Quantum storage of entangled photons at telecom wavelengths in a crystal

Quantum storage and distribution of entanglement are the key ingredients for realizing a global quantum internet. Compatible with existing fiber networks, telecom-wavelength entangled photons and corresponding quantum memories are of central interest. Recently, 167Er3+ ions have been identified as a promising candidate for an efficient telecom quantum memory. However, to date, no storage of entangled photons, the crucial step of quantum memory using these promising ions, 167Er3+, has been reported. Here, we demonstrate the storage and retrieval of the entangled state of two telecom photons generated from an integrated photonic chip. Combining the natural narrow linewidth of the entangled photons and long storage time of 167Er3+ ions, we achieve storage time of 1.936 μs, more than 387 times longer than in previous works. Successful storage of entanglement in the crystal is certified using entanglement witness measurements. These results pave the way for realizing quantum networks based on solid-state devices.


INTRODUCTION
For fiber-based quantum networks, the distance over which entanglement can be distributed is limited to around 100 km, due to losses in the optical fiber.The quantum-communication efficiency can be greatly enhanced, however, by harnessing quantum-repeater architectures [3][4][5][6][7] .The key building block of such architectures is quantum memory, wherein photonic quantum states are stored in quantum states of matter.Quantum memories have been realized with atomic ensembles [9][10][11][12][13] , single atoms [14][15][16][17][18] and solid-state systems [19][20][21][22][23][24][25][26][27][28] .For the integration of these elements into a quantum network, three general criteria have to be met 7,29,30 : 1. wavelength compatibility with existing telecom networks (i.e., the natural choice for the level transition in the storage device should be around 1.5 µm for low propagation loss of photons in fiber); 2. long storage times; and 3. multiplexed storage capability.One of the most promising candidates for realizing such a memory are solids doped with rare-earth ions.Several recent experiments with non-Kramers ions (that is, ions with an even number of electrons), such as praseodymium or europium, have established the potential to realize practical memories by demonstrating storage in long-lived spin states [31][32][33] , multimode storage 29,33,34 , high efficiencies 35,36 and long storage times 37,38 .These successful demonstrations built on the long ground-state hyperfine lifetimes of non-Kramers ions, which enable efficient optical pumping for high-fidelity initial-state preparations and long hyperfine coherence times.These are inherent properties of non-Kramers ions, as the crystal field for sites with sufficiently low symmetry quenches the electronic angular momenta of these ions.They are essential for realizing an efficient, long-lived quantum memory.However, none of the non-Kramers ions have suitable optical transitions in any of the telecom bands; nonetheless, flying photon at telecom wavelength can be realized either by frequency conversion 11,12,18,[39][40][41] or entanglement heralding with frequency non-degenerate photon-pair sources 20,21,[42][43][44][45][46] .
The erbium ion, a Kramers ion (with an odd number of electrons), has optical transitions in the telecom band around 1,536 nm.However, unlike non-Kramers ions, the electronic magnetic moment of Kramers ions (with halfinteger spin) cannot be quenched by a crystal field, resulting in a short electron spin lifetime 47,48 , making optical pumping of the ground-state electron-spin levels inefficient.Previous studies towards developing quantum memories using erbium ions have suffered from this shortcoming.Previous pioneering works used Er-doped glass fiber and showed the storage of entangled states 49 with an efficiency of ∼1% and storage times of 5 ns, and the storage of heralded single-photon state an efficiency of ∼0.2% and storage times of 50 ns 50 .The fundamental limitations of the memory performance using the Er-doped glass fiber are due to the complex interactions between Er ions and its glassy hosts, posing significant challenges of realizing scalable quantum memory with it, as analyzed in Ref 49 .Moreover, in a crystal waveguide, it was demonstrated a storage efficiency of ∼0.1% and a storage time of around 50 ns 51 .A two-level gradient-echo memory technique was employed to store weak coherent states in a crystal, with a reported efficiency of 0.25% 48 .
Recently, there is a rising interest in isotopically purified Kramers ions due to their long coherence time compared with unpurified ions 8,52-55 .Rančić et al. 8 showed that in a high magnetic field, 167 Er 3+ ions with I = 7/2 possess a hyperfine coherence time of 1.3 s and efficient spin pumping of the ensemble into a single hyperfine state.This seminal work triggered a recent resurgence of interest in using erbium ions for quantum memory, e.g. for on-chip storage of telecom-band classical light at the single-photon intensity level 56 , for efficient initialization using the resolved hyperfine structure for quantum memories 57 , and for on-demand storage of weak coherent light with laser-written waveguides 58 .The next milestone of quantum memory in this system is to store quantum entanglement in 167 Er 3+ ions and show that entanglement is preserved after storage.Our work achieves this goal by implementing following steps: 1.We create a pair of entangled (signal and idler) photons with central wavelengths in the telecom C-band and narrow bandwidth (∼185 MHz) compatible with 167 Er 3+ optical transition; 2. we initialize the 167 Er 3+ quantum memory and then send the signal photon into the memory for quantum storage up to 1.936 µs; 3. after storage, the signal photon is released from the memory; and 4. we analyze the correlation between the released signal photon and the idler photon, which has not been stored, and verify the preservation of entanglement after the quantum memory.

EXPERIMENT AND RESULTS
The schematics of our experimental setup is shown in Fig. 1.The setup consists of an entanglement source (Fig. 1a), a quantum memory (Fig. 1b) and an entanglement analyzer (Fig. 1c).The time-bin entangled photon pairs are generated from an integrated silicon nitride (SiN) [59][60][61][62][63][64][65][66] dual Mach-Zehnder interferometer micro-ring (DMZI-R) resonator [67][68][69][70] , which uses the spontaneous four-wave mixing (SFWM) process (inset of Fig. 2b).As shown in Fig. 1a, the output of a continuous-wave pump laser is chopped by an intensity modulator (IM) into pulses.These pulses are then further amplified with an erbium-doped fiber amplifier (EDFA).Several wavelength-division multiplexers (WDM) are used to clean the spectrum of the pulses, which are subsequently injected into the 'In' port of the SiN DMZI-R resonator (Fig. 2a).A pair of telecom-wavelength photons that are non-degenerate in frequency, signal and idler photons, are generated from the resonator and coupled out from the 'Drop' port.Signal and idler photons are then separated with a WDM.The remaining pump pulses are coupled out from the 'Through' port and detected with a photodiode (PD).We use the detected power signal to monitor the frequency drift between the resonance of the DMZI-R and the pump 66 .The additional 'Add' port is used for calibrating the DMZI-R resonance conditions.The unique structure of the DMZI-R source allows us to independently tune the coupling between the waveguides and the ring resonator for the pump pulses, signal and idler photons.In this way, the pump laser and generated photon pair are coupled at different ports to reduce the on-chip and in-fiber Raman noise generated from the strong pump [67][68][69][70] .The SiN DMZI-R resonator chip is both optically and electrically packaged for long-time stable operation.
Cavity enhanced spontaneous parametric down-conversion has been employed as photon pair source for rare-earth quantum memory, providing narrow-band photons compatible with the memory in the absence of any in-band narrowband filters 71 .The transmission spectrum of this DMZI-R source is shown in Fig. 2b.The quality factors of the signal (about 1536 nm), pump (about 1538 nm) and idler (about 1540 nm) wavelengths are around 1.05 × 10 6 , 0.92 × 10 6 and 1.06 × 10 6 , respectively.Cavity-enhanced SFWM processes enable us to generate high-quality telecom entangled photons with high brightness and narrow linewidth, which are the essential requirements for telecom-compatible quantum memory.Fig. 2c shows the coincidence histogram for a 2.9 mW pulsed pump, with a coincidence window of about 4 ns.The full width at half maximum (FWHM) of the coincidence peak is 1370 ps, which corresponds to a coherence time of 997 ps and 980 ps for the idler and signal photons, respectively 72,73 (see SI for details).These photon-pair coincidence results are consistent with the linewidth of the classical transmission spectrum.To characterize our source, we further measure the coincidence counts (C.C.) rate and the coincidence-to-accidental ratio (CAR) as a function of average pump power with continuous wave (CW) and pulsed pump, shown in Fig. 2d and Fig. 2e, respectively.When we increase the pump power, due to the nature of SFWM, on one hand, we observe the enhancement of coincidence counts; on the other hand, high-order photon pairs reduce the CAR.
In the pulsed-pump case, the output of pump laser is chopped with the IM into pulses with a 4-ns pulse duration and a 32-ns period.By using these pump pulses, we generate time-bin entangled qubit state: in which |e⟩ and |l⟩ represent early and late temporal modes of the single photons, respectively.Photon pairs generated by the DMZI-R are time-bin entangled and the pair-creation time is uncertain within the coherence time of the pump laser.In order to analyze the two-photon entanglement, we send them into two Franson interferometers 74 .Each interferometer has two unbalanced optical paths, where the temporal difference between two optical paths is approximately 32 ns.Note that there are two time parameters that need to be treated carefully: the first one is the time difference between optical paths of one interferometer, ∆T , which needs to match the period of the pump pulses and be larger than the single-photon coherence time; the second one is the difference between this parameter for two interferometers, ∆T 1 − ∆T 2 , which needs to be smaller than the coherence time of the signal and idler photons.We fulfill both requirements by adjusting the pump-pulse period and accurate fiber splicing for both Franson interferometers.We scan the phase of the two unbalanced interferometers by tuning the setpoints of the two proportional-integral-derivative (PID) phase-locking systems for them, and obtain the two-photon quantum interference for the full 2π period, as shown in Fig. 2f.For entanglement analysis, we use the average pulsed pump power of about 2.9 mW, where the CAR decreases to about 12.3.The visibilities (V = max−min max+min ) for these two curves are 78.0 ± 0.4% and 70.5 ± 0.5%.The non-ideal visibilities are mainly due to the high-order photon pairs generated from SFWM process, and the phase fluctuations of the Franson interferometers.To confirm the high-order photon-pair emission's impact on visibilities, we reduce the average power of the pulsed pump to 1.4 mW, and obtain visibilities of 84.8 ± 0.3% and 86.4 ± 0.3% (see SI for details).The phase fluctuations of the Franson interferometers are mainly due to frequency instability of the partial pump laser used as the reference for PID locking (Fig. 1c).
The quantum memory is a 50 ppm doped 167 Er 3+ :Y 2 SiO 5 crystal, which is cut along its D 1 , D 2 and b axes with dimensions of 4 × 5 × 9 mm 3 .A photon-echo-type interaction using an atomic frequency comb (AFC) 75 enables the quantum state to transfer between the single photon and the ensemble of 167 Er 3+ ions.To create an AFC, we use the optical pumping technique to shape the absorption profile of the ionic ensemble into a comb-like structure.The input photon is then absorbed and re-emitted into a well-defined spatial mode because of a collective rephasing of the ions in the AFC.The period of the comb determines the re-emission time and can be reconfigured.
Here we use the 167 Er 3+ ions at site 1, with the 4 I 15/2 → 4 I 13/2 transition at ∼1536.17 nm. 167Er 3+ exhibits eight hyperfine spin states due to a nuclear moment of I = 7/2 (see Fig. 3a).The crystal is placed inside a dilution refrigerator equipped with a superconducting magnet.The pump laser and signal photons propagate along the b axis of the crystal.A magnetic field of about 1.5 T is applied in the D 1 -D 2 plane with an angle of about θ = 120 • to the D 1 axis for a large ground-state Zeeman splitting.The crystal's temperature is about 230 mK, deduced from the thermal-equilibrium population between Zeeman ground levels as a function of magnetic field strength (see SI for details).In this case, the ground-state Zeeman splitting is about 50 times k B T , so that the electron spin is frozen to m e = −1/2, ensuring long lifetimes and coherence times 8 .
To improve the storage efficiency, a polarization laser is applied to enhance the absorption depth by polarizing the nuclear spin before AFC preparation.The polarization is performed partially because the transitions of ∆m I = ±1 and ∆m I = 0 cannot be resolved 56,58 .This is because the inhomogeneous broadening of our sample is larger than the hyperfine splitting.The ions are pumped away from "on" hyperfine states (resonant with the laser) and stored on "off" hyperfine states (off-resonant with the laser).Consequently, the population is still distributed over 8 hyperfine states, but the spectrum profile of optical absorptions has been changed.We show the whole absorption spectrum in Fig. 3b, in which the polarization laser scans from about 550 MHz to 750 MHz blue shifted from the center of the AFC, creating a pit there and consequently enhancing the absorption depth of the AFC.In our experiment, the magnetic field slightly deviates from the D 1 -D 2 plane, lifting the degeneracy of the two classes of 167 Er 3+ ions.To create the desired AFC profiles, we modulate the intensity of the AFC laser into pulses with a period equal to the storage time t M .Its frequency spectrum will be a comb with 1/t M period modulated by a sinc function whose main peak's envelop spans about 200 MHz.A close view of AFC is shown in Fig. 3c, compared with the spectral line-shape of the input signal photon, which shows the bandwidth matching between AFC and the signal photon.In Fig. 3d, we show the zoom-in views of AFC spectrum for 336 ns (upper blue) and 1936 ns (lower red) storage times with frequency periods of about 3 MHz and 0.5 MHz, respectively.For the details on the optimization of storage time, see section 5 of SI.
In order to store the heralded single photon, we align the central frequency of the signal photon with respect to that of the quantum memory.To achieve that, we first coarsely tune the frequency of the photon-pair source by adjusting the temperature of the DMZI-R source.The DMZI-R resonance is sensitive to temperature, which is monitored with a thermistor, and stabilized with a thermoelectric cooler with feedback control.The resonance between the pump laser and the DMZI-R is maintained with a feedback loop by monitoring the remaining pump power at the through port 66 .Another knob we have is the magnetic field applied to the quantum memory.We vary the magnetic-field amplitude to tune the Zeeman splitting and hence the optical transition frequency of 167 Er 3+ ions.We present a typical result for the frequency alignment in Fig. 4a.We show the single counts (S.C.) of the signal (blue) and idler (red) photons as a function of the magnetic-field amplitude.The clear drop of counts of signal photon shows the matching of the absorption frequency of the memory with respect to that of the signal photon.However, it is also important to have a stable count rate for idler photon, as the drop of signal-photon counts can also come from the frequency drift of the pump laser with respect to the DMZI-R.Only by observing the drop of signal-photon counts and, simultaneously, the constant idler-photon counts, we are certain that frequency alignment of the resonance of The second-order correlations (blue) and storage efficiencies (red) as functions of storage time, integrated in 100 s (square) and 40000 s (circle).The second-order correlations stay well above the classical limit, g 2 si (0) = 2. Error bars are derived from Poissonian statistics and error propagation.
167 Er 3+ ions and the signal photon has been achieved.For a more precise alignment of signal photon to the AFC, we scan the pump laser's frequency for SFWM generation and the voltage on the on-chip resistors in finer steps to tune the frequency of the signal photon for achieving maximal storage efficiency, with the magnetic field fixed to 1.5 T. A typical result of 1936 ns storage time is shown in Fig. 4b.
After achieving the frequency alignment, we proceed with storage of the heralded signal photons.The time sequence of signal photons and lasers is controlled by the optical switch and optical shutter, with a 1.8 s polarization window, a 1.9 s AFC pump window, a 0.2 s delay and a 1 s memory window.An acousto-optic modulator (AOM) is inserted to gate the idler photons in synchronization with the memory window (see SI for details).In Fig. 4c, we show the coincidence histograms for different predetermined storage times of 1296 ns, 1616 ns and 1936 ns.The 32-ns period of the side peaks is due to the periodic pulses of the pump laser, which creates accidental coincidence (AC) counts.The cross-correlation function is calculated as g 2 si (0) = psi pspi , where p si is the probability of coincidence detections of idler and signal photons, and p s (p i ) are the probabilities of single detections of signal (idler) photons, respectively.As shown in Fig. 4d, the cross-correlation remains well above the classical bound of thermal light 76,77  The maximum number of temporally multiplexed modes is approximately equal to the time-bandwidth product (TBP) 75 , which is the storage time divided by the time width of the stored photons.In this work, the TBP is about 1936 ns/4 ns = 484.The realized mode number is 60.5, with 32 ns repetition time and 1936 ns storage time.One limitation here is the 32 ns repetition time, which is equal to the time difference of each unbalanced interferometer and should be larger than the single-photon coherence time, as discussed above.This can be solved by either coding the qubits on other degrees of freedom (such as polarization), or still using time-bin qubits but with time multiplexing, in which the 'early' mode of N time-bin qubits can be inserted before the the 'late' mode of the first qubit, thus enhancing the mode capability by a factor of N 78 .
After showing the storage of the heralded single photon, we now present the entanglement-storage results, in which the entanglement of the photon pair is preserved after the signal photon has been stored in the crystal for 1936 ns.To do so, we sent the stored and re-emitted signal photon and the not-stored idler photon into the entanglement analyzer (Fig. 1c), consisting of two unbalanced interferometers, for performing the Franson-type quantum interference experiment.In Fig. 5a, we show the histogram of coincidence between output port 1 for the signal photon and the output port for the idler photon.There are five peaks spanning from 1900 to 1980 ns.The central peak corresponds to the quantum interference peak of the entangled state (Eq.1).By setting the phase of the two unbalanced interferometers in the entanglement analyzer to 0 • and 180 • , we observe fully constructive and destructive interference.The contrast of the central peaks are 76.0 ± 1.8%.In Fig. 5b, the coincidence between output port 2 for the signal photon and the output port for the idler photon is reversed for the same phase setting as in Fig. 5a.This is due to the complementary properties of the interferometers.The contrast of the central peaks are 68.5 ± 2.1%.The outmost two peaks in Fig. 5a,b are phase insensitive, as they correspond to the |el⟩ and |le⟩ coincidence counts, which are distinguishable in time.The other two peaks are the accidental coincidence peaks mentioned above.The results in Fig. 5a and b are integrated in 40000 s.Furthermore, we scan the phase of the two unbalanced interferometers by tuning the setpoints of the two PID phase-locking systems (see SI for details), and obtain two-photon quantum interference for the full 2π period at 1936 ns storage time, as shown in Fig. 5c.
An entanglement witness 79 is employed to determine whether entanglement exists.Existence of entanglement is TABLE 1. Two-fold coincidence visibility (V), the second-order correlation function (g 2 si (0)), and the expectation value of the entanglement witness (⟨W ⟩) for storage time tM = 1936 ns.The coincidence is between the idler photon and one of output ports of the signal photon, port 1/2, see Fig. 1c.

tM(ns)
Signal port V g proved by determining a negative expectation value of the witness operator.The witness used here is given by where 79,80 .Projections onto the X-Y plane can be obtained from the visibility of the Franson interference.Combined with the results for Z basis (Fig. 4d) when the unbalanced interferometers are removed, the expectation value of the witness can be calculated using (see SI for detailed derivation): The results of entanglement witness measurements are shown in Tab. 1, where all values are below the separable boundary of 0, by more than 23 standard deviations.Therefore, our results unambiguously show the successful storage of entangled photons in a crystal for 1936 ns.

DISCUSSIONS AND CONCLUSIONS
Our results represent a significant advancement of quantum memory system.First, we show the storage of entangled photons in 167 Er 3+ :Y 2 SiO 5 , a quantum memory at telecom wavelength, which is a promising candidate for realizing an efficient, long-storage time and broadband quantum memory 8,[56][57][58] .In our work, we have extended the storage time of entangled photons at telecom wavelength more than 387 times longer than previous work 49 .Second, we show a successful combination of quantum memory with an integrated quantum-entanglement source, which generates narrowband entangled photons, is CMOS compatible and hence suitable for scalable fabrication, and easier to use than sources based on bulk optics.We emphasize that the scalable entangled photon-pair sources we use here are essential to the absorptive quantum memory.Unlike emissive quantum memories 81,82 , each absorptive quantum memory requires an entangled photon-pair source.A scalable platform for entangled photon-pair sources is particularly important when a quantum network with multiple entangled photon sources and quantum memories with spatial mode multiplexing are constructed.
Despite these important results, there are several aspects that need to be further improved in our system.To improve the storage efficiency, one could optimize the AFC parameters 75,83 with more efficient initialization protocols with a resolved, long-lived hyperfine structure 8,57 , and enhance the light-matter interactions with impedance-matched cavity 84 and integrated nano-structures 56,58,[85][86][87] .The atomic frequency comb spin wave protocol will facilitate the realization of a quantum memory with longer storage time and on-demand readout.One of such possible protocols was recently demonstrated with Kramers ions in 171 Yb 3+ :Y 2 SiO 5 54 .The level structure of 167 Er 3+ is more complicated than 171 Yb 3+ , which requires more complicated optical pumping and coherent control pulse sequences.On the other hand, the rich level structure of 167 Er 3+ may also bring new possibilities in quantum engineering of photon-atom interactions.With these experimental improvements, we anticipate 167 Er 3+ ions and integrated quantum photonics to become a versatile platform for high-performance quantum memory, enabling the realization of large-scale quantum networks.We note that during the completion of this project, a related work has shown the storage of heralded single photons in Er-doped fiber for up to 230 ns 88 .
The time sequence of the experiment is shown in Fig. S1.First, the polarization laser sweep between 550 MHz and 750 MHz blue shifted from the center of the AFC for 1.8 s, partially polarize the ions and increase the optical depth at the AFC's band.Second, the AFC laser is intensity modulated into pulses with a period equal to the storage time t M and a pulse duration of 6 ns.The AFC preparation process continues for 1.9 s.After a 0.2 s delay, the pump laser of the photon source is intensity modulated into pulses with a period of 32 ns and a pulse duration of 4 ns.The generated signal photons are stored in the memory and retrieved for entanglement analysis.This memory window continues for 1 s, followed by another 0.1 s delay, resulting in a 20% duty cycle of the memory.

Entangled photon pair source
The chip-integrated silicon nitride (SiN) dual Mach-Zehnder interferometer resonator (DMZI-R) source is fabricated by advanced SiN fabrication technology (Ligentec), which provides ultra-low propagation loss.The fibre polarization controller before the two H48 wavelength division multiplexers (WDM) makes sure the light coupled to the chip is in single polarization mode.The light is coupled into or out from the chip by a V groove fibre array with a pitch of about 127 µm.
Our DMZI-R has a radius of about 230 µm and the free spectral range (FSR) is close to 100 GHz for TM mode.The length difference of the two unbalanced MZIs is about 240 µm and hence the DMZI interference period is about 600 GHz.The gaps between the waveguide to the ring at the In-Through side and Add-Drop side are both nominally 500 nm.The relatively large size of components and the small thermo-optic coefficient of silicon nitride reduce the thermal crosstalk between different thermo-optical phase shifters.The resistors on the In-Through MZI, Add-Drop MZI and the central ring are about 3130, 1350, and 2270 Ohms, respectively.The resistor on the ring, in conjunction with the TEC for the whole chip, tunes the wavelength of the photon pairs to match quantum storage and the relative phase between the different paths of the Add-Drop MZI at the same time.
As discussed in main text, the non-ideal visibilities of Franson interference are mainly due to the high-order photon pairs generated from SFWM process, and the phase fluctuations of the Franson interferometers.To confirm the high-order photon-pair emission's impact on visibilities, we reduce the average power of the pulsed pump to 1.4 mW, and obtain visibilities of 84.8 ± 0.3% and 86.4 ± 0.3%, as shown in Fig. S2.

Time correlation of the idler and signal photons
The idler and signal photons are generated simultaneously by a SFWM process, resulting in a defined time correlation.However, the photons are trapped by the MRR cavity and the correlation peak is broadened.The average lifetime of photons in a cavity is given by where ∆ν is the linewidth of the cavity.The probability that a photon escapes from the cavity with a delay of t after its generation is proportional to e −t/T cav .For an idler-start-and-signal-stop detection, the probability of a coincidence with a time difference of τ is given as below: where T i and T s are the cavity lifetime for the idler and signal photons, respectively.By using this model, we obtain the lifetime for the signal and idler photons to be 980 ps and 997 ps respectively, as presented in the Fig. 2c of the main text.  16Er 3+ are not splitted clearly in a low magnetic field.Therefore, we use another 10 ppm doped non-isotopic purified Er 3+ :Y 2 SiO 5 crystal to calibrate the temperature under the similar experiment configuration (such as power and beam size), as shown in Fig. S3.

Optimization of storage time
As shown in Fig. S4, when increasing the magnetic field applied to the crystal, we find 2 side holes splitting from the central hole we burnt.The splitting of the side holes is proportional to the magnetic field (∼ 2.11 MHz/T), which is similar to that in Er 3+ :Ti 4+ :LiNbO 3 waveguide 51 and may also arise from the interactions between the erbium electronic spin and the nuclear spin of Y in the host crystal.With a field of about 1.5 T, the side hole splitting is about 3.17 MHz, corresponding to an AFC spectrum with the storage time of about 315 ns.We optimize the AFC storage time based on: 1.It is half-integer times of 32 ns (time difference of the two arms of the AMZIs), so that the retrieved coincidence peak is at the middle of two accidental peaks (see Fig. 5a, b); 2. It is approximately integer times of 315 ns for reducing the side hole spectrum influences.In this way, we realize quantum storage of the entangled photons for up to 1936 µs, as presented in the main text.Note that these side holes may limit optical excited state storage time in 167 Er 3+ :Y 2 SiO 5 .

Theoretical storage efficiency
In AFC scheme, the theoretical storage efficiency can be calculated from the comb profile as where d and d 0 are the optical depth of AFC and background absorption, and F is the finesse of the AFC 75 .The AFC teeth are considered as Lorentzian peaks here.For a maximal efficiency, the AFC teeth should have a square shape 83 , with an optimized half width of where t M is the storage time.For low optical depth d, the optimized finesse is F =2.The corresponding storage efficiency is given by In this experiment, the optical depth at the AFC's band is about d = 2.1, corresponding to a theoretical efficiency of η S OPT (d) = 17.4%.The background absorption of d 0 = 0.8 reduces the efficiency to η S OPT − d 0 ) × e −d0 = 4.2%.The maximal efficiency we measured is η = 3.5% for 1296 ns storage.The efficiency can be improved by reducing the background absorption and optimizing the finesse and lineshape of the AFC.Moreover, to further enhance the memory efficiency to unity in AFC protocol, one can use the cavity enhanced scheme 84 .

Phase lock of the unbalanced interferometers
In this experiment, the time difference of the unbalanced interferometers is much longer than the coherence time of idler and signal photons, eliminating the single photon interference.The Franson interference of coincidence arises from the coherence of the pump laser, which makes it the natural choice for the reference of the Franson interferometers.
The phase of the Franson interferometers is locked with two PID feedback controllers by using the transmission of the pump laser as a reference.With PID controllers, we cannot lock the phase of each interferometer to the top or bottom point, but the total phase of the two interferometers can reach the full 2π period.The phase is determined by the central coincidence peaks of port 1/2 and the relative phase to the maximal/minimal points.The phase of the Franson interference agrees with the sum of the pump laser's phases on the two interferometers, as shown in Fig. S5.The output of the photodetectors for different phases are shown in Tab.S1, where the sign denotes the positive or negative edge of the PID controllers.

Calculation of entanglement witness
When the AMZIs are not employed, the quantum state of the photon pair (Eq (1) in the main text) is projected onto Z basis.The coincidence for |ee⟩ or |ll⟩ states will be at the time difference of 0, while that of the |el⟩ or |le⟩ states will be at the time difference of ±32 ns.Since the cross-correlation is calculated as g When the AMZIs are employed, the photon pair is projected onto the X-Y plane.A photon will be projected to the |x + ⟩, |x − ⟩, |y + ⟩ or |y − ⟩ states with its AMZI set to 0, π, −π/2 or π/2, respectively.The projections onto |x + x − ⟩ and |x − x + ⟩ (|y + y − ⟩ and |y − y + ⟩) states will result in a total phase of π (0), which is the fully destructive (constructive) point of the Franson interference.As a result, we will obtain

FIG. 1 .
FIG. 1. Schematics of the experimental setup.a.An integrated silicon nitride (SiN) dual Mach-Zehnder interferometer micro-ring resonator (DMZI-R) generates time-bin entangled photon pairs via spontaneous four-wave mixing process.See text for details. b.Quantum memory based on 167 Er 3+ :Y2SiO5.The frequency of the 1536.17nm continuous-wave AFC laser is locked to an ultra-stable Fabry-Pérot cavity (F-P cavity) using Pound-Drever-Hall (PDH) technique, and its intensity is modulated with an intensity modulator (IM) to prepare atomic frequency combs (AFC).The polarization laser is used to polarize the nuclear spin before AFC to enhance the absorption.The signal photon, the AFC laser and the polarization laser are combined and controlled with an optical switch.The memory 167 Er 3+ :Y2SiO5 crystal is cooled to about 200 mK in a dilution refrigerator and exposed to a 1.5-T magnetic field aligned in the D1-D2 plane of the crystal with an angle of about θ = 120 • to the D1 axis.The signal photons propagate along the b axis of the crystal.The time sequence of signal photons and AFC laser is controlled by the optical switch and optical shutter.c.Time-bin qubit entanglement analyzer.We send the signal photon to the quantum memory and then to a Franson interferometer.The idler photon is sent to a Franson interferometer directly.Both interferometers are phase stabilized with proportional-integral-derivative (PID) controllers by using a fraction of pump laser as reference light (Ref), and analyze the entanglement between both photons.See text and SI for details.

FIG. 2 .
FIG. 2. Entangled photon-pair source based on integrated photonics.a. Optical micrograph of the integrated silicon nitride (SiN) dual Mach-Zehnder interferometer micro-ring resonator (DMZI-R) for generating pairs of time-bin entangled photons.b.Transmission spectra of the SiN DMZI-R source for In-Through, Add-Drop and In-Drop as input-output ports, shown in blue, red and yellow, respectively.Insets: The experimental spectra (blue) and the fitting Lorentzian functions (red) for the signal, pump and idler photons.Their full widths at half maximum (FWHM) are about 185 MHz, 212 MHz and 183 MHz, respectively.Upper-right: Two identical pump photons generate a pair of frequency non-degenerate signal and idler photons via the spontaneous four-wave mixing process.c.Typical coincidence histogram with a 2.9-mW pulsed pump, shows a slight asymmetric feature, resulting from different linewidths of signal and idler photons.The left and right decay times are around 997 ps and 980 ps, respectively.We choose 4 ns as the coincidence window, indicated with two dashed vertical lines.d/e.The coincidence counts (C.C.) rate and coincidence-to-accidental ratio (CAR) for continuous wave (CW)/pulsed pump (with 4-ns on-time and 32-ns period) as a function of average pump power.f.Two-photon coincidence counts as functions of the phase between two Franson interferometers with 2.9-mW pulsed pump.The blue/red circles are the raw data of coincidence counts between idler and port 1/2 of the signal photon, respectively.Their visibilities are 78.0 ± 0.4% and 70.5 ± 0.5%.See text for details.Error bars are derived from Poissonian statistics and error propagation.

FIG. 3 .
FIG. 3.An atomic-frequency-comb (AFC) quantum memory based on a 167 Er 3+ :Y2SiO5 crystal.a.The energy level diagram of 167 Er 3+ :Y2SiO5.The Zeeman upper states are frozen under our experimental conditions.See text for details. b.The full absorption spectrum after AFC preparation for 1936 ns storage time.Arrow AFC pump: central frequency of the AFC pump laser, denoted as 0 MHz for the detuning.Arrow polarization: the polarization laser scans from about 550 MHz to 750 MHz detuning to enhance absorption.c.The AFC spectrum for 1936 ns storage time matches the spectrum of the input signal photon (orange).d.The zoom-in views of AFC spectrum for 336 ns (upper blue) and 1936 ns (lower red) storage times with frequency periods of about 3 MHz and 0.5 MHz, respectively.

FIG. 4 .
FIG. 4. Quantum storage of the heralded single photon in an 167 Er 3+ :Y2SiO5 crystal.a. Frequency alignment between the input-signal photon and the absorption of 167 Er 3+ ions.The single counts (S.C.) of the signal (blue) and idler (red) photons are shown as a function of the magnetic-field amplitude.The clear drop of the counts of signal photon shows the matching of the absorption frequency of the memory with respect to that of the signal photon.b.We scan the pump laser's frequency for SFWM generation in finer steps to tune the frequency of the signal photon for achieving maximal storage efficiency, with the magnetic field fixed to 1.5 T. c The coincidence counts (C.C.) histograms for storage times of 1296 ns (blue), 1616 ns (red) and 1936 ns (yellow), vertically offset for clarity.The data beyond 1200 ns are magnified by a factor of 3. d.The second-order correlations (blue) and storage efficiencies (red) as functions of storage time, integrated in 100 s (square) and 40000 s (circle).The second-order correlations stay well above the classical limit, g 2 si (0) = 2. Error bars are derived from Poissonian statistics and error propagation.

FIG. 5 .
FIG. 5.Quantum storage of entanglement.a.After a storage time of 1936 ns, the signal photon is re-emitted from the quantum memory.By using two Franson interferometers for the re-emitted signal photon and the not-stored idler photon, we select the central peak (at 1936 ns) to verify the entanglement between them.The coincidence counts between idler photons and port 1 of the Franson interferometer for signal photons are shown in solid/dashed blue curves for a phase of 0/180 • , respectively.b.The coincidence counts between idler photons and port 2 of the Franson interferometer for signal photons are shown in solid/dashed red curves for the phase of 0/180 • , respectively.Complementary counts at the same phase setting are clearly seen from in panels a and b, as expected for interferometric measurements.c.Full-period interference fringes show the coherence of the entangled state of Eq. 1.We scan the phase of the two Franson interferometers and obtain two-photon quantum interference for the full 2π period.The coincidence counts between port 1/2 of the Franson interferometer for signal photons and idler photons are shown in blue/red curves, respectively.Error bars are derived from Poissonian statistics and error propagation.
FIG. S3.Temperature estimation.a. Zeeman splitting of the non-isotopic Er 3+ :Y2SiO5 crystal.b.The populations ratio between the two Zeeman levels in Fig. S3a are extracted, and fit to Boltzmann distribution with T = 230 mK.

FIG. S4 .
FIG. S4.Side holes in 167 Er 3+ :Y2SiO5.a. Two side holes split from the central spectral hole with the magnetic field increased.b.Side hole splitting as a function of the magnetic field.
FIG. S5.Phase of the Franson interferometers.The total phases of the pump laser on the two interferometers as a function of the phase setpoint.