Entanglement of Trapped-Ion Qubits Separated by 230 Meters

We report on an elementary quantum network of two atomic ions separated by 230 m. The ions are trapped in different buildings and connected with 520(2) m of optical fiber. At each network node, the electronic state of an ion is entangled with the polarization state of a single cavity photon; subsequent to interference of the photons at a beam splitter, photon detection heralds entanglement between the two ions. Fidelities of up to $(88.0+2.2-4.7)\%$ are achieved with respect to a maximally entangled Bell state, with a success probability of $4\times {10}^{-5}$. We analyze the routes to improve these metrics, paving the way for long-distance networks of entangled quantum processors.

Figure 1

The two-node quantum network. (a) Satellite image (Google Earth, image: Landsat/Copernicus). Nodes A and B are located in separate buildings, connected via a 520(2) m optical-fiber link and have a 230 m line of sight separation. (b) Nodes consist of an ion, a linear Paul trap (four yellow electrodes), and a cavity comprised of two mirrors. The PBSM setup contains a beam splitter (BS), polarizing beam splitters (PBSs), and photon detectors. (c) Energy-level diagram for ${}^{40}{\mathrm{Ca}}^{+}$. When an ion is in state $|S⟩$ and no photons are in the cavity, a laser pulse containing two tones generates the ion-photon entangled state $1/\sqrt{2}(|DV⟩+e^{i\theta }|D^{\prime }H⟩)$, where $|V⟩$ and $|H⟩$ are the polarization components of a cavity photon and $\theta$ is a phase [34]. The frequency difference ${\mathrm{\Delta }}_2-{\mathrm{\Delta }}_1$ is equal to the one between $|D^{\prime }⟩=3{}^2{D}_{5/2}$, $m_j=-3/2$ and $|D⟩=3^2{D}_{5/2}$, $m_j=-5/2$.

Figure 2

Entanglement between ion qubits. (a) Single-photon wave packets measured at each node in a separate calibration experiment. Shown are histograms of photon counts per $1\mathrm{\mu }\mathrm{s}$ time bin for ion-entangled photons from Node A only (orange) and Node B only (green). The gray region indicates when the Raman laser pulse is on. The dashed black lines indicate the window within which coincidence events are evaluated during entanglement experiments. (b) Success probability for a coincidence event heralding either $|{\psi }^{+}⟩$ or $|{\psi }^{-}⟩$ to occur as a function of $T$. (c) Experimentally reconstructed density matrices ${\rho }^{+}(T)$ and ${\rho }^{-}(T)$, for $T=1\mathrm{\mu }\mathrm{s}$. Bar heights indicate amplitudes of matrix entries; colors indicate phases. Amplitudes of the entries for $|{\mathrm{\Psi }}^{\pm }⟩⟨{\mathrm{\Psi }}^{\pm }|$ are outlined for comparison. (d) Fidelity $F^{\pm }$ as a function of $T$. Markers indicate measured values; error bars correspond to 1 standard deviation. Solid lines show an empirical model discussed in the main text, with shaded regions indicating uncertainties. Dashed lines show a partial model omitting photon distinguishability.

Figure 3

(a) Number of coincidences recorded for orthogonal (blue) and parallel (red) polarization projections of photons from Nodes A and B, for the same dataset as in Fig. 2, where the axes are scaled by the ratio of detector efficiencies. Data are plotted as a function of the time difference $\tau$ between photon detection events, binned in $0.5\mathrm{\mu }\mathrm{s}$ intervals. Error bars indicate Poissonian statistics. (b) Diamonds show the two-photon interference visibility calculated from the coincidence data after correction for background counts and detector efficiencies, using Eq. (2). The shaded region indicates the propagation of Poissonian uncertainties. Lines show a master-equation model discussed in the main text.