Spin-Echo Silencing Using a Current-Biased Frequency-Tunable Resonator

V. Ranjan, Y. Wen, A. K. V. Keyser, S. E. Kubatkin, A. V. Danilov, T. Lindström, P. Bertet, and S. E. de Graaf

Phys. Rev. Lett. 129, 180504 – Published 28 October 2022

Abstract

The ability to control microwave emission from a spin ensemble is a requirement of several quantum memory protocols. Here, we demonstrate such ability by using a resonator whose frequency can be rapidly tuned with a bias current. We store excitations in an ensemble of rare-earth ions and suppress on demand the echo emission (“echo silencing”) by two methods: (1) detuning the resonator during the spin rephasing, and (2) subjecting spins to magnetic field gradients generated by the bias current itself. We also show that spin coherence is preserved during silencing.

Received 9 June 2022
Revised 22 August 2022
Accepted 6 October 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.180504

Physics Subject Headings (PhySH)

Optical & microwave phenomena Quantum memories

Rare-earth doped crystals

Cavity resonators

Quantum Information, Science & TechnologyAtomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

V. Ranjan ^1,*, Y. Wen ², A. K. V. Keyser^1,3, S. E. Kubatkin ⁴, A. V. Danilov⁴, T. Lindström¹, P. Bertet², and S. E. de Graaf^1,†

¹National Physical Laboratory, Teddington TW11 0LW, United Kingdom
²Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette Cedex, France
³Imperial College London, Exhibition Road, SW7 2AZ, United Kingdom
⁴Department of Microtechnology and Nanoscience MC2, Chalmers University of Technology, SE-41296 Goteborg, Sweden

^*vishal.ranjan@npl.co.uk
^†sebastian.de.graaf@npl.co.uk

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Vol. 129, Iss. 18 — 28 October 2022

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Images

Figure 1
The principle of revival of silenced echo (ROSE) [29] protocols to implement controlled suppression (at $time = 2 τ$ ) and retrieval (at $time = 4 τ$ ) of echoes by (a) fast detuning of the resonator frequency and (b) generating an inhomogeneous phase encoding on spins. The phase evolution of spins (only three plotted for clarity) are for a single excitation stored at $time = 0$ , and the refocusing pulses $π 1$ and $π 2$ are ideal. Echo emission at $2 τ$ is not desirable since it contains noise from spontaneously emitting spins excited by $π 1$ .
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Figure 2
Experimental setup. (a) An optical picture of the tunable resonator, the relative position of the ${CaWO}_{4}$ crystal, and a simplified measurement protocol. Horizontal zigzag discontinuities in the picture hide the long repetitive vertical features. Signal quadratures $X$ , $Y$ are measured in transmission of the feedline to which the resonator is inductively coupled. The injection and exit routes of the bias current $I_{bias}$ are shown by the dashed red line. LO represents the local oscillator. Bottom right: the resonator frequency shift $Δ ω$ in response to $I_{bias}$ . (b) Numerically calculated electron spin transition frequencies. $I = 0$ , $7 / 2$ refers to two Er isotopes, and $m_{I}$ the nuclear-spin projection on the $B$ -field axis. (c) Echo-detected spin spectroscopy and (d) decoherence (measured: symbols, fits: lines) at the transition with $m_{I} = 7 / 2$ as marked by the star in Fig. 2.
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Figure 3
Echo silencing with resonator tuning in config. I. (a) Measurement scheme. Square $I_{bias}$ pulses of fixed duration $20 μ s$ detune the resonator frequency by $Δ ω$ near the time of echo emission, $2 τ = 200 μ s$ . (b) Echo shapes for various detuning. $R$ represents the signal magnitude $\sqrt{X^{2} + Y^{2}}$ . (c) Measured (symbols) and numerically simulated (line) echo areas with increasing detuning. Measurement bandwidth (BW) is also shown. (d) Numerically simulated echo shapes.
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Figure 4
Selective retrieval of microwave fields after a multimode storage. (a) Sketches of retrieval after storage of three identical input states for unit (top) and low (bottom) memory efficiency $ζ$ using echo silencing by resonator detuning. Labels ( $L$ , $M$ , and $R$ ) help identify the storage and rephasing times within the same memory mode. (b) Corresponding measured signal quadratures of retrieved states for different permutations of $I_{bias}$ pulses. The $I_{bias}$ pulses of amplitude 2 mA (yielding $- Δ ω / κ = 15$ ) and $20 μ s$ total duration are made out of two halves of positive and negative current. The refocusing pulses are applied along the same axis. (c) Comparison of retrieved quadratures for cases when no $I_{bias}$ (top) or $60 μ s$ long $I_{bias}$ pulses centered at $time = 0.27$ ms are applied with the same polarity (middle) or dual polarity (bottom) before the retrieval. (d) Area of retrieved echoes, primary as circles and secondary as crosses, for cases numbered in panel (b). Dashed horizontal lines represent signal magnitude of secondary echoes for case I with $I_{bias} = 0$ .
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Figure 5
Echo silencing with magnetic field gradients in config. II. (a) Signal quadrature of a train of echoes created by unevenly spaced control pulses. echo 1 (echo 2) is primary (secondary) rephasing of spin coherence created by $θ / 2$ , echo 3 is three-pulse stimulated echo. (b) Signal magnitude of two echoes measured with even spacing of pulses. In both panels, each bias pulse is of single polarity, duration $20 μ s$ and amplitude 3 mA (positions shown as black rectangles). The curves are vertically offset for clarity. All control pulses are applied along the same axis, with Rabi angles of $θ = θ 1 = θ 2$ .
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