Multimode Ion-Photon Entanglement over 101 Kilometers

A three-qubit quantum network node based on trapped atomic ions is presented. The ability to establish entanglement between each individual qubit in the node and a separate photon that has traveled over a 101-km-long optical fiber is demonstrated. By sending those photons through the fiber in close succession, a remote entanglement rate is achieved that is greater than when using only a single qubit in the node. Once extended to more qubits, this multimode approach can be a useful technique to boost entanglement-distribution rates in future long-distance quantum networks of light and matter.

Popular Summary

Envisioned networks of entangled quantum systems that span cities and countries would enable a variety of new scientific tools and technological applications. However, the rate at which entanglement can be established between two quantum systems that are tens of kilometers apart or more is strongly limited by the time light takes to travel between them. A proposed solution is to perform many entanglement distribution attempts in parallel (or in close succession) using many quantum systems at each location. Here, we demonstrate this multimoding approach to quantum networking using a multiparticle network node.

Our network node consists of three cotrapped atomic ions at the focus of an optical cavity for efficient photon collection. Using tightly focused laser pulses, ion-entangled photons are generated from each ion sequentially. The three-photon train is then frequency converted to the telecom $C$-band wavelength of 1550 nm and sent over a 101-km-long fiber spool.

First, we observe entanglement between each ion and its photon after the 101 km of travel: a significantly greater distance than the previous state of the art and a precursor to realizing, in the future, remotely entangled ions over this distance via entanglement swapping. Second, by sending those photons through the fiber in close succession, a remote entanglement rate is achieved that is greater than it would be when using only a single ion in the node. Once extended to more ions, this multimode approach can be a useful technique to boost entanglement distribution rates in future long-distance quantum networks of light and matter.

Figure 1

The experimental schematic. (a) Three ${}^{40}$$\mathrm{Ca}$${}^{+}$ ions at neighboring antinodes of an 854-nm vacuum standing-wave mode in an optical cavity. Sequential laser pulses, one on each ion, generate three photons, each entangled by polarization to the ion that emitted it. The inset shows the atomic energy-level diagram: $|S⟩=|4^2{S}_{1/2,m_j=-1/2}⟩$, $|P⟩=|4^2{P}_{3/2,m_j=-3/2}⟩$, $|D⟩=|3^2{D}_{5/2,m_j=-5/2}⟩$, and $|D^{\prime }⟩=|3^2{D}_{5/2,m_j=-3/2}⟩$. The frequency difference ${\mathrm{\Delta }}_2-{\mathrm{\Delta }}_1$ is equal to that between $|D^{\prime }⟩$ and $|D⟩$. (b) The photons are converted to 1550 nm via quantum frequency conversion (QFC), using the system of Refs. [17, 35]. (c) A 101-km-long single-mode spooled fiber channel (SMF-28). (d) Polarization analysis involving half ($\lambda /2$) and quarter ($\lambda /4$) wave plates, a filter network, a polarizing beam splitter (PBS), and superconducting nanowire single-photon detectors (SNSPDs). The narrowest element of the filter network is an air-spaced Fabry-Perot cavity with a 250-MHz line width, centered at 1550 nm [17].

Figure 2

Ion-photon entanglement over 0 km. (a) Histograms of 854-nm photon arrival times. Probability densities are shown on the vertical axis: the number of counts normalized by the number of attempts $A$ and by the time-bin width of $1\text{μ}\mathrm{s}$, measured before QFC in Fig. 1 and without the fiber channel. Three single-photon wave packets are visible. Color is used to demarcate the ion that is expected to have produced the photon, following the ion-coloring scheme in Fig. 1. Time zero is when an acousto-optic modulator received a radio-frequency signal to send a laser pulse to ion 1. The detection efficiencies and quantum states are determined within the 65-$\text{μ}\mathrm{s}$-long time windows shown via the colored vertical lines. The dashed black lines show the results of a theoretical model. (b) Absolute values of the measured density matrices ${\rho }_{ij}^0$ of all nine ion-photon pairs. The ion (photon) involved in each row (column) is constant and is indicated by the colored ball on the left (photon wave packet above). States ${\rho }_{i=j}^0$ are colored red, green, and blue. States ${\rho }_{i\ne j}^0$ are shown in gray. The fidelities $F_{i=j}^0$ of the states ${\rho }_{i=j}^0$ with the state $|\psi (0)⟩⟨\psi (0)|$ (wire mesh) are labeled. For $i\ne j$, the wire mesh shows the fully depolarized states.

Figure 3

Ion-photon entanglement over 101 km. (a) Histograms of 1550-nm-photon arrival times. Probability densities are shown on the vertical axis: normalized by the number of attempts $A^{101}$ and by the time-bin width of $1\text{μ}\mathrm{s}$, measured using the setup of Fig. 1. The color scheme is as described in Fig. 2. The dashed black lines show the results of a theoretical model. (b) The absolute values of the measured ion-photon density matrices ${\rho }_{i=j}^{101}$. The presented states are locally rotated from those reconstructed directly from the data, as described in the text. The fidelities $F_{i=j}^{101}$ of the states ${\rho }_{i=j}^{101}$ with the state $|\psi (0)⟩⟨\psi (0)|$ (wire mesh) are labeled. (c) The conceptual schematic of the experimental sequence. One attempt—involving three Raman laser pulses—took $757\text{μ}\mathrm{s}$ (dashed line labeled “ii”). Attempts using a single ion would have taken $633\text{μ}\mathrm{s}$ (dashed line labeled “i”). “Re. Init.” is the 70-$\text{μ}\mathrm{s}$-long cooling and optical pumping performed after each attempt.

Figure 4

The decoherence of the ion qubit in the absence of spin echoes. The qubit is encoded into the states $|S⟩$ to $|D^{\prime }⟩$. The Ramsey contrast is measured as a function of the waiting time. No spin-echo pulses are executed and the position of a nearby magnetic elevator is fixed. For each value of the waiting time, the following experiment is performed: After a single ion is initialized in the $|S⟩$ state, two laser-driven $\pi /2$ pulses are performed on the qubit transition, separated by the waiting time. By scanning the optical phase $\varphi$ of the second $\pi /2$ pulse, and measuring the excitation probability $P_e$ of the ion, standard Ramsey oscillations are obtained. The Ramsey contrast of the oscillation $C$ is obtained as a fit parameter using the fitting function $P_e=y_0+C\sin (\varphi -{\varphi }_0)/2$. The error bars represent the statistical uncertainty of the fit.