Abstract
Electron spin resonance spectroscopy is the method of choice for characterizing paramagnetic impurities, with applications ranging from chemistry to quantum computing1,2, but it gives access only to ensemble-averaged quantities owing to its limited signal-to-noise ratio. Single-electron spin sensitivity has, however, been reached using spin-dependent photoluminescence3,4,5, transport measurements6,7,8,9 and scanning-probe techniques10,11,12. These methods are system-specific or sensitive only in a small detection volume13,14, so that practical single-spin detection remains an open challenge. Here, we demonstrate single-electron magnetic resonance by spin fluorescence detection15, using a microwave photon counter at millikelvin temperatures16. We detect individual paramagnetic erbium ions in a scheelite crystal coupled to a high-quality-factor planar superconducting resonator to enhance their radiative decay rate17, with a signal-to-noise ratio of 1.9 in one second integration time. The fluorescence signal shows anti-bunching, proving that it comes from individual emitters. Coherence times up to 3 ms are measured, limited by the spin radiative lifetime. The method has the potential to be applied to arbitrary paramagnetic species with long enough non-radiative relaxation times, and allows single-spin detection in a volume as large as the resonator magnetic mode volume (approximately 10 μm3 in the present experiment), orders of magnitude larger than other single-spin detection techniques. As such, it may find applications in magnetic resonance and quantum computing.
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Data availability
The data presented in the figures and raw data of photon intensity autocorrelation measurements with analysis code are available at https://doi.org/10.7910/DVN/DSNXXO.
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Acknowledgements
We acknowledge technical support from P. Sénat, D. Duet, P.-F. Orfila and S. Delprat, and are grateful for fruitful discussions within the Quantronics group. We acknowledge support from the Agence Nationale de la Recherche (ANR) through the Chaire Industrielle NASNIQ under contract ANR-17-CHIN-0001 cofunded by Atos, and through the MIRESPIN (ANR-19-CE47-0011) and DARKWADOR (ANR-19-CE47-0004) projects. We acknowledge support of the Région Ile-de-France through the DIM SIRTEQ (REIMIC project), from CEA through the DRF-Impulsion programme (grant no. RPENANO), from the AIDAS virtual joint laboratory and from the France 2030 plan under the ANR-22-PETQ-0003 RobustSuperQ grant. This project has received funding from the European Union Horizon 2020 research and innovation programme under Marie Sklodowska-Curie grant no. 792727 (SMERC), and from the European Research Council under grant no. 101042315 (INGENIOUS). Z.W. acknowledges financial support from the Sherbrooke Quantum Institute, from the International Doctoral Action of Paris-Saclay IDEX and from the IRL-Quantum Frontiers Lab. We acknowledge IARPA and Lincoln Labs for providing the Josephson TWPA. We acknowledge the crystal lattice visualization tool VESTA.
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A.F. and P.G. grew the crystal, which M.L.D., Z.W., E.B., T.C. and S.B. characterized through CW and pulse EPR measurements. Z.W., D.V., P.B. and E.F. designed the spin resonator. Z.W. fabricated the spin resonator. L.B. and E.F. designed the SMPD. L.B. fabricated the SMPD. M.R. designed and installed the magnetic field stabilization. Z.W., L.B. and E.F. took the measurements. Z.W., P.B. and E.F. analysed the data. Z.W., P.B., D.E., D.V. and E.F. wrote the article, with contributions from all the authors. P.B. and E.F. supervised the project.
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Extended data figures and tables
Extended Data Fig. 1 Crystal structure of Er3+: CaWO4.
Tetragonal unit cell of CaWO4 crystal with central Ca2+ substituted by Er3+. This central site has a S4 symmetry.
Extended Data Fig. 2 Sample.
(a) Schematic of the sample. A niobium resonator (blue) is fabricated on top of the CaWO4 crystal (gray). The inductive wire (pink) at the center of the resonator is defined as the z-axis. The xy plane is perpendicular to z, with the y axis in the sample plane and the x axis orthogonal to it. β is the angle between the crystal c-axis and the sample plane. θ is the angle between the projection of c-axis in the yz plane and the magnetic field B0 (which is also applied in the yz plane). (b) The design of the “bow-tie” shaped resonator, where top and bottom pads form interdigitated capacitors at the left and right with a 10 μm width for both finger and gap (Bottom capacitor is annotated with red dashed box). Strips with 20 μm width are created on capacitor pads. (c) Scanning electron microscope image on a lithographically identical sample. The inductive wire has a length of 94 μm and a width of 600 nm.
Extended Data Fig. 3 SMPD characteristics.
(a) SMPD efficiency. Detected click rate (red) and efficiency (blue) as a function of input photon flux. Below 104 s−1 (linear regime), an efficiency of 0.32 is obtained. (b) SMPD bandwidth. Average number of detected counts as a function of photon frequency when the input microwave tone is switched on (red dots) or off (gray dots). The solid line is a Lorentzian fit to the data yielding a FWHM bandwidth of 0.9 MHz.
Extended Data Fig. 4 Magnetic field alignement.
Measured (dots) magnetic field \({B}_{0}^{peak}\) at which the center of the spin ensemble line is found, as a function of the angle θ that the field makes with the c axis projection. The fit with eq. (5) (line) to the data yields the θ = 0° origin (see text), as well as the angle between the c axis and the sample plane, β = 0.5°.
Extended Data Fig. 5 Transient response of the system after microwave excitation.
Measured average click rate versus time before and after a 6 μs-long microwave excitation pulse is applied at time 0, for cases 1 (red), 2 (blue) and 3 (orange) - see text. SMPD is switched off during excitation. Dark count background is indicated in grey. Inset is a zoomed-in view around time 0.
Extended Data Fig. 6 Heating versus spin excitation duration and amplitude.
Measured average counts integrated over a 8 ms-long window after an excitation pulse as a function of pulse duration and amplitude A, obtained when the spin resonator is detuned from (dash line) or in resonance with (solid line) the SMPD buffer. The excitation pulse frequency is always tuned to the SMPD buffer one.
Extended Data Fig. 7 Photon intensity auto-correlation function g(2) within one sequence.
(a) Average count rate ⟨Ċ⟩ as a function of delay time after a π-excitation pulse, for all recorded sequences (red) and for sequences with a first click detected before 0.45ms (dark red). The reduction of ⟨Ċ⟩ in the second case indicates the anti-bunching of spin fluorescence photons. (b) Average count rate ⟨Ċ⟩ as a function of delay time, for all recorded background traces (gray) and for traces with a first click detected before 0.45 ms (dark gray). The unchanged ⟨Ċ⟩ in the second case indicates a Poissonian background made of independent dark count events. (c) Extracted g(2) function for dark counts (gray dots) and spin fluorescence signal (red dots) as a function of delay time τ. Expected g(2) functions for the Poissonnian background (grey solid line) and for an ideal single emitter in presence of the same background (\({g}_{se}^{(2)}\) - red solid line) fit well the experimental data. (d) Uncorrected g(2)(k) (blue columns) and corresponding ± 1-standard deviation error bars (red) as a function of inter-sequence offset k.
Extended Data Fig. 8 Spin-Lattice relaxation time.
Measured with inversion-recovery sequence at 10 mK, with B0 along the c axis, and ω0/2π = 7.853 GHz. Green dots are data, solid line is a fit yielding T1 = 0.213 ± 0.001 s.
Extended Data Fig. 9 Schematic of the setup.
Wiring and all the components used in this experiment at room temperature and cryogenic temperature are shown.
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Wang, Z., Balembois, L., Rančić, M. et al. Single-electron spin resonance detection by microwave photon counting. Nature 619, 276–281 (2023). https://doi.org/10.1038/s41586-023-06097-2
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DOI: https://doi.org/10.1038/s41586-023-06097-2
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