Coherent control of interacting solid-state spins below the diffraction limit

Nature Physics (2026) Cite this article Optically addressed atomic defects in the solid state are widely used as single-photon sources and memories for quantum network applications. The solid-state environment allows for a high density of electron and nuclear spins with the potential to form registers for coherent information processing. Interactions between the spins could enable computational gates, but it is challenging to reliably address individual spins at nanometre separations at which interactions are large. Rare-earth ions offer a promising solution, as their narrow homogeneous optical linewidth allows the frequency-domain resolution of a large number of emitters independent of their spatial separation. Here we realize the coherent optical and spin control of a pair of interacting Er3+ ions, together with a nearby nuclear spin ancilla. We demonstrate two-qubit electron–electron gates and use them to perform repeated quantum non-demolition measurements on one of the Er3+ ions. We also use electron–nuclear gates to coherently store and retrieve qubit information in a nuclear spin, and show that the nuclear spin coherence survives read-out of the electron spin. These techniques can be readily scaled to larger numbers of electron and nuclear spins, providing a platform for massively multiplexed quantum network nodes.This is a preview of subscription content, access via your institution Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription $32.99 / 30 days cancel any timeSubscribe to this journal Receive 12 print issues and online access $259.00 per yearonly $21.58 per issueBuy this articleUSD 39.95Prices may be subject to local taxes which are calculated during checkoutSource data are provided with this paper.The codes and algorithms that have been used to support the findings of this study are available from the corresponding author upon request.Togan, E. et al. Quantum entanglement between an optical photon and a solid-state spin qubit. Nature 466, 730–734 (2010).Article ADS Google Scholar Bernien, H. et al. Heralded entanglement between solid-state qubits separated by three metres. Nature 497, 86–90 (2013).Article ADS Google Scholar Knaut, C. M. et al. Entanglement of nanophotonic quantum memory nodes in a telecom network. Nature 629, 573–578 (2024).Article ADS Google Scholar Fang, R.-Z. et al. Experimental generation of spin-photon entanglement in silicon carbide. Phys. Rev. Lett. 132, 160801 (2024).Article ADS Google Scholar Ruskuc, A. et al. Multiplexed entanglement of multi-emitter quantum network nodes. Nature 639, 54–59 (2025).Article ADS Google Scholar Uysal, M. T. et al. Spin-photon entanglement of a single Er3+ ion in the telecom band. Phys. Rev. X 15, 011071 (2025).

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Lett. A 303, 249–252 (2002).Article ADS MathSciNet Google Scholar Download referencesWe acknowledge helpful conversations with P. Bertet, N. de Leon and J. Rovny. This work was supported by the US Department of Energy, under contract number DE-SC0020120 (supporting research on interacting spins), and by the Office of Science, National Quantum Information Science Research Centers, Co-design Center for Quantum Advantage (C2QA), under contract number DE-SC0012704 (supporting device fabrication, materials spectroscopy and improvements).These authors contributed equally: Haitong Xu, Mehmet T. Uysal.Department of Electrical & Computer Engineering, Princeton University, Princeton, NJ, USAHaitong Xu, Mehmet T. Uysal, Łukasz Dusanowski, Adam T. Turflinger, Ashwin K. Boddeti, Joseph Alexander & Jeff D. ThompsonDepartment of Electrical and Computer Engineering, FAMU-FSU College of Engineering, Florida State University, Tallahassee, FL, USAŁukasz DusanowskiSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarH.X. and M.T.U. performed all the experiments involved in this work. Ł.D. designed and fabricated the photonic device. A.B. stamped the photonic device onto the sample. A.T.T., A.B. and J.A. helped improve the experimental setup. H.X. and M.T.U. wrote the paper with contributions from all authors.Correspondence to Jeff D. Thompson.The authors declare no competing interests.Nature Physics thanks John Bartholomew, Priyash Barya and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.a, DEER spectroscopy (blue markers) reveals two dips in spin coherence, fitted by the solid line. One of the dips overlap with the Er-1 optically detected magnetic resonance (ODMR) (orange markers), and another dip suggests the existence of an interacting Er3+ neighbor, Er-2. b, The selectivity of MW assisted PLE spectroscopy with respect to the MW frequency (MW detuning compared to Rabi frequency, δ/Ω) can be adjusted by varying the number of optical pulses per MW remixing pulse N compared to the cyclicity C of the optical transition. For non-selective experiments (N/C ≪ 1), fluorescence is still observed when the MW detuning from the spin transition δ is larger than the drive Rabi frequency, Ω. c, Non-selective MW assisted PLE with N = 1 reveals most of the ions in the cavity (blue trace), while a selective experiment with N = 50 only excites one ion with the corresponding MW frequency (orange trace). The two peaks for the selective (N = 50) case are the A and B optical transitions of the same ion, Er-2. d, Exciting Er-2 before the DEER sequence shelves the spin and changes the DEER contrast (orange). The change in contrast overlap with the PLE of Er-2 (black). e, ODMR on Er-1 (green markers) and on Er-2 (orange markers), fitted by Lorentzians (black solid line) yield linewidths of 246(16) kHz and 488(22) kHz of Er-1 and Er-2 respectively. The calculated population change under a π-pulse (dotted trace) shows negligible crosstalk with probability of accidental spin flip less than 0.1%. f, Cumulated distribution function of the largest Ising interacting strength of an ion with its neighbors (blue) yields a probability of 26% to have an interacting neighbor with J≥5.40 kHz Ising interaction (black dashed line).Source dataa, Circuits for running experiments on two ions consist of initializations, experiments, and readouts. b, Each initialization round consists of optical excitations followed by MW pulses to pump the population out of the cycling transition. c, Readout consists of repeated optical excitations on the cycling transitions to collect enough photons for thresholding. The excitations on the two ions are performed sequentially for temporal separation of their photons. d, The histograms of photon detection events for reading out two ions, thresholding with one photon detection event gives readout fidelities of 0.947(2) and 0.927(3) on Er-1 (right) and Er-2 (left) respectively.Source dataa, Er-2 spin coherence under the XY-8 sequence (markers) shows ESEEM features due to surrounding nuclear spins.

Correlated Cluster Expansion (CCE) simulation of two measured strongly coupled nuclear spins (Extended Data Table 1) and a randomly generated weakly coupled bath (black solid line) show agreement with the data23. b, Zoomed-in Er-2 spin coherence under the XY-8 sequence (markers) shows a contrast of \({p}_{(XY-8)}^{(2)}=-0.86(2)\) at the evolution time of 16τ = 99.3 μs (vertical dashed line) that is used for the entangling gate. c, Er-1 spin coherence under the XY-6 sequence (markers) shows a contrast of \({p}_{(XY-6)}^{(1)}=0.87(1)\) at the evolution time of 12τ = 74.6 μs (vertical dashed line). d, Shifting the time offset δτ between two overlapping dynamical decoupling sequences changes the effective interaction time Tint. The horizontal dashed line corresponds to the required interaction time for maximal entanglement. e, Er-2 spin coherence when sweeping δτ after being initialized into two different bases (red and orange markers) matches the calculated result based on Tint (red and orange lines). The maximal entanglement is reached when δτ = 2.3 μs, where no contrast is observed when only measuring Er-2. f, The pulse sequence for CZ gate is placed between π/2-pulses at the beginning and end of the sequence to create and measure the Bell state. The final π/2-pulses in the dashed box are the analysis pulses for reading out different bases, and extra π-pulses are used for refocusing.Source dataa, Nuclear spin free precession (markers) shows the sum of two oscillations at frequencies ω+ and ω− fitted by the solid line. b, The Fourier transform of the free precession shows two peaks corresponding to ω+ = 458 kHz and ω− = 219 kHz. c, The measured ESEEM features in XY-96 on Er-2 (markers) show disagreement with simulation with ωL0, the ideal Larmor frequency, from which we estimated the actual Larmor frequency to be around 0.993ωL0. d, Varying the number of pulses and the inter-pulse spacing of the pulse sequence on the electron spin results in a chevron pattern on the nuclear spin evolution. The chevron pattern is distorted because the parallel hyperfine coupling strength is comparable to the Larmor frequency, A∥ ≈ ωL.Source dataa, 183W nuclear spin Hahn experiment with an additional optical pulse drawn as the shaded orange rectangle. The optical pulse is off-resonant with all the Er3+ ions but is still in the photonic cavity linewidth. The nuclear spin coherence decays when the timing of the optical pulse approaches the refocusing operations. b, Er-2 Er3+ electron spin Hahn experiment with additional off-resonance optical pulse. The Er3+ coherence decays when the optical pulse is approaching the refocusing pulse, as also reported in6. c, Coherence time of Er-2 (orange markers) and the 183W spin (purple markers) as a function of laser pulse width. The two fitted curves (orange and purple lines) are offset by a factor of 3.2 × 104, roughly matching the ratio of ∣A∣/ωMWg = 2.7 × 104.Source dataa, Schematic diagram of pulse sequence concatenation in part of the circuit in d. (1) The three CX operations are formed by π/2-pulses, the CZ gate, and the CX gate. (2) The CZ and CX gates are constructed from pulse sequences. (3) The pulse sequences are concatenated. The last π/2-pulse along X is skipped, because it does not affect the readout on \(\left|\pm \right\rangle\) (projected to \(\left|0/1\right\rangle\) by π/2 along Y). b, Circuit diagram for Bell state creation and measurement in the ZZ basis. c, Pulse sequences in I/Q channels of the ZZ basis measurement on Er-1 and Er-2 are shown. d, Circuit diagram of the XX basis measurement is shown. e, Pulse sequences on Er-1 and Er-2 are shown.Source dataPLE, 2D MW-PLE, 2D MW chevron data, spin Hahn echo data and DEER data.Read-out index versus fidelity and read-out index versus support vector machine fidelity/post-selection fidelity read-out index versus acceptance rate for two cases.Number of XY pulses versus Z expectation for Er-2, evolution time for nuclear spin Ramsey (ms) versus ZZ for Er-2 and evolution time for nuclear spin Hahn (s) versus ZZ correlation for Er-2.Bar chart data and number of optical excitations versus Z/X expectation value for Er-2.MW freq (MHz) versus contrast in DEER/population in ODMR, simulated counts in MW-PLE, laser frequency (MHz) versus MW PLE counts (1 pulse/50 pulse), PLE and DOER spectroscopy, measured/simulated ODMR for Er-1/Er-2 and Monte Carlo simulation for the probability of interacting pairs.Probability density of receiving different numbers of photon given the Er-1/Er-2 spin state.Measured and simulated XY-8 for Er-2, measured and simulated XY-8 for Er-2, measured and simulated XY-6 for Er-1, offset time (µs) between XY-8 and XY-6 for two ions versus effective interaction time T_int (µs) and simulated/measured Z expectation value for Er-2 versus offset time (µs).Nuclear spin Ramey data, FFT for nuclear spin Ramsey: frequency (kHz) versus amplitude (kHz−1), measured/simulated ESEEM features in XY-96 in Er-2 and 2D chevron pattern for nuclear spin control.Contrast of nuclear spin Hahn under different optical pulses, contrast of electron spin Hahn under different optical pulses and fitted decoherent rate.Pulse sequence for the quantum circuit.Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.Reprints and permissionsXu, H., Uysal, M.T., Dusanowski, Ł. et al. Coherent control of interacting solid-state spins below the diffraction limit. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03319-yDownload citationReceived: 18 August 2025Accepted: 27 April 2026Published: 26 June 2026Version of record: 26 June 2026DOI: https://doi.org/10.1038/s41567-026-03319-yAnyone you share the following link with will be able to read this content:Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative