Microwave Fluorescence Detection of Spin Echoes

E. Billaud, L. Balembois, M. Le Dantec, M. Rančić, E. Albertinale, S. Bertaina, T. Chanelière, P. Goldner, D. Estève, D. Vion, P. Bertet, and E. Flurin

Phys. Rev. Lett. 131, 100804 – Published 8 September 2023

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 $π / 2_{X} - τ - π_{Y} - τ - π / 2_{Φ}$ sequence, dependent on the relative phase $Φ$ . We demonstrate experimentally this detection method using an ensemble of ${Er}^{3 +}$ ion spins in a scheelite crystal of ${CaWO}_{4}$ . 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 ${}^{183}W$ 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.

Received 30 August 2022
Accepted 19 July 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.100804

Physics Subject Headings (PhySH)

Quantum circuits Quantum sensing Spin dynamics

Electron spin resonance Fluorescence spectroscopy Microwave techniques

Quantum Information, Science & TechnologyGeneral Physics

Authors & Affiliations

E. Billaud ¹, L. Balembois¹, M. Le Dantec¹, M. Rančić¹, E. Albertinale¹, S. Bertaina ², T. Chanelière³, P. Goldner⁴, D. Estève ¹, D. Vion¹, P. Bertet^1,*, and E. Flurin^1,†

¹Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette Cedex, France
²CNRS, Aix-Marseille Université, IM2NP (UMR 7334), Institut Matériaux Microélectronique et Nanosciences de Provence, 13397 Marseille, France
³Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
⁴Chimie ParisTech, PSL University, CNRS, Institut de Recherche de Chimie Paris, 75005 Paris, France

^*patrice.bertet@cea.fr
^†emmanuel.flurin@cea.fr

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Vol. 131, Iss. 10 — 8 September 2023

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Figure 1
Experiment principle and spectroscopy. (a) Schematic of the experiment. $N$ spins are coupled (with strength $g_{0}$ ) to a resonator of frequency $ω_{0} / 2 π = 6.999 GHz$ damped by internal losses at a rate $κ_{int} = 3.6 \times 10^{5} s^{- 1}$ , coupled to a transmission line at a rate $κ_{c} = 2 \times 10^{6} s^{- 1}$ . In the ID echo detection scheme, a Hahn echo pulse sequence $π / 2_{X} - τ - π_{Y}$ is applied to the spins, inducing the emission of a coherent echo of amplitude $⟨ X_{e} ⟩$ at time $2 τ$ which is then amplified. In the FD echo detection scheme, a three-pulse sequence $π / 2_{X} - τ - π_{Y} - τ - π / 2_{Φ}$ is used. The echo is detected by counting the incoherent photons emitted subsequently with a SMPD. The number of photons in the FD scheme $⟨ C_{e} ⟩ = N / 2$ is much larger than in the coherent echo $⟨ X_{e} ⟩^{2}$ , explaining why a larger SNR can be reached with a low-noise SMPD. (b) Sketch of the niobium planar resonator fabricated on top of the ${CaWO}_{4}$ sample in the $a b$ plane. The $630 μ m$ -long wire is along the x axis ( $φ_{w} = 51 °$ ), and $B_{0}$ is in the $a b$ plane ( $φ = 30 °$ ). The cross section of the sample below the $2 μ m$ -wide wire (shown as a red rectangle) displays the spatial distribution of the coupling $g_{0}$ , which we assume to be constant across the wire length. (c) Fluorescence-detected EPR spectrum of ${Er}^{3 +} : {CaWO}_{4}$ . The number of counts with background subtracted $⟨ C_{spin} ⟩$ (open blue circles) is shown as a function of $B_{0}$ (bottom axis), also converted into frequency detuning from the center of the line (top axis). The solid line is a fit to a Lorentzian with FWHM 1.6 MHz. Data were obtained with SMPD1.
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Figure 2
Fluorescence detection of spin echo. Error bars are $1 σ$ statistical. Data were obtained with SMPD1. Insets represent the pulse sequence used for each dataset. (a) Integrated counts with background subtracted $⟨ C_{spin} ⟩$ as a function of the restoring pulse phase $Φ$ . Blue open circles (red crosses) are experimental (simulated) points, with $τ = 100 μ s$ , $T_{rep} = T_{int} = 1.52 s$ , $β = 10 {ns}^{- 1 / 2}$ , $Δ t = 5 μ s$ , and $η = 0.1$ . The solid line is a fit yielding $⟨ C_{e} ⟩ = 42.6$ counts (blue double arrow) and $⟨ C_{0} ⟩ = 457.3$ counts (horizontal black dashed line). (b) $⟨ C_{e} ⟩$ (open blue dots) as a function of delay $Δ τ$ with $β = 28 {ns}^{- 1 / 2}$ , $Δ t = 5 μ s$ , and $T_{int} = T_{rep} = 1.52 s$ . The solid line is a Gaussian fit yielding $T_{e} = 6.1 μ s$ . (c) $⟨ C_{e} ⟩$ as a function of delay $2 τ$ showing ESEEM, with $β = 10 {ns}^{- 1 / 2}$ , $Δ t = 5 μ s$ , and $T_{int} = T_{rep} = 1.52 s$ . The vertical dashed line is $τ = 100 μ s$ used in (a). The blue and red open circles are the results from two successive runs.
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Figure 3
Fluorescence detection of the spin coherence time. Error bars are $1 σ$ statistical. Data were obtained with SMPD1. (a) $⟨ C_{e} ⟩$ as a function of the echo delay $2 τ$ (blue open circles) with $β = 100 {ns}^{- 1 / 2}$ , $Δ t = 5 μ s$ , and $T_{int} = T_{rep} = 8.16 s$ . The orange line is a fit yielding $T_{2, q} = 3.6 ms$ and exponent $x_{q} = 1.7$ . (b) Standard deviation $⟨ σ ⟩$ over the phases $Φ \in [0, π / 2, π, 3 π / 2]$ as a function of the delay $2 τ$ (green open diamonds) with $β = 10 {ns}^{- 1 / 2}$ , $Δ t = 5 μ s$ , $T_{int} = 0.55 s$ , and $T_{rep} = 1.52 s$ . The orange line is a stretched exponential fit, yielding the coherence time $T_{2, m} = 19 ms$ and exponent $x_{m} = 1.13$ .
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Figure 4
SNR comparison between ID and FD detection methods. (a) Setup. A JPA is installed behind the SMPD2 for ID echo measurement. $B_{0}$ is applied with an angle $φ = 47 °$ . (b) Echo histograms detected with FD (red dots, 4000 iterations) and ID (blue dots, 9000 iterations) taken in the same conditions with $β \approx 2.5 {ns}^{- 1 / 2}$ and $Δ t = 4 μ s$ , and their Gaussian fits (line). The data have been averaged over 20 iterations, corresponding to a measurement time of 8.6 s. The horizontal axes for FD and ID detection are chosen such that the standard deviations have the same width, to allow for visual comparison of the distributions’ mean (dashed lines).
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