Fig. 1. Schematic diagram of quantum link with quantum repeater. (a) Entanglement swapping between two neighboring elementary links. Each elementary link includes two sources of entangled photon pairs (EPPs), two quantum memories (QMs), and the Bell-state measurement (BSM) device composed of a beam splitter (BS) and two single photon detectors (SPDs). At each end of the elementary link, one member of EPPs is transmitted to the middle point of an elementary link to perform BSM through a long fiber. The result of BSM becomes a heralding signal to herald the establishment of entangled quantum memories at the two end points of each elementary link via entanglement swapping. The other member of EPPs is transmitted to the QM for storage and recall until the entanglement is established for the neighboring elementary link. The recalled member is sent to perform BSM, producing another heralding signal to announce the entanglement between the two neighboring elementary links. The achievement of long-distance entanglement relies on a hierarchical entanglement swapping among these adjacent elementary links. (b) Spectrally multiplexed light–matter interface. A spectrally multiplexed source of EPPs is generated with signal photons at 1532 nm and idler photons at 1549 nm. The signal photons are sent to the on-chip spectrally multiplexed quantum memory (on-chip SMQM) for simultaneous storage and recall, which is based on a fiber-pigtailed laser-written Er3+:LiNbO3 (Er3+:LN) waveguide. The spectrally multiplexed idler photons and recalled signal photons are sent to a BSM for entanglement swapping.

Fig. 2. Schematics of the experimental setup. (a) Source of EPPs. A series of double pulses at 1540.60 nm is sent to pump a fiber-pigtailed periodically poled LiNbO3 (PPLN) waveguide module. Through cascaded second-harmonic generation and spontaneous parametric down conversion processes, the time-bin EPPs are generated with idler photons at 1549.37 nm and signal photons at 1531.93 nm. The idler photons are directly sent to one of the qubit analyzers, and the signal photons are transmitted into the on-chip SMQM. (b) On-chip SMQM. Combining the optical frequency comb (OFC) and the sideband-chirping technology, five AFC sections are prepared in a fiber-pigtailed laser-written Er3+:LN waveguide placed in a dilution refrigerator. The storage time is set to 152 ns. (c), (d) Qubit analyzers. The signal photons recalled from different frequency channels and the corresponding idler photons are filtered by fiber Bragg gratings (FBGs). The entangled states are analyzed using two unbalanced Mach-Zehnder interferometers (UMZIs). The superconducting nanowire single photon detectors (SNSPDs) and the time-to-digital converter (TDC) are used to detect the photons and record the coincidence counts of the detection events, respectively. CW laser: continuous-wave laser; PM: phase modulator; VOA: variable optical attenuator; OS: optical switch; PC: polarization controller; IM: intensity modulator; EDFA: erbium-doped fiber amplifier; DWDM: dense wavelength division multiplexer; CIR: circulator; ISO: isolator. (e) Time sequence. The sequence is continuously repeated during the experiment. A whole time period is 500 ms. The pump laser of AFCs preparation continues for 200 ms. After a waiting time of 20 ms, the continuous pump laser of EPPs is intensity modulated into a series of double pulses with a period of 16 ns, a pulse interval of 1.25 ns, and single pulse duration of 300 ps. We repeatedly send, store, and recall signal photons for a total of 280 ms.

Fig. 3. Storage of correlated photons pairs. (a) Storage and recall of heralded single photons. The storage time is set to 152 ns. The full width at half maximum (FWHM) of a temporal mode is 300 ps. (b) Values of gs,i(2) for correlated photon pairs before quantum storage. (c) Values of gs,i(2) between the idler photons and signal photons recalled from different channels. The measurement time is 200 s and the time-bin width is 100 ps. The error bars are evaluated from the counts assuming the Poissonian detection statistics.

Fig. 4. Tests of the CHSH Bell inequality after quantum storage for channel 1. (a), (b) The phase β dependence of the three-fold coincidence counts CAiBj(α=0,β) involving the port combinations of A1&B1 (blue square), A1&B2 (red circle), A2&B1 (orange diamond), or A2&B2 (green triangle) triggered by the system clock (i, j=1, 2). The error bars represent one standard deviation deduced from Poissonian detection statistics. The time window of the three-fold coincidence counts is 600 ps, and each point was obtained by integrating for 250 s. The blue, red, orange, and green lines are the fitting curves with a 100-time Monte Carlo method. (c) The phase β dependence of the correlation coefficient E(α,β) with the phase α set at 0 and π/2. The error bars are evaluated via propagation of statistical errors. The blue lines are the fitting curves with a 100-time Monte Carlo method.

Fig. 5. Measurement of density matrices for channel 1. (a), (b) The real and imaginary parts of density matrices before quantum storage. (c), (d) The real and imaginary parts of density matrices after quantum storage. Density matrices are calculated using a maximum likelihood estimation for the two photon states.

Fig. 6. The five AFC sections. (a) Optical frequency comb. The five central wavelengths of OFC are λ1=1531.69  nm, λ2=1531.82  nm, λ3=1531.93  nm, λ4=1532.05  nm, and λ5=1532.12  nm. (b) Creation of AFCs. There are five 4-GHz-wide AFC sections with the channel spacing of 15 GHz. The teeth spacing of AFCs is ∼6.58  MHz, corresponding to a storage time of 152 ns. For each AFC, a 50-MHz-wide section is shown.

Fig. 7. A set of typical histograms of coincidence counts in the quantum state tomography of entangled photon pairs after quantum storage for channel 1. (a) Idler-signal coincidence histograms. (b)–(d) Three-fold coincidence histograms corresponding to the orange, green, and purple peaks in the idler-signal coincidence histograms. The time window of the coincidence counts is 600 ps. These typical raw data are measured in the energy-basis projection measurement to states |DD⟩.