Heralded entanglement of on-demand spin-wave solid-state quantum memories for multiplexed quantum network links

TL;DR

This work demonstrates telecom-band heralded entanglement between distant spin-wave quantum memories using rare-earth-doped crystals, achieving on-demand retrieval and temporal multiplexing across 15 modes. By combining narrowband cavity-enhanced SPDC sources with spin-wave AFC memories and active feedforward, the authors reach high heralding rates (up to 510 cps with phase correction) and show unconditional multiplexing yielding 22 cps per heralding detector, all while verifying entanglement via tomography and a positive concurrence. The results establish a scalable, high-rate quantum-network interface with clear paths toward metropolitan-scale repeater implementations, including improvements in memory efficiency, longer storage, and multi-degree multiplexing. Collectively, this architecture advances practical quantum communication by enabling fast, telecom-wavelength entanglement distribution between solid-state quantum memories.

Abstract

The ability to distribute heralded entanglement between distant matter nodes is a primitive for the implementation of large-scale quantum networks. Some of the most crucial requirements for future applications include high heralding rates at telecom wavelengths, multiplexed operation and on-demand retrieval of stored excitations for synchronization of separate quantum links. Despite tremendous progress in various physical systems, the demonstration of telecom-heralded entanglement between quantum nodes featuring both multiplexed operation and on-demand retrieval remains elusive. In this work, we combine narrowband parametric photon-pair sources and solid-state quantum memories based on rare-earth doped crystals to demonstrate telecom heralded entanglement between spatially separated spin-wave quantum memories with fully adjustable recall time and temporal multiplexing of 15 modes. In a first experiment, the storage in the spin-state is conditioned on the entanglement heralding. We take advantage of the control over readout pulse phase to achieve feed-forward conditional phase-shifts on the stored photons depending on which heralding detector clicked. We exploit this effect to double the entanglement heralding rate for a given quantum state up to 510 cps, with an associated detection rate of 0.32 cps and measured positive concurrence by up to 6 standard deviations. In a second experiment, we simulate the communication time of a long-distance link by implementing an unconditional storage scheme with a dead-time of 100 $μ$s. We take advantage of temporal multiplexing to increase the entanglement rates by a factor of 15 with respect to single mode storage, reaching a value of 22 cps per heralding detector. These results establish our architecture as a prime candidate for the implementation of scalable high-rate quantum network links.

Figures (11)

• Figure 1: (a) Experimental setup. Each quantum node consists of a non-degenerate cSPDC source and a Pr^3+:Y_2SiO_5 solid-state QM. Heralding is performed at an intermediate station by mixing the idler fields on a 50/50 beam splitter and recording single photon detection events, which herald an entangled state of a delocalized excitation shared across the two QMs. For density matrix reconstruction, single photons retrieved from the memory crystals are either (b) directly detected (diagonal elements measurement) or (c) interfered at a 50/50 BS (off-diagonal elements measurement). ppLN: Periodically Poled Lithium Niobate. FC: Filter Cavity. BPF: Bandpass Filter. PZ: Piezoelectric Fiber Stretcher. PolC: Polarization Controller. QM: Quantum Memory. CP: Control Pulse. SPD: Single Photon Detector. TS: Translational Stage. Et: Etalon Filter. (d) Energy levels corresponding to the the $^{3}H_4(0) \leftrightarrow ^{1}D_2(0)$ transition in Pr^3+:Y_2SiO_5. Input signal photons at 606nm from the cSPDC sources are resonant with the $1/2_g\leftrightarrow3/2_e$ transition, where they are absorbed. The optical excitation is then stored into and then retrieved from the $3/2_g$ spin level using control pulses and finally is re-emitted optically as photon echo at the frequency of the $1/2_g\leftrightarrow3/2_e$ transition.
• Figure 2: (a) Schematic representation of the spin-wave AFC storage sequence in conditional operation. Upon detection of an idler photon the pump of the cSPDC source is turned off and a pair of control pulses is sent into the memory with an arbitrary temporal separation $T_S$. A photon echo is then re-emitted after a time $\tau_{\text{AFC}}+T_S$. The memory remains closed for a fixed period of time (memory dead time) to allow for the CP2 fluorescence noise to decay before the next storage trial. The SPDC pump is also being turned off for a fixed time of 20µs (see main text for details). (b-c) Time-correlation histograms between detection of an idler photon and a signal photon retrieved from the on-demand spin-wave AFC QM at (b) Node A and (c) Node B. The dark orange region highlights the selected 280ns-long detection window. Grey areas indicate the noise windows. The errors on the value of $g^{(2)}_{si}$ are given assuming poissonian statistics. Integration times are of 5 minutes and 15 minutes respectively for nodes A and B.
• Figure 3: Verification of entanglement between spin-wave quantum memories. (a-b) Single photon interference of the signal modes at the memory output upon heralding from (a) detector $i_1$ and (b) detector $i_2$. Yellow (dark red) curve denotes the coincidences recorded with signal detector $s_1$ ($s_2$) and integration time is 10min per point. As expected from the unitarity of BS operation, we observe a $\pi$ phase shift between the interference measured at a given signal detector when considering heralding from one of the other idler detector. (c-d) Reconstructed density matrix for the quantum state heralded by (c) detector $i_1$ and (d) detector $i_2$. The total storage time is 16.5µs.
• Figure 4: Dynamical phase feed-forward using conditional readout of the spin-wave memories. Single photon interference at the signal 50/50 BS upon heralding at (a) idler detector $i_1$ and (b) idler detector $i_2$. Solid lines represent a sinusoidal fit of the data. Dashed lines correspond to the expected unshifted interference fringe in the absence of conditional phase feed-forward. We observe that, as a result of the feed-forward, interference fringes are identical between $i_1$ and $i_2$ indicating that both idler detectors now herald the same quantum state. The integration time is 10min per point. (c) Reconstructed density matrix of the state of photonic modes at the output of the QMs including phase-corrected heralding from both idler detectors. The total storage time is 16.5µs. (d) Evolution of measured concurrence with total storage time in the spin wave quantum memories. The grey dashed line denotes the $\mathcal{C}=0$ threshold for the state to be entangled.
• Figure 5: Temporally-multiplexed entanglement generation. (a) Sketch of the unconditional storage sequence used in this measurement. The SPDC pump is turned on and off and CPs are being sent at a fixed repetition rate, defining a memory acceptance window of 15 temporal modes. (b) Single-photon visibility at the signal 50/50 BS with heralding on both $i_1$ and $i_2$ detectors (left y-axis) and corresponding heralding rates (right y-axis) as a function of the number of stored temporal modes. The total storage time is 16.5µs and the integration time is 1h per point. The dashed line is a linear fit of the average heralding rate with the number of modes.