Spatially-Multiplexed Quantum Memory Array

• Spatially-multiplexed solid-state quantum memory arrays use individually addressable cells in a Pr3+:Y2SiO5 crystal to store photonic states via AFC and spin-wave protocols.
• The approach leverages ten spatial cells with temporal multimodality to achieve up to 250 spatio-temporal modes, enabling arbitrary addressing for qubit storage.
• Experimental performance shows high fidelities (up to 95%), robust SNR, and scalability potential with independent control and collective readout.

A spatially-multiplexed solid-state quantum memory array is a solid-state light–matter interface in which several spatially distinct memory cells are individually addressable and can store photonic states with on-demand readout. In current rare-earth implementations, the platform is a Pr$^{3+}$:Y$_2$SiO$_5$ crystal operated at about $3\ \mathrm{K}$ with the atomic frequency comb (AFC) protocol and spin-wave storage. The defining feature is the combination of spatial multiplexing across ten memory cells with temporal multimodality within each cell, yielding up to $250$ spatio-temporal modes at the single-photon level; subsequent experiments extended the same architecture to quantum storage of path and time-bin qubits with arbitrary cell selection, collective readout, and random-access-style control (Teller et al., 16 Jul 2025, Teller et al., 15 Sep 2025).

1. Conceptual definition and multimode structure

In this context, spatial multiplexing denotes the division of one solid-state memory medium into multiple independently controllable spatial channels. The ten-cell Pr$^{3+}$:Y$_2$SiO$_5$ array realizes this by assigning distinct optical spots in a single crystal to separate memory cells. Temporal multiplexing is provided by AFC storage, which can accept sequences of pulses in a first-in/first-out manner. The combined system is therefore a two-dimensional multimode memory: ten spatial channels, each supporting multiple temporal modes (Teller et al., 16 Jul 2025).

A central point in the literature is that the array is not merely a passive multimode buffer. The later qubit-storage experiment emphasizes individual control, arbitrary addressing of single cells or cell pairs, and on-demand readout in arbitrary combinations, framing the platform as a step toward a random-access quantum memory (RAQM) for quantum repeaters and photonic quantum processors (Teller et al., 15 Sep 2025).

The broader multimode-memory theory provides context for why such architectures are attractive. In an idealized extended $\Lambda$-type atomic ensemble, forward multimode capacity scales as $C_{\mathrm f}\sim F^2$, and for fixed efficiency threshold the number of forward modes scales as $_2$0, where $_2$1 is the Fresnel number and $_2$2 the peak optical depth. That analysis concerns atomic ensembles rather than rare-earth crystals, but it formalized the idea that spatial channels can function as a high-capacity memory resource rather than as a single optical mode (Grodecka-Grad et al., 2011).

2. Physical implementation in Pr$_2$3:Y$_2$4SiO$_2$5

The principal solid-state implementation uses a $_2$6 doped Pr$_2$7:Y$_2$8SiO$_2$9 crystal cooled to about $_5$0. AFC preparation and storage are performed on the $_5$1 transition between $_5$2 and $_5$3, while spin-wave storage uses the ground-state sublevel $_5$4, enabling on-demand retrieval after transfer by control pulses (Teller et al., 16 Jul 2025).

One implementation realizes the array with four acousto-optic deflectors (AODs) in a $_5$5 geometry using lenses of focal length $_5$6. These AODs perform four distinct functions: AFC preparation, spatial multiplexing of the input signal, addressing of cell-specific spin-wave control pulses, and demultiplexing of the retrieved light into a common output mode. Individual memory cells occupy spots with a $_5$7 diameter of about $_5$8, and adjacent cells are separated by $_5$9, which is large compared with the control-beam size and suppresses direct optical overlap between cells. The multiplexing AOD introduces a frequency shift while steering the input to a chosen cell, and the demultiplexing AOD removes that shift when recombining retrieved photons (Teller et al., 16 Jul 2025).

The qubit-storage implementation retains the same ten-cell architecture but highlights a different control abstraction. The array is described as ten individually controlled memory cells, equivalently five memory pairs, with cells separated by $3\ \mathrm{K}$0 and frequency-separated by $3\ \mathrm{K}$1. Two AODs and two lenses symmetrically placed around the crystal are used to encode arbitrary path superpositions at the input and to project the retrieved light onto arbitrary measurement bases at the output. This arrangement supports storage in arbitrary combinations of memory cells, including non-neighboring cells, and redirects all spatial modes into a single output mode for tomography (Teller et al., 15 Sep 2025).

3. Storage protocol, temporal multiplexing, and encoded qubits

The storage mechanism is AFC spin-wave storage. After optical pumping prepares the comb structure with tooth spacing $3\ \mathrm{K}$2, an absorbed excitation rephases after

$3\ \mathrm{K}$3

For on-demand recall, a first control pulse transfers the excitation to the spin state, and a second control pulse later transfers it back, giving a total storage time

$3\ \mathrm{K}$4

where $3\ \mathrm{K}$5 is the programmable spin-wave storage time (Hänni et al., 7 Jan 2025).

In the ten-cell single-photon-level array, the sequence is: prepare the AFC in all ten cells; send a train of $3\ \mathrm{K}$6 signal pulses into one cell; apply the first control pulse to transfer the optical excitation to $3\ \mathrm{K}$7; wait for a programmable $3\ \mathrm{K}$8; apply the second control pulse to restart AFC rephasing; demultiplex the retrieved light into a common output fiber; and repeat for the next cell. The input pulses have a Gaussian FWHM of $3\ \mathrm{K}$9, and the control pulses are $250$0 long with a chirp of $250$1. Two operating points were demonstrated: $250$2 spatio-temporal modes with $250$3 and $250$4, and $250$5 spatio-temporal modes with $250$6 and $250$7. The stored states were weak coherent pulses with mean photon number $250$8 (Teller et al., 16 Jul 2025).

The qubit-storage experiment used two distinct photonic encodings. For path qubits, the input state is

$250$9

and the six standard states $^{3+}$0 were stored in arbitrary cell pairs. The pulses were Lorentzian with FWHM $^{3+}$1, mean photon number $^{3+}$2 in front of the crystal, a first control pulse of duration $^{3+}$3 with Gaussian envelope and $^{3+}$4 chirp, spin-state storage time $^{3+}$5, and total storage time $^{3+}$6. For time-bin qubits, the six states $^{3+}$7 were stored directly in a single memory cell as two Lorentzian pulses separated by $^{3+}$8, with mean photon number $^{3+}$9 and spin-wave storage time $_2$0. Superposition-basis readout used a solid-state Franson interferometer implemented by two control pulses separated by $_2$1, producing three detection peaks with the central peak corresponding to the desired basis projection (Teller et al., 15 Sep 2025).

A recurrent ambiguity in the literature is whether time-bin qubits must be converted into path qubits before storage. In this architecture they do not: each AFC cell is intrinsically temporally multimode, so time-bin qubits can be stored directly in a single cell (Teller et al., 15 Sep 2025).

4. Experimental performance and state preservation

The reported performance spans single-photon-level multimode storage and qubit storage with full-state tomography.

System	Capacity or encoding	Reported performance
Ten-cell array, $_2$2	$_2$3 spatio-temporal modes	average SNR $_2$4; average device efficiency $_2$5
Ten-cell array, $_2$6	$_2$7 spatio-temporal modes	average SNR $_2$8; average device efficiency $_2$9
Ten-cell qubit array, path encoding	arbitrary memory-cell pairs	average fidelity $_5$0
Ten-cell qubit array, time-bin encoding	direct single-cell storage	average fidelity $_5$1

For the multimode array, the cumulative signal counts per trial were $_5$2 and $_5$3, so the $_5$4-mode setting yielded a higher total successful detection probability even though each individual mode was weaker. The system characterization with classical light reported multiplexing AOD efficiencies from $_5$5 to $_5$6, demultiplexing AOD efficiencies from $_5$7 to $_5$8, fiber coupling efficiencies from $_5$9 to $\Lambda$0, AFC efficiencies from $\Lambda$1 to $\Lambda$2 at $\Lambda$3 and from $\Lambda$4 to $\Lambda$5 at $\Lambda$6, and two-way spin-state transfer efficiency from $\Lambda$7 to $\Lambda$8. Cross-talk measured over all $\Lambda$9 mode pairs ranged from approximately $C_{\mathrm f}\sim F^2$0 to $C_{\mathrm f}\sim F^2$1, with an average cross talk of $C_{\mathrm f}\sim F^2$2; the remaining contribution was attributed mainly to control-pulse fluorescence, imperfect alignment in the AOD-based $C_{\mathrm f}\sim F^2$3 relay, leakage of off-resonant AFC echoes and two-pulse photon echoes, and detector dark counts of about $C_{\mathrm f}\sim F^2$4 on average (Teller et al., 16 Jul 2025).

For non-classical-state readiness, the same array study inferred fidelities up to $C_{\mathrm f}\sim F^2$5 for the $C_{\mathrm f}\sim F^2$6-mode configuration and up to $C_{\mathrm f}\sim F^2$7 for the $C_{\mathrm f}\sim F^2$8-mode configuration, remaining above the threshold $C_{\mathrm f}\sim F^2$9 for all spatial modes. This suggests that the measured SNR is already sufficient, in principle, for storage and retrieval of non-classical states while preserving quantum correlations (Teller et al., 16 Jul 2025).

For path qubits, the average infidelity across all pairs and states was $_2$00, corresponding to an average fidelity of about $_2$01. The classical benchmark was $_2$02, and the significance measure

$_2$03

showed violations for all five pairs, with minimum $_2$04 and maximum $_2$05 for pair $_2$06. For time-bin qubits, the average infidelity across ten cells was $_2$07, corresponding to an average fidelity of about $_2$08; the classical bound was $_2$09, and the violations ranged from $_2$10 to $_2$11 across all ten cells for detection window $_2$12. For detection windows up to $_2$13, all ten cells still violated the classical limit by more than $_2$14. Spin-wave memory efficiencies, including AFC and two control pulses, ranged from $_2$15 to $_2$16 across the path-qubit array (Teller et al., 15 Sep 2025).

5. Independent control, collective operations, and random-access functionality

The defining advance beyond passive multimode storage is independent controllability. In the qubit-array experiment, the first AOD encoded arbitrary path superpositions and could direct light into arbitrary combinations of memory cells, including non-neighboring cells. The second AOD acted as a spatial demultiplexer, projected the retrieved light onto arbitrary measurement bases, and redirected all spatial modes into a single output mode. This enabled full-state tomography, independent preparation and readout, and selective access to cell pairs or individual cells (Teller et al., 15 Sep 2025).

The same platform demonstrated operations associated with RAQM-like behavior. Time-bin qubits were sequentially stored in different memory cells, two qubits were maintained simultaneously in the array, and collective readout was performed by recalling two stored qubits together and interfering them. In one implementation, a $_2$17 qubit was stored in the first cell of a pair, a second $_2$18 qubit in the second cell, both were recalled simultaneously after $_2$19, and an extra $_2$20 delay with phase shift $_2$21 was introduced. The counts followed

$_2$22

with extracted visibilities between $_2$23 and $_2$24. This indicates that the array can not only store multiple qubits but also interfere them pairwise after storage (Teller et al., 15 Sep 2025).

The network significance of this functionality is clarified by a related temporally multiplexed Pr$_2$25:Y$_2$26SiO$_2$27 system for telecom-heralded entanglement between two spin-wave memories. There, a $_2$28 acceptance window was divided into $_2$29 temporal bins of $_2$30, the heralding rate increased linearly with the number of stored modes, and under a simulated $_2$31 communication dead time the entanglement rate reached $_2$32 per heralding detector, enhanced by a factor of $_2$33 by temporal multiplexing. Feed-forward conditional phase correction doubled the useful heralding rate for a chosen state to about $_2$34 (Hänni et al., 7 Jan 2025). A plausible implication is that adding spatial multiplexing to this networking logic would increase the number of independent storage opportunities per communication round still further.

6. Comparative context, limitations, and scaling directions

A recurring misconception is that a spatially multiplexed memory array must consist of fully separate devices. The solid-state rare-earth implementations instead use multiple independently addressable cells inside one crystal. In the wider literature, even non-solid-state systems have been described as array-like when spatial channels inside a single medium are independently usable. A cold-atom dual-rail memory for polarization qubits, for example, used a single spatially multiplexed cesium ensemble as the functional equivalent of a two-channel memory array, with average conditional fidelity $_2$35, rising to $_2$36 after background correction, and storage-and-retrieval efficiency $_2$37 (Vernaz-Gris et al., 2017). Likewise, a wavevector-multiplexed cold-$_2$38 memory accessed $_2$39 conjugate spatial mode pairs simultaneously and measured $_2$40 for correlated modes (Parniak et al., 2017). These are not solid-state arrays, but they clarify that “array” in quantum-memory practice often denotes independently usable spatial channels rather than only separate hardware modules.

The rare-earth solid-state arrays nevertheless have distinctive constraints. Their dominant limitation is fluorescence noise from the control pulses; the qubit-array study reports that the noise floor is constant across the array and independent of the number of cells and stored qubits, so the present performance is limited mainly by SNR rather than by the scaling of cell count (Teller et al., 15 Sep 2025). Spatial performance is nonuniform: central cells have higher counts per trial, better fidelities, and larger violations of classical bounds than edge cells. The shortest possible storage time in the current setup is $_2$41, limited by AFC storage time and control-pulse duration; the maximum storage time is limited to tens of microseconds by spin inhomogeneous broadening, although dynamical decoupling could extend storage times (Teller et al., 15 Sep 2025).

The multimode-array experiment identified additional system-level efficiency bottlenecks: overall device efficiency averaged $_2$42 for $_2$43 and $_2$44 for $_2$45, reflecting the usual AFC tradeoff that longer storage reduces retrieval efficiency (Teller et al., 16 Jul 2025). Proposed improvement paths include stronger filtering such as a double-pass filtering crystal, better preparation of individual memories, longer crystals, spatially multimode cavity enhancement, more uniform fiber coupling efficiencies, and extension from ten cells to hundreds using two-dimensional AODs (Teller et al., 15 Sep 2025). This suggests that current arrays are best understood as proof-of-principle RAQM nodes whose spatial addressing, temporal multimodality, and collective operations are already established, while efficiency, uniformity, and storage time remain the principal barriers to large-scale deployment.

A further point of comparison is integration strategy. A warm-atom EIT platform based on 3D-nanoprinted hollow-core “light cages” demonstrated multiple memory structures on one chip with nearly identical behavior inside a single cesium vapor cell, showing that spatially multiplexed memory arrays can also be pursued through chip-level fabrication rather than rare-earth bulk crystals (Gómez-López et al., 28 Mar 2025). That system is not solid-state in the rare-earth sense, but it indicates that spatial multiplexing can be coupled to microfabrication and dense integration. In the solid-state rare-earth setting, the corresponding scaling path is explicit: more cells, more uniform control, and eventual two-dimensional addressing.