43}\mathrm{Ca}^{+}$ hyperfine clock states

In an experiment using the odd calcium isotope ${}^{43}\mathrm{Ca}^{+}$, we combine the merits of a high-fidelity entangling operation on an optical transition (optical qubit) with the long coherence times of two “clock” states in the hyperfine ground state (hyperfine qubit) by mapping between these two qubits. For state initialization, state detection, global qubit rotations, and mapping operations, errors smaller than 1% are achieved, whereas the entangling gate adds errors of 2.3%. Based on these operations, we create Bell states with a fidelity of 96.9(3)% in the optical qubit and a fidelity of 96.7(3)% when mapped to the hyperfine states. In the latter case, the entanglement is preserved for $96\left(3\right)\mathrm{ms}$, exceeding the duration of a single gate operation by three orders of magnitude.

Figure 1

(Color online) (a) Energy levels of ${}^{43}\mathrm{Ca}^{+}$ showing the hyperfine splitting of the atomic states $S_{1∕2}$ and $D_{5∕2}$. Microwave radiation applied to an electrode close to the ions drives the hyperfine qubit encoded in the states ∣↓⟩ and ∣↑⟩. A laser at $729\mathrm{nm}$ excites the ions on the transition from the $S_{1∕2}(F=4)$ to the $D_{5∕2}(F=2,\dots ,6)$ states. It is used for ground-state cooling, state initialization and state discrimination and to excite the optical qubit comprised of the states ∣↓⟩ and ∣⇑⟩ or $\mid {\Uparrow }^{\prime }⟩$. (b) Alignment of the trap axis with respect to the magnetic field. Laser light at $729\mathrm{nm}$ can be directed to the ions from two alternative directions with ${\sigma }^{+}$ polarization (beam 1, ∣⇑⟩) and linear polarization perpendicular to the magnetic field (beam 2, $\mid {\Uparrow }^{\prime }⟩$).

Figure 2

(Color online) Using a bichromatic laser beam, two ${}^{43}\mathrm{Ca}^{+}$ ions are entangled on an optical transition with a maximum target state fidelity of 96.9(3)% at a magnetic field of $6\mathrm{G}$. By introducing a waiting time between creation and the analysis of the Bell state we observe a Gaussian decay of Bell state fidelity (●) (black solid line). Data for the first $3\mathrm{ms}$ are displayed as an inset. When the optical qubit is mapped to the hyperfine qubit subsequent to the gate operation, we obtain a maximum Bell-state fidelity of 96.7(3)% and the lifetime of the entanglement increases to 96(3) ms (★). Measurements taken at a magnetic field of $3.4\mathrm{G}$ give similar results (▲) for the coherence time. Here, the optical qubit $\mid \downarrow ⟩\leftrightarrow D_{5∕2}(F=4,m_F=2)$ in combination with laser beam 2 was used for entangling the ions. Each data point represents 18 000–24 000 individual measurements.