Memory-assisted multimode microwave-to-optical transduction

Abstract

Microwave-to-optical quantum transducers will enable coherent interconnection between distant superconducting quantum devices. Ongoing explorations have shown promising results at single-photon levels. However, eliminating noise arising from the concurrence of weak transduced signals with intense pump pulses remains a challenge, requiring high-suppression filtering. Memory-assisted transduction offers a versatile noise-mitigation approach and enables on-demand retrieval of transduced signals. Here, we integrate a quantum memory protocol with transduction in a three-level atomic system. Leveraging zero-first-order Zeeman transitions at zero magnetic field, providing long optical and spin coherence times, and GHz-range hyperfine splitting, we use a low-doping concentration ¹⁷¹Yb³⁺:Y₂SiO₅ crystal at 30 mK. We achieve on-demand memory-assisted transduction with 0.4 (and 0.3) noise photons at a storage duration of 460 (and 620) μs. Further, we establish coherence via interference patterns and demonstrate multimode capacity, utilizing spin and optical inhomogeneous broadening. The on-demand retrieval enables qubit synchronization in quantum repeaters, while multimode capacity boosts entanglement generation rates.

Current demonstrations of microwave-to-optical transduction suffer from noise due to the pump field. Here, the authors demonstrate memory-assisted microwave-to-optical transduction to avoid noise in a Yb:YSO crystal at 30 mK with zero B-field and multimode functionality.

Introduction

Reliable and fast distribution of entanglement between quantum devices is a hallmark of future quantum networks^1,2. With long-distance communication relying on flying optical qubits while microwave (MW) qubits are used for local information processing³ or sensing^4,5, a microwave-to-optical (M2O) transducer will be essential to bridge these disparate modalities^6–10. M2O transducers also find near-term application as interconnects between superconducting quantum circuits (SQCs) in a distributed quantum computing architecture¹¹, to overcome scalability issues that currently limit these systems¹². An M2O transducer must meet several challenging requirements, such as operating at  ≪ 1 noise photons per qubit mode for quantum applications, while achieving high efficiency and large bandwidth, for faster operation^9,10,13. Moreover, a large multiplexing capacity will enable simultaneous transduction of several modes¹⁴, further increasing the qubit transfer rate while storage and on-demand retrieval of the transduced optical qubit¹⁵ are paramount for synchronization in a path-erasing entanglement scheme¹³. Finally, since magnetic (B) fields induce noise in SQCs¹⁶, an M2O transducer should ideally operate at B = 0.

Several platforms have demonstrated M2O transduction, including electro-optics¹⁷, opto-mechanics^18,19, and atomic ensembles^6,20, and some integration with SQCs for coherent control and readout^21,22. As an alternative to direct M2O transduction, MW-optical entangled photon pairs have also been generated^23,24. Since M2O transduction relies on a strong pump field to achieve significant non-linear response and energy-conservation¹⁰, suppression of noise photons stemming from the pump field remains a significant challenge, typically necessitating lossy filtering setups²⁵. Memory-assisted transduction¹⁵, on the other hand, delays the transduced optical signals with respect to the pump field and associated noise⁶. In addition, memory-assisted transduction is less sensitive to the temporal shape/mode of signal photons and, thus, more practical for qubit encoding, e.g., as time-bins²⁶. The quest for systems that can deliver on all transduction figures-of-merit, together with memory capability continues to be of high priority.

One approach to quantum transduction is based on the coupling of optical and MW transitions in ensembles of rare-earth ions (REIs), e.g., Er^3+25,27–29 and Yb³⁺⁶ doped in various host crystals. Although Er³⁺ conveniently possesses an optical transition in the telecom band ( ~ 1530nm), the application of a B-field is required (even isotopes) to split its Zeeman levels for the MW spin transition, complicating integration with SQCs²⁷. A transduction efficiency of 10⁻⁵ was shown for a 10 ppm-doped Er:YSO crystal placed in an optical cavity and a 3D loop-gap resonator (LGR)³⁰ with a 146 mT external B-field³¹. In contrast, ¹⁷¹Yb³⁺ inherently possesses hyperfine and zero first-order Zeeman (ZEFOZ) transitions at zero B-field³². The 1% efficiency demonstrated in a 340 ppm-doped Yb:YVO crystal with a planar MW resonator and a weak optical cavity⁶, has served as a benchmark for REI-based transduction.

In this work, the MW spin and optical electron transitions in a 5 ppm-doped Yb:YSO crystal with no applied B-field are employed to demonstrate on-demand, memory-assisted M2O transduction of up to ten multiplexed modes. The unique memory functionality not only enables on-demand retrieval of the transduced signal but also eliminates the need for lossy spectral filtering of the pump. We report an internal transduction efficiency of 4 × 10⁻⁸ for a 460 μs storage time, without the aid of an optical cavity. The storage-time-dependent noise floor in the output optical signal, dominated by free-induction decay (FID) from the co-propagating frequency-chirped memory control pulses, is measured at 0.4 (and 0.3) photons for 460 μs (and 620 μs) storage time. We verify the preservation of coherence of the transduced optical signals by observing interference between two MW pulses with varying phase and frequency differences and between the transduced optical signal and a reference local oscillator. Finally, we demonstrate spectral and temporal multiplexing enabled by the broad inhomogeneous spin and optical linewidths of the Yb:YSO system.

Results

Memory-assisted M2O transduction protocol

Generally, M2O transduction converts an MW signal at frequency ω_M to a transduced optical signal at frequency ω_T using an optical pump field at frequency ω_P, while maintaining energy conservation, ω_T = ω_P ± ω_M. We choose a three-level sub-system of Yb:YSO at zero B-field (Fig. 1a) and drive the excited state spin transition $\mid 1_e⟩\leftrightarrow \mid 2_e⟩$ (blue) at ω_M = 2623.35 MHz with an LGR at 2625.3 MHz and 4 MHz linewidth (Fig. 1b). The optical transitions $\mid 4_g⟩\leftrightarrow \mid 2_e⟩$ and $\mid 4_g⟩\leftrightarrow ∣1_e⟩$ at ω_P and ω_T ( = ω_P − ω_M) respectively, are coupled by free-space optical fields, and the weak transduced signal is detected on an avalanche photodiode (APD). Although the optical transitions are ZEFOZ at zero magnetic field, we do not actively compensate for residual environmental magnetic field, which is likely on the order of a few μT ³³.

Fig. 1. Protocol sequence.

a A three-level system in Yb:YSO with excited state spin transition showing respective colour-coded transitions used in (c). b Experimental setup depicting a Yb:YSO crystal (cyan) kept at the center loop of a 3D loop-gap resonator. SMA antenna pin couples MW in and out via an isolator. A pair of GRIN lenses is used for optical coupling through the crystal. c Schematic of the pulse sequence. An intense pump pulse (yellow) is followed by a weak coherent MW pulse (blue) after a time τ₀ (inset). RAP1 and RAP2 pulses (red) of duration τ_R are applied after τ₁ from the pump pulse and after τ₂ from RAP1, respectively. Transduced optical signal (red) is emitted at τ₂ − τ₁ from RAP2. Total storage time is 2(τ₂ + τ_R). d Simulated evolution of relevant coherences excited by the corresponding colour pulses. Coherence in $⟨4_g\mid {\overline{\sigma }}_x\mid 1_e⟩$ is a result of a two-pulse excitation, which is then rephased with RAP1 and RAP2. e Mean photon counts per 500 ns bin, averaged over 200 experimental cycles. The tall bar at t = 0 is the leaked part of the pump pulse. Leaked RAP1 and RAP2 are seen in the gate-off windows. Decaying counts after the RAP pulses are the corresponding free-induction decay. The transduced echo is visible when the MW is ON. (Inset) Zoom-in view around the transduced echo showing signal versus the noise floor counts.

The memory-assisted M2O transduction sequence (shown in Fig. 1c) is an extension from a two-level QM protocol in which rephasing of a collective atomic excitation is achieved on-demand using a pair of Rapid Adiabatic Passage (RAP) pulses^34–36. To understand the atomic rephasing, it is informative to visualize the evolution of relevant collective ensemble coherences $⟨{\overline{\sigma }}_{x,y}⟩$ (Supplementary Note 2) during the transduction sequence as shown in Fig. 1d (Supplementary Fig. S5 for all the coherence components). An intense pump pulse of duration τ_P at frequency ω_P, initiates $⟨4_g\mid {\overline{\sigma }}_y\mid 2_e⟩$ optical coherence at t = 0. A weak MW pulse applied after a delay τ₀ interacts with the excited state population and generates $⟨2_e\mid {\overline{\sigma }}_y\mid 1_e⟩$ spin coherence. The cumulative effect of the two-pulse excitation results in $⟨4_g\mid {\overline{\sigma }}_x\mid 1_e⟩$ optical coherence on the transduced signal transition, which dephases and averages out to zero over the ensemble (Fig. 1d). Similar to that for an optical QM in a two-level system³⁴, this coherence is rephased by a pair of RAP pulses centred at frequency ω_R ~ ω_T. Both the RAP pulses are identical, amplitude- and phase- modulated pulses, with duration τ_R and linear frequency chirp bandwidth Δ_ch corresponding to a chirp rate of R_ch = Δ_ch/τ_R. For optimal rephasing, the RAP pulses must satisfy the adiabaticity condition ${\mathrm{\Omega }}_R^2/R_{\mathrm{ch}}\gg 1$, where Ω_R is the resonant Rabi frequency of the RAP pulses. After τ₂ − τ₁ duration from RAP2, the collective coherence, $⟨4_g\mid {\overline{\sigma }}_x\mid 1_e⟩$ rephases and emits at frequency ω_T in the optical domain. Here, the temporal mark and the temporal profile of the transduced signals are based on the initial pump pulse, thereby defining the storage time as τ_s = 2(τ₂ + τ_R). Note that the temporal separation between the transduced signal and the control pulses avoids the need for spectral filtering.

Figure 1e is an experimental result of the protocol for which the unabsorbed pump-pulse (τ_P = 4 μs) at t = 0, results in the initial peak. The MW pulse of duration τ_M = 2 μs is applied right after the pump pulse (τ₀ = 0 μs) followed by the RAP pulses with τ_R = 60 μs and R_ch = 2π × 25 MHz/ms are applied with τ₁ = 50 μs, and τ₂ = 170 μs. This results in the emission of a transduced signal at t = 460 μs following the pump pulse. During the intense RAP pulses, the APD is gated OFF to avoid detector damage and saturation. The exponentially decaying counts after the RAP pulses are coherent FID emission³⁷ (Sec. Noise Characterization).

Protocol characterization

Input MW photons and efficiency

The transduction efficiency in Fig. 2a is characterized under optimal pulse parameters for τ_s = 460 μs. The input MW photons are varied in the weak-power regime to ensure that the spin transition remains unsaturated. After accounting for losses and inefficiencies of the experimental setup, the internal memory-assisted transduction efficiency is 4 × 10⁻⁸. A detailed discussion of the efficiency budget is presented in Sec. Efficiency Budget.

Fig. 2. Characterizations.

Sweep of various parameters showing mean transduced signal counts and standard deviation over 100-experimental cycles in a 4 μs detection bin. The yellow ring depicts the parameters used across experiments. a Sweep of number of input MW photons per pulse resulting in a linear rise in transduced counts. The slope of the linear fit gives an overall photon conversion efficiency of 4 × 10⁻¹¹. b Sweep of storage duration vs transduced signal counts adjusted for the noise floor. An exponential decay fit function of the form $A\times \exp -2t/T_{2,m}$, resulted in T_2,m = 475 μs as the memory coherence time. c Sweep of pump-MW delay τ₀, resulted in a phenomenological decay with time constant of T_d = 1.56 ± 0.08 μs.

Memory coherence time

The collective coherence created on the $\mid 4_g\left(\right.⟩\leftrightarrow \mid 1_e\left(\right.⟩$ transition decoheres due to the finite optical coherence time, thus degrading the transduction efficiency at longer storage durations. To quantify this effect, we vary τ₂ in τ_s in Fig. 2b, and baseline-correct the counts to subtract the noise floor. The exponential fit yields memory coherence time T_2,m = 475 μs, well within the optical coherence time of the transition T_2,o = 801 μs (Supplementary Fig. S7f).

Pump-MW delay

Following the pump pulse, each atom accumulates a phase determined by both its optical and spin detunings. Over time, the dephasing of the spin transition leads to phase scrambling of the atomic coherence. As a result, any delay in transferring the collective coherence from the pump transition reduces the final coherence on the RAP transition, as confirmed by simulations (Supplementary Fig. S6). Fig. 2c presents the experimental data fitted with exponential decay, yielding a time constant of T_d = 1.56 ± 0.08 μs ~ 641 kHz, matching the spin-inhomogeneous broadening Γ_s (Supplementary Fig. S7c).

Noise characterization

The protocol provides some freedom to choose the recall time of the transduced signal. With the goal of achieving the optimal signal-to-noise ratio, the transduced signal should avoid overlap with noise expected at certain times in the protocol, indicated by the shaded pulses in Fig. 3a. We, thus, characterize the noise, taken as the integrated optical photon counts within a window of 4 μs, corresponding to the duration of a potential transduced signal, at different times in the sequence.

Fig. 3. Noise and transduced echo placement.

a Schematic of optical pulse (solid) and noise regions (shaded) around transduced echo. b Level diagram with sources of noise from pump (yellow) and RAP (red). c Average noise photon counts and standard deviation due to pump pulse and RAP1. Each data point is photon counts in 4 μs integration window with bottom time axis referenced to the pump, while top time axis referenced to tail of RAP1. Green data points are noise due to only pump (Photoluminescence), red due to only RAP1 (Free-Induction Decay), and blue due to both pump and RAP1. d Average photon counts and standard deviation around the expected transduced signal region for two storage durations with pump and both the RAP pulses ON while keeping the MW pulse OFF. The valley (box) between the peak and the higher counts towards the end is the region where the echo needs to be placed.

One source of noise is caused by the excitation of population by the pump pulse from the ground state, $\mid 4_g\left(\right.⟩$, to the excited state, $\mid 2_e\left(\right.⟩$, which decays back to the ground state via photoluminescence (PL), as illustrated in Fig. 3b. As this PL frequency is distinct from that of the transduced signal, spectral filtering is possible. Engaging only the pump pulse, we see from Fig. 3c that PL from the pump pulse contributes only  ~ 0.02 photons to the noise floor, comparable to the detector’s dark count rate, rendering any spectral filtering to be of low priority.

Another more significant contribution to the noise counts arises from the FID due to the co-propagating RAP pulses^37–39, as illustrated in Fig. 3b. The FID could be avoided by a slight spatial mismatch between the RAP and pump pulses⁴⁰, but this was not possible in our setup due to practical limitations. We measure the FID noise by applying only the first RAP pulse and find in Fig. 3c that at τ_s = 460 μs, RAP1 contributes  ~ 0.15 photons to the noise floor. Assuming FID counts from RAP1 and RAP2 have similar decay patterns, RAP2 will contribute  ~ 0.25 photons after τ₂ − τ₁ = 120 μs from the end of the RAP pulse.

By engaging the full optical pulse sequence, we can assess the total noise contribution at τ_s = 460 μs from the pump and both the RAP pulses with MW OFF is 0.4 photons (Fig. 3d), matching the sum of the individual contributions. However, in this case we also observe an undesired echo (peaks at  ~ 420 μs and  ~ 480 μs, for the two storage times, respectively), as well as an RAP echo responsible for the increase of noise at the tail of the two traces of Fig. 3d. Note that noise at the start of the two traces corresponds to FID from the RAP pulses as also visible in Fig. 3c. The undesired echo arises from a two-pulse photon-echo (2PPE)-like process between the pump and the RAP pulses due to the zeroth order of the phase modulator (PM) leaking light at the same fixed frequency, resonant with a separate atomic sub-ensemble (Supplementary Fig. S2). Such an undesired echo also arises when the MW is ON, and the adiabaticity condition is weakly satisfied (orange bumps in Fig. 1e). The RAP echo arises due to the 2PPE-like scheme between the RAP pulses, i.e., the RAP2 pulse acts as a rephasing pulse for RAP1.

Returning to the objective of avoiding noise, we conclude that the valley between the undesired echo and the RAP echo is the sweet spot for retrieving the transduced signals, with less stringent temporal placement and lower noise counts for longer τ_s (0.3 for τ_s = 620 μs) (Fig. 3d).

Coherent M2O conversion

To demonstrate coherent information mapping, we apply an optical pump pulse followed by two sequential MW pulses with either varying phase difference (Δϕ) or detuning (Δν) (Fig. 4a). Each MW pulse determines the axis of rotation of the spin ensemble (Bloch vector) on the Bloch sphere based on its phase and detuning from the centre of the spin inhomogeneous broadening (Fig. 4b). For instance, the first MW pulse with Δν = 0 and Δϕ = 0, rotates the Bloch vector about the  + x-axis, whereas the second MW pulse with Δν = 0 and Δϕ = π, rotates it about the  − x-axis, effectively reversing the initial rotation (Fig. 4c). In another instance, if the first MW pulse is the same i.e. rotates about the  + x-axis (Δν = 0 and Δϕ = 0), while the second MW pulse has Δν ≠ 0 and Δϕ = 0, the axis of rotation tilts in the x-z plane, effectively bringing (taking) the Bloch vector closer (away) to (from) the pole (Fig. 4d)⁴¹. See Supplementary Note 4 for a detailed description of two-pulse ensemble interaction.

Fig. 4. Interference.

a Schematic of the pulse sequence consisting of a pump pulse (yellow) followed by two MW pulses (blue) with detuning (Δν) and phase difference (Δϕ) resulting in a single transduced echo. There is no delay between the pulses. Gaps are shown to highlight the individual pulses. b Schematic of the overlap between the Fourier spectrum of the individual pulses and the spin inhomogeneous broadening. c Sweep of the phase difference (Δϕ) showing interference pattern after adjusting for noise-level. Data fit with a sinusoidal interference function $I_1+I_2+2\sqrt{I_1{I}_2}\cos \left(\mathrm{\Delta }\varphi +{\varphi }_0\right)$), where I₁(1.93) and I₂(0.39) correspond to the amplitudes of the transduced signals due to MW1 and MW2, respectively and ϕ₀ ( − 7. 3°) is a fit parameter. d Sweep of Frequency of MW2 for a set phase difference (Δϕ  = 0) showing interference pattern after adjusting for noise level. Data is fitted with a Lorentzian modulated interference function to account for the spin inhomogeneous broadening: $I_1+I_2\alpha +2\sqrt{I_1{I}_2\alpha }\cos \left(k\mathrm{\Delta }\nu \right)$, where α = L(ν, ν₀) is the Lorentzian function at frequency ν centered at ν₀. I₁(1.83) and I₂(0.46) correspond to the amplitudes of the transduced signals due to MW1 and MW2, respectively. Here, k(0.0181) is a fit parameter that denotes the wavenumber of the optical fields. e Schematic of a pulse sequence showing a pair of pump and MW pulses being transduced to a pair of optical signals. Local oscillator (LO) pulses are synchronized to arrive with the transduced signals at the APD. f Sweep of phase of MW1, ϕ₁ and MW2 with ϕ₂ = ϕ₁ + π/2, showing interference pattern with LO pulses of constant phase. Data is fitted with $A\left(1+V\cos \left({\varphi }_{1,2}+{\varphi }_{1,2}^{\mathrm{LO}}\right)\right)+C$, where V ( ~ 82% for both MW1 and MW2) is the visibility of the interference, ${\varphi }_{1,2}^{\mathrm{LO}}$ are the phases of the LO pulses for each mode and C(26) is fit parameter for the noise level due to leak light. Fit values are mentioned in the parentheses. c, d, f, The error bars correspond to the standard deviation of the photon-count statistics.

The ensemble Bloch vector after the sequence of MW pulses is mapped onto the transduced optical field, resulting in interference patterns as shown in Fig. 4c, d. The fitting function described in the caption of Fig. 4c fits well with I₁ = 1.93 and $I_2=0.39~I_1\times \exp \left(-{\tau }_M/T_d\right)=0.54$, close to the photon count expected due to τ₀ = τ_M for the second MW pulse (Fig. 2c). The observed visibility can be calculated as $V=2\sqrt{I_1{I}_2}/\left(I_1+I_2\right)=75\%$, while the expected visibility, if I₂ is adjusted for decay $I_2^{*}=I_2\exp \left({\tau }_M/T_d\right)=1.39$ is $V_{\exp }=98.7\%$. In Fig. 4d, the observed and expected visibility at Δν = 0 are V = 80% and $V_{\exp }=99.8\%$, respectively. As Δν varies, the modulation decays due to the Lorentzian shape of the spin inhomogeneous broadening. This interference is well described by a Lorentzian-modulated cosine function, directly demonstrating that phase information encoded in the MW field is coherently preserved and transferred to the transduced optical mode. Such faithful mapping of phase coherence enables protocols such as quadrature phase-shift keying (QPSK) for quantum information processing⁴².

An alternative method to show coherent information transfer is by using Homodyne interference of the transduced signal with an optical local oscillator (LO) pulse (Fig. 4e). To achieve high-visibility interference, the LO pulses must be precisely synchronized in time, matched in optical frequency, and have similar photon counts as the transduced pulses. The lowest photon counts we could reach in LO pulses were almost the same as the transduced optical counts, but with comparatively large leak photon counts, which shifted the base level of the interference pattern. In Fig. 4f the phases of the MW pulses were varied with ϕ₁ varying from 0 to 2π and ϕ₂ = ϕ₁ + π/2. A sinusoidal fit to the data maintains the constant phase of the LO pulses, thereby proving the coherent phase transfer. Further data on interference are presented in Supplementary Fig. S11.

Spectro-temporal multiplexing

Highly multimode QMs significantly enhance the entanglement generation rate in a repeater protocol⁴³. Here, we demonstrate spectrally and temporally multiplexed M2O transduction, capitalizing on the large optical and spin inhomogeneous broadening in Yb:YSO as illustrated in Fig. 5a.

Fig. 5. Spectro-temporal multiplexing.

a Schematic of the pulse sequence to store n-temporal modes and retrieve them in FIFO scheme using a pair of RAP pulses either at single or multiple frequencies. b Experimental histogram data (orange) for 10-temporal modes. Gray areas represent potential temporal bins for transduced signals. The first two bins represent the noise level. Blue data points are the mean photon counts with the error bars representing Poissonian uncertainty over 100 cycles in the respective bin. c Mean photon counts in bins for different numbers of temporal modes. d(i) Schematic of Fourier spectra of two pump pulses symmetrically detuned from the offset centre of the RAP spectrum. d(ii) Sweep of the pump detuning with MW frequency fixed at the spin resonance. The inset shows the corresponding temporal histogram. e(i) Schematic of two RAP windows placed around the centre of the optical inhomogeneous broadening. e(ii) 10 spectro-temporal modes stored in 4-memory cells defined by two pump frequencies ( ± ) in two RAP windows (α/β) each. Bit strings of 1s and 0s correspond to ON and OFF states of the MW in each mode, while a dash denotes the OFF state for both the pump and the MW and corresponds to noise. Spectral coordinates are mentioned as (RAP α/β, Pump  + / − ). b, c, d(ii), e(ii), The error bars correspond to the standard deviation of the photon-count statistics.

Temporal multiplexing

Here we transduce ten modes with all pump pulses at the same frequency, and MW pulses at the spin resonance, rephased by a pair of spectrally identical single-tone RAP pulses in a First-In-First-Out (FIFO) sequence. In Fig. 5b, the photon counts in each gray bin spaced by 5.4 μs, correspond to the temporal modes, where the first two labeled bins represent the noise counts. The transduction efficiency varies over the modes with the highest for the first mode, decreasing over the subsequent modes, and then increasing again for the final few modes. This behaviour is explained by the first pump pulse interacting with the largest ground-state population, which enables a stronger population transfer to the $\mid 2_e\left(\right.⟩$ state. For the subsequent pulses, the available population in $\mid 4_g\left(\right.⟩$ decreases, leading to reduced efficiency. However, given the excited-state lifetime of approximately 1.3 ms⁴⁴ and a total multiplexing duration of only 100 μs, some atoms repopulate the $\mid 4_g\left(\right.⟩$ state before the arrival of the last pump pulses, resulting in a partial recovery of transduction efficiency towards the end.

In order to better understand the effect of temporal multiplexing on efficiency, the experiment is performed with a varying number of temporal modes as shown in Fig. 5c. A similar trend of decreasing efficiency over the modes is observed. The transduction efficiency of the first mode also decreases with an increasing number of temporal modes. This is because of the congestion of modes going to the same spectral window in the optical inhomogeneous broadening, and it can be overcome by optical spectral multiplexing.

Opto-spectral multiplexing within single RAP window

We utilize the broad chirp bandwidth of the RAP pulses (Δ_ch = 1.5 MHz) to rephase two spectrally distinct pump modes with the same individual Fourier bandwidth of 250 kHz (τ_p = 4 μs), as illustrated in Fig. 5d(i). The pump frequency for the early and the late temporal modes are blue- ( + ) and red-shifted ( − ) respectively, by Δω_P < Δ_ch/2 from the offset centre of the RAP window such that ${\omega }_P^{\pm }={\omega }_R+{\omega }_M\pm \mathrm{\Delta }{\omega }_P$ define two spectral cells. The transduced counts for the early and the late modes are plotted with varying Δω_P in Fig. 5d(ii). From temporal multiplexing, we know that the first temporal pulse supports the highest efficiency. This efficiency decreases with Δω_P due to the reduced efficiency of the rephasing by the RAP pulses. However, the late transduced counts with increasing Δω_p initially rise, due to the decreasing overlap of the spectrum of the late pump pulse with that of the early pump pulse, before dropping again due to the inefficient RAP rephasing. We find that Δω_P = 200 kHz is optimal for balancing the efficiencies without sacrificing overall efficiency. Therefore, we can transduce pulses in any temporal order with the spectral cells symmetrically separated by 400 kHz within a single RAP window.

Opto-spectral multiplexing with multiple RAP windows

It is also possible to exploit the broad optical inhomogeneous broadening of Yb:YSO ( ~550 MHz from Supplementary Fig. S2) to enable multi-window spectral multiplexing. Fig. 5e(i) illustrates two RAP windows (α and β) centred within the optical inhomogeneous profile, and can be extended to accommodate additional windows. Each RAP window can independently accommodate at least two spectral cells corresponding to different pump frequencies. Furthermore, within each pump frequency mode, multiple MW frequencies lying within the spin inhomogeneous broadening can be addressed (Supplementary Note 5), thereby enhancing the overall multiplexing capacity. An additional advantage of using multiple RAP windows is the ability to selectively retrieve stored modes from any chosen window at different times. While this approach is conceptually similar to the spectral multiplexing discussed in ref. ³⁴, here all the modes are retrieved together for simplicity.

For experimental demonstration, we define two RAP windows separated by 4 MHz, each containing two cells, established by applying two pump frequencies detuned by Δω_P = 200 kHz from the offset centre of their respective RAP windows. In total, this configuration yields four distinct spectral cells, each capable of storing multiple MW spectral modes. The cells are named after their corresponding RAP and pump frequencies e.g., α − represents RAPα and a red-detuned pump pulse. Fig. 5e(ii) presents the experimental results for ten spectro-temporal modes, where the bit-strings in the legend represent the ON (1) or OFF (0) state of the MW pulse in the respective temporal mode. The pump pulses are ON for all the modes. In any particular temporal bin, the transduced counts are the same if the MW is ON, and they fall to the noise level if the MW is OFF. Therefore, a discriminator level shown by the horizontal dashed line can be used to determine the state of MW for that particular temporal bin. The transduction efficiency of the first four modes is higher than that of the next group of four modes due to the temporal-mode congestion within the same spectral cell. These observations highlight that distributing temporal modes across multiple RAP windows and pump frequency cells supports almost uniform efficiency across modes, demonstrating the effectiveness of spectro-temporal multiplexing. Note that the reduced counts in the even modes are not consistent in all the experiment trials, but are an effect of the spatial inefficiency of the AOM at the shifted frequency (another trial is presented in Supplementary Fig. S13).

Discussion

In this work, we present a memory-assisted M2O transduction protocol along with its implementation in Yb:YSO placed in a 3D LGR. The internal transduction efficiency, at 460 μs storage time and 641 kHz bandwidth, is 4 × 10⁻⁸ with  ~ 0.4 photons as noise floor. We show coherent information transfer from MW to optical modes, facilitating phase-encoding schemes such as QPSK. We further show spectro-temporal multiplexing capability, useful for time-bin qubit applications. Such a memory-assisted transducer with multiplexing is an important enabler for fast and efficient entanglement generation between SQCs.

To be clear of noise from FID decay from the RAP pulses and undesired echoes, extended storage times are required, impacting the M2O transduction efficiency. Introducing a small angle between the RAP and the pump pulses would suppress the noise, and combining it with a higher pump Rabi frequency, using higher optical power, would allow higher efficiency, e.g., a 3.7-fold increase at 150 μs storage time. In the optical domain, a broader chirp range of the RAP pulses (only limited by the optical inhomogeneous broadening) would allow higher spectral multiplexing capacity. Naturally, this will necessitate higher laser power to drive multiple RAP transitions simultaneously.

The low efficiency of our system is due to several factors, including low concentration of spins in the mode volume, small Rabi frequency at the pump transition, single-pass optical configuration, small optical-MW mode overlap, and low LGR quality factor. These factors result in weak MW and atomic cooperativities, and similar efficiencies have been observed for Er:YSO without an optical cavity ( ~ 10⁻¹²)⁴⁵ and rise to 10⁻⁵ with an optical cavity³¹. A planar superconducting MW resonator together with an optical cavity can provide a small mode volume with increased mode overlap, thereby enhancing the optical Rabi frequency, as well as large MW and atomic cooperativities, as demonstrated with Yb:YVO⁶. However, the short microwave/spin and optical memory coherence times (T_m,s = 910 ns, T_m,o = 140 ns)⁶ make Yb:YVO less suited for memory-assisted transduction. With Yb:YSO in 3D-LGR and an optical cavity under optimized conditions, the CW transduction efficiency can reach up to 10⁻⁴, and the memory efficiency can reach unity.

The memory-assisted transducer benefits from the long optical coherence time and high doping concentration (improving cooperativity) in REI crystals. However, higher doping concentration decreases the optical coherence time⁴⁶. Therefore, based on specific applications, the coherence time can be traded off with high doping concentration to enable either long storage or high-efficiency memory-assisted transduction. Higher doping also results in broader inhomogeneous linewidths and can improve the MW bandwidth of the transducer^6,31.

The protocol presented in this paper can be implemented in other systems, with the necessary coherence time and bandwidth, allowing for flexibility in matching wavelengths to other components over a link between remote SQCs. Furthermore, our system can provide a valuable microwave-qubit memory interface for quantum computers. Even for purely optical QM realizations, the enhanced MW coupling of our system can be used to implement dynamical-decoupling sequences to increase the storage time.

Methods

Experimental setup

The experimental setup is presented in Supplementary Fig. S1. A Toptica DL Pro laser is locked to an external reference cavity (Stable Laser System) at 1150 MHz blue-detuned from $\mid 4_g⟩\leftrightarrow ∣1_e⟩$ f transition. The laser beam passes through two acousto-optic modulators (AOMs). AOM1 (Model: AA Opto-Electronic: MT200-B100A0,5-1064) is used to create optical pulses and fine frequency shifts (0-5 MHz). AOM2 (Model: Brimrose: TEM-85-10) suppresses the first-order leak light from AOM1,which is helpful forsingle-photonn detection with minimal background noise. A phase modulator (PM) (Model: iXblue: NIR-MPX950) is used to coarse-shift ( ~ GHz) the frequencies for optical pumping, pump, and RAP pulses. The limited shift efficiency of the PM (70%) creates undesired noise (2PE with leak light) and limits the pump pulse power. Optical powers mentioned in the text account for this inefficiency. Two polarization controllers (half-wave plates) are placed before and after the PM for efficient frequency shift and for aligning the polarization along the ${\vec{D}}_2$-crystal axis to achieve maximum absorption³², respectively. Optical coupling efficiency through the crystal, including fiber and splice losses, is about 10%. The output fiber is coupled to an avalanche photodetector (APD - Model: PerkinElmer SPCM-AQRH-14-FC) via a free-space gating AOM (AOM3 - Model: AA Opto-Electronic: MT200-B100A0,5-1064) with 40% shift efficiency. The APD detection efficiency is 12% at 980 nm.

MW pulses are generated from an Arbitrary Waveform Generator (AWG - Tektronix - AWG70002A) and gated via an electronic switch (Model: ZASWA-2-50DRA+) before entering the dilution fridge. The overall loss of the MW line from the AWG to the input port of the cavity is -15.58 dB, including losses in the switch, isolators, and the transmission lines.

Experimental sequence

Due to the intense pulses involved in the transduction sequence, the population in the three-level system changes. To provide a consistent initial population, an optical pumping sequence is applied. The population is initialized to $\mid 4_g⟩$ level by applying a set of chirped pulses around $\mid 3_g⟩\leftrightarrow \mid 2_e⟩$ and $\mid 2_g⟩\leftrightarrow \mid 1_e⟩$ transitions. After optical pumping, the population is allowed to relax to the ground state for 1 s. This also allows the local heat to dissipate. Optical depth of about 1.4 is reached after population initialization, as shown in Supplementary Fig. S2. Then the transduction protocol is applied as shown in Fig. 1 and outlined in Sec. Memory-assisted M2O Transduction Protocol. The gating AOM is shut throughout the experiment except (i) between the pump pulse and RAP1, (ii) between RAP1 and RAP2, and (iii) between RAP2 and RAP echo. After the transduction protocol ends, we wait for another 1 s before restarting the sequence to allow the excited state population to decay back to the ground level.

Pulse shaping

The optical pulses are temporally shaped with AOM1, and its coarse ( ~ GHz) and fine ( < 5 MHz) frequencies are adjusted with the PM and AOM1, respectively. AOM2 is turned ON with a delay of 400 ns to account for signal propagation delay. The RAP pulses employed in this work have sinc temporal profile with linearly chirped frequency, similar to that used in the QM paper³⁴.

$$P\left(t\right)=A\left(t\right)\sin \left({\omega }_{R}t+\phi \left(t\right)\right),$$ 1

with the phase and amplitude terms given by

$$A\left(t\right)=A_0\mathrm{sinc}\left(\frac{2\left(t-t_0\right)}{{\tau }_R}\right),$$ 2

$$\phi \left(t\right)=\frac{{\mathrm{\Delta }}_{\mathrm{ch}}}{{\tau }_R}{\left(t-t_0\right)}^2,$$ 3

where, A₀ is an amplitude factor, τ_R is the duration, Δ_ch is the chirp bandwidth and t₀ is the center of the RAP pulse.

The MW pulse frequency and phase are defined from the AWG using the function $A\left(t\right)\sin \left(2\pi {\nu }_{M}t+\varphi \right)$, where A(t) = sinc(2t/τ_M) is the temporal envelope of the pulse, ν_M is the frequency of the MW, ϕ is the phase and τ_M is the duration of the MW pulse. We employed sinc temporal profiles (sinc(2t/τ_P,M)) for both pump and MW pulses throughout, except for spin inhomogeneous broadening characterization in Supplementary Fig. S7(c), where both the pulses are square in shape. For interference experiments, we vary the phase of the late MW pulse relative to the early one. For Homodyne measurements, the LO pulses are also sinc-shaped with the minimum possible amplitude from the AWG to keep the photon counts per pulse to the lowest. Lower counts in the LO pulses ensure high visibility of the interference patterns.

For multiplexing experiments, the MW pulse power was high ( ~ 2 × 10¹¹ photons per pulse for temporal modes;  ~ 1 × 10¹¹ photons per pulse for opto-spectral modes) for a better SNR over all the temporal modes to counter the lower efficiency at the longer storage durations employed. Also, the temporal gap between each mode is set to resolve the individual peaks. For demonstration with multiple RAP windows, we used AOM1 to shift the RAP central frequency by  ± 2 MHz on either side of the AOM1 drive frequency. The 4 MHz frequency separation is enough to avoid crosstalk between the cells in different RAP windows. At smaller frequency separations, the transduction efficiency of the modes is lower than the maximum. If there is no separation, the RAP power will be just doubled, causing weak rephasing across all the modes due to a larger-than-π pulse area for the RAP pulses.

Choice of transitions

Due to the weak branching ratio of 0.04⁴⁷ at the pump transition $\mid 4_g\left(\right.⟩\leftrightarrow \mid 2_e\left(\right.⟩$, we could achieve only a 0.009 π-pulse, instead of a π/2-pulse required for maximum coherence (Supplementary Note 2), with a sinc-shaped pump pulse with Rabi frequency Ω_P = 2π × 7 kHz at 2.5 mW optical power. In contrast, the significantly stronger branching ratio of 0.72⁴⁷ at $\mid 4_g\left(\right.⟩\leftrightarrow \mid 1_e\left(\right.⟩$ transition enables efficient rephasing with the RAP pulses at 850 μW peak optical power (Ω_R = 2π × 75 kHz) (Supplementary Fig. S7a). The corresponding adiabaticity condition ${\mathrm{\Omega }}_R^2/R_{\mathrm{ch}}=1.41>1$ is satisfied. The MW frequency sweep characterizes the spin resonance to be 2623.35 MHz with a bandwidth of Γ_s = 642 kHz (Supplementary Fig. S7c), matching well to the Fourier bandwidth of the MW pulses.

Efficiency budget

The memory-assisted transduction efficiency (4 × 10⁻⁸) depends on the memory and continuous-wave (CW) transduction efficiencies. The optical memory efficiency measured using the same pulse parameters is approximately 7%. The CW transduction efficiency is measured to be  ~ 1 × 10⁻⁸ under comparable pump powers, albeit with slightly different field configurations. In the CW measurement, the optical pump is applied on the $\mid 4_g⟩\leftrightarrow \mid 1_e⟩$ transition, whereas in the memory-assisted protocol the pump addresses the $\mid 4_g⟩\leftrightarrow \mid 2_e⟩$ transition. As a consequence, in the CW case the generated optical field at the $\mid 4_g⟩\leftrightarrow \mid 2_e⟩$ transition spectrally overlaps with the inhomogeneously broadened $\mid 2_g⟩\leftrightarrow \mid 1_e⟩$ transition, leading to partial reabsorption and attenuation of the transduced optical signal. In addition, the CW transduction experiment employs longer and stronger microwave and optical fields, resulting in lower efficiency due to saturation of the spin transition²⁵.

Author contributions

U.G. performed the experiments, prepared a theoretical model, and conducted numerical simulations. U.G. worked on the microwave aspect of the setup, and N.G.K. worked on the optical setup. U.G. and N.G.K. analysed the measurements. U.G., N.G.K., and S.K. contributed to the design and implementation of the cryogenic setup. U.G., N.G.K., and D.O. wrote the paper. All authors contributed to the ideation of the experiment and reviewed and edited the manuscript. D.O. supervised the research.

Peer review

Peer review information

Nature Communications thanks the anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Funding

This work was supported by the Government of Alberta Major Innovation Fund Project on Quantum Technologies, Alberta Innovates Advance Grant, Mitacs through the Mitacs Accelerate program, the Canadian Foundation for Innovation Infrastructure Fund (CFI-IF), and the Natural Sciences and Engineering Research Council of Canada (NSERC) through the Alliance Quantum Consortia Grants CanQuest and ARAQNE.

Data availability

The raw, processed, and simulated data generated in this study and its relevant codes have been deposited in the Figshare database under accession code⁴⁸ https://doi.org/10.6084/m9.figshare.32816873.

Competing interests

N.G.K. and D.O. declare that they hold an equity stake in Quantized Technologies Inc, which owns the commercial rights to the optical memory protocol utilized in this study. All other authors declare that they have no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s41467-026-77057-3.