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arXiv:2208.13586 · Physical Review Letters

Microwave Fluorescence Detection of Spin Echoes

Eric Billaud, Léo Balembois, Marianne Le Dantec, Miloš Rančić, Emanuele Albertinale, Sylvain Bertaina, T. Chanelière, Philippe Goldner, D. Estève, D. Vion, Patrice Bertet, Emmanuel Flurin

Published Sep 8, 2023• 16 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.131.100804

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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 \ensuremathπ/2X\ensuremath−\ensuremathτ\ensuremath−\ensuremathπY\ensuremath−\ensuremathτ\ensuremath−\ensuremathπ/2\ensuremathΦ\ensuremath{\pi}/{2}_{X}\ensuremath{-}\ensuremath{\tau}\ensuremath{-}{\ensuremath{\pi}}_{Y}\ensuremath{-}\ensuremath{\tau}\ensuremath{-}\ensuremath{\pi}/{2}_{\mathrm{\ensuremath{\Phi}}}\ensuremathπ/2X​\ensuremath−\ensuremathτ\ensuremath−\ensuremathπY​\ensuremath−\ensuremathτ\ensuremath−\ensuremathπ/2\ensuremathΦ​ sequence, dependent on the relative phase \ensuremathΦ\mathrm{\ensuremath{\Phi}}\ensuremathΦ. We demonstrate experimentally this detection method using an ensemble of Er3+{\mathrm{Er}}^{3+}Er3+ ion spins in a scheelite crystal of CaWO4{\mathrm{CaWO}}_{4}CaWO4​. 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 183W^{183}\mathrm{W}183W 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.
Quantum emitters respond to resonant illumination by radiating electromagnetic fields. A component of these fields is phase-coherent with the driving tone, while another one is incoherent, consisting of spontaneously emitted photons and forming the fluorescence signal. Atoms and molecules are routinely detected by their fluorescence at optical frequencies, with important applications in quantum technology and microscopy. Spins, on the other hand, are usually detected by {their coherent response} at radio- or microwave frequencies, either in continuous-wave or pulsed magnetic resonance. Indeed, fluorescence detection of spins is hampered {by their low spontaneous emission rate} and by the lack of single-photon detectors in this frequency range. Here, using superconducting quantum devices, we demonstrate the detection of a small ensemble of donor spins in silicon by their fluorescence at microwave frequency and millikelvin temperatures. We enhance the spin radiative decay rate by coupling them to a high-quality-factor and small-mode-volume superconducting resonator, and we connect the device output to a newly-developed microwave single-photon counter based on a superconducting qubit. We discuss the potential of fluorescence detection as a novel method for magnetic resonance spectroscopy of small numbers of spins.
A new method for detecting the magnetic resonance of electronic spins at low temperature is demonstrated. It consists in measuring the signal emitted by the spins with a superconducting qubit that acts as a single-microwave-photon detector, resulting in an enhanced sensitivity. We implement such an electron-spin resonance spectrometer using a hybrid quantum circuit in which a transmon qubit is coupled to a spin ensemble consisting of nitrogen-vacancy (NV) centers in diamond. With this setup we measure the NV center absorption spectrum at 30 mK at an excitation level of $\ensuremath{\sim}15\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{B}$ out of an ensemble of 1011{10}^{11}1011 spins.
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.
Hybrid quantum systems combining circuit QED with spin-doped solids are an attractive platform for distributed quantum information processing. There, the magnetic ions serve as coherent memory elements and reversible conversion elements of microwave to optical qubits. Among many possible spin-doped solids, erbium ions offer the unique opportunity for a coherent conversion of microwave photons into the telecom C band at $1.54\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$ employed for long distance communication. In our work, we perform a time-resolved electron spin resonance study of an Er3+:Y2SiO5{\mathrm{Er}}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Er3+:Y2​SiO5​ spin ensemble at millidegrees Kelvin temperatures and demonstrate multimode storage and retrieval of up to 16 coherent microwave pulses. The memory efficiency is measured to be ${10}^{\ensuremath{-}4}$ at a coherence time of ${T}_{2}=5.6\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{s}$. We observe a saturation of the spin coherence time below 50 mK due to full polarization of the surrounding electronic spin bath.
There are summarized our results obtained when studying the entangled electron-hole pairs by the direct and indirect electron paramagnetic resonance methods. These results demonstrate rather peculiar response of the spins in the entangled state to the manipulations with the external microwave fields: intensities of lines in the electron paramagnetic resonance spectra should oscillate; the echo type signal is expected as the response to only one microwave pulse; the primary spin echo signal has anomalous phase compared to the phase of the echo signal in a case of spins in a non-entangled state; the two-quantum transitions can be manifested even in the absence of the spin-spin interaction if the electron paramagnetic resonance is detected indirectly, e.g., optically. A possible scenario for the quantum teleportation experiment is suggested.
Coherent spin resonance techniques, such as nuclear and electron spin resonance spectroscopy, have revolutionized non-invasive imaging by providing spectrally resolved information about spin dynamics. Motivated by the recent emergence of electron microscopy methods capable of sensing microwave-excitations, we establish a theoretical framework for Spin Resonance Spectroscopy (SRS) in transmission electron microscopy (TEM). This technique combines microwave pump fields with focused electron probe beams to enable state-selective spin imaging at the atomic scale. Using scattering theory, we model the interaction between free-space electrons and electron spin systems, capturing both elastic and inelastic processes. The strongest effect of the spin system on the free electron is a magnetic phase shift. Our simulations demonstrate that phase shifts from individual electron spins are detectable in both image mode and diffraction mode. In principle, differential measurements under microwave control allow the extraction of local resonance frequencies that are influenced by the surrounding spin environment. By evaluating the Classical Fisher Information (CFI), we identify imaging conditions that maximize the signal-to-noise ratio (SNR), showing how defocus and beam width affect the measurement sensitivity. These findings establish a foundation for integrating SRS with high-resolution TEM, bridging spin spectroscopy and atomic-scale imaging, and enabling new capabilities in quantum spin research and nanoscale materials characterization.