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arXiv:2504.12957 · PRX Quantum

Cavity-Enhanced Spectroscopy of Individual Nuclear Spins in a Dense Bath

Alexander Ulanowski, Olivier Kuijpers, Benjamin Merkel, Adrian Holzäpfel, Andreas Reiserer

Published Jun 5, 2025• 5 citations

Abstract

Echo-based spectroscopy of the superhyperfine interaction of an electronic spin with nuclear spins in its surroundings enables detailed insights into the microscopic magnetic environment of spins in solids. Still, it is an outstanding challenge to resolve individual nuclear spins in a dense bath, in which many of them exhibit a comparable coupling strength. This simultaneously requires a high spectral resolution and a large signal-to-noise ratio. However, when probing spin ensembles, dipolar interactions between the dopants can lead to a concentration-dependent trade-off between resolution and signal. Here, we fully eliminate this limitation of previous optical-echo-envelope-modulation spectroscopy experiments by integrating the emitters into a high-finesse resonator, which allows for strong optical echoes even at very low concentrations. To demonstrate its potential, the technique is applied to erbium dopants in yttrium orthosilicate ( Er : YSO ). Achieving an unprecedented spectral resolution enables precise measurements of the superhyperfine interaction with four of the Y nuclear spins densely surrounding each emitter. The achieved boost of the signal, enabled by the resonator, allows for extending the approach to the lowest concentration possible—to the level of single dopants, thereby providing a tool for detecting and studying individual nuclear spins. Thus, our technique paves the way for an improved understanding of dense nuclear-spin baths in solids.

DOI: 10.1103/prxquantum.6.020344

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Their exceptional coherence makes nuclear spins in solids a prime candidate for quantum memories in quantum networks and repeaters. Still, the direct all-optical initialization, coherent control, and readout of individual nuclear spin qubits have been an outstanding challenge. Here, this is achieved by embedding 167-Er dopants in yttrium orthosilicate in a cryogenic Fabry-Perot cavity, whose linewidth of 65 MHz is much smaller than the 0.9 GHz separation of neighboring hyperfine levels. Frequency-selective emission enhancement thus enables a single-shot readout fidelity of 91(2)%. Furthermore, a large magnetic field freezes paramagnetic impurities, leading to coherence times exceeding 0.2 s. The combination of nuclear-spin qubits with frequency-multiplexed addressing and lifetime-limited photon emission in the minimal-loss telecommunications C-band establishes 167-Er as a leading platform for long-range, fiber-based quantum networks.

Counting the microwave photons emitted by an ensemble of electron spins when they relax radiatively has recently been proposed as a sensitive method for electron paramagnetic resonance spectroscopy, enabled by the development of operational single microwave photon detectors at millikelvin temperature. Here, we report the detection of spin echoes in the spin fluorescence signal. The echo manifests itself as a coherent modulation of the number of photons spontaneously emitted after a $\ensuremath{\pi}/{2}_{X}\ensuremath{-}\ensuremath{\tau}\ensuremath{-}{\ensuremath{\pi}}_{Y}\ensuremath{-}\ensuremath{\tau}\ensuremath{-}\ensuremath{\pi}/{2}_{\mathrm{\ensuremath{\Phi}}}$ sequence, dependent on the relative phase $\mathrm{\ensuremath{\Phi}}$. We demonstrate experimentally this detection method using an ensemble of

{\mathrm{Er}}^{3+}

ion spins in a scheelite crystal of

{\mathrm{CaWO}}_{4}

. We use fluorescence-detected echoes to measure the erbium spin coherence time, as well as the echo envelope modulation due to the coupling to the

^{183}\mathrm{W}

nuclear spins surrounding each ion. We finally compare the signal-to-noise ratio of inductively detected and fluorescence-detected echoes, and show that it is larger with the fluorescence method.

Rare-earth related electron spins in crystalline hosts are unique material systems, as they can potentially provide a direct interface between telecom band photons and long-lived spin quantum bits. Specifically, their optically accessible electron spins in solids interacting with nuclear spins in their environment are valuable quantum memory resources. Detection of nearby individual nuclear spins, so far exclusively shown for few dilute nuclear spin bath host systems such as the nitrogen-vacancy center in diamond or the silicon vacancy in silicon carbide, remained an open challenge for rare earths in their host materials, which typically exhibit dense nuclear spin baths. Here, we present the electron spin spectroscopy of single Ce^{3+} ions in a yttrium orthosilicate host, featuring a coherence time of T_{2}=124 μs. This coherent interaction time is sufficiently long to isolate proximal ^{89}Y nuclear spins from the nuclear spin bath of ^{89}Y. Furthermore, it allows for the detection of a single nearby ^{29}Si nuclear spin, native to the host material with ∼5% abundance. This study opens the door to quantum memory applications in rare-earth ion related systems based on coupled environmental nuclear spins, potentially useful for quantum error correction schemes.

Rare-earth ions in solids are under active investigation for quantum microwave-optical signal converters. Here, light passed through an Er:YSO crystal sitting in a driven microwave resonator develops modulation due to three-wave mixing in the erbium dopants. Strong coupling between the microwave cavity and the spins causes modulation when the microwaves are resonant with the spin-cavity polaritons rather than the spins. This work extends the rare-earth microwave-optical conversion to both millikelvin temperatures and isotopically pure dopants.

Single-spin magnetic resonance spectroscopy promises to yield structural and chemical information at the level of individual atoms or molecules, in a non-invasive way. Here, we use an Er3+ paramagnetic center in a CaWO4 crystal, detected by microwave photon counting at 10 mK, as a nanoscale magnetic sensor to measure the NMR spectrum of a proximal individual nuclear-spin-9/2 93Nb impurity with Hertz spectral resolution. From these measurements, we determine the 93Nb insertion site, its position relative to the Er3+ , and its complete quadrupolar tensor. We moreover harness the high spectral resolution of our measurements to establish the presence of two previously unobserved terms in the spin Hamiltonian. The first describes a coupling between the Er3+ spin and the 93Nb nuclear quadrupole; it possibly originates from a spin-dependent electrostatic interaction between the two systems. The second is a nuclear hexadecapolar term, and may be caused by the coupling of the electric field third derivative to the 93Nb nuclear hexadecapolar moment.

In Er^{3+}:Y_{2}SiO_{5}, we demonstrate the selective optical addressing of the ^{89}Y^{3+} nuclear spins through their superhyperfine coupling with the Er^{3+} electronic spins possessing large Landé g factors. We experimentally probe the electron-nuclear spin mixing with photon echo techniques and validate our model. The site-selective optical addressing of the Y^{3+} nuclear spins is designed by adjusting the magnetic field strength and orientation. This constitutes an important step towards the realization of long-lived solid-state qubits optically addressed by telecom photons.