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Physical Review Applied

High-Cooperativity Coupling of Rare-Earth Spins to a Planar Superconducting Resonator

Sihao Wang, Likai Yang, R. L. Cone, Charles W. Thiel, Hong X. Tang

Published Jul 28, 2022• 7 citations
Publisher

Abstract

In one branch of quantum information processing, high cooperativity between spins and a resonator is essential. Planar superconducting resonators present an opportunity for miniaturization and fully integrated circuitry, but unfortunately their cooperativity is a fraction of that of their bulk counterparts. This study designs a planar microwave resonator to achieve homogeneous magnetic field, and utilizes the anisotropic g-factor tensor of erbium spins in yttrium orthosilicate for maximum spin-photon coupling. Cooperativity on par with that of a three-dimensional cavity is achieved, marking an exciting step toward integrated circuits for spin quantum information processing.

DOI
10.1103/physrevapplied.18.014071

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In one branch of quantum information processing, high cooperativity between spins and a resonator is essential. Planar superconducting resonators present an opportunity for miniaturization and fully integrated circuitry, but unfortunately their cooperativity is a fraction of that of their bulk counterparts. This study designs a planar microwave resonator to achieve homogeneous magnetic field, and utilizes the anisotropic g-factor tensor of erbium spins in yttrium orthosilicate for maximum spin-photon coupling. Cooperativity on par with that of a three-dimensional cavity is achieved, marking an exciting step toward integrated circuits for spin quantum information processing.
Interfacing superconducting microwave resonator with rare earth doped crystals presents a promising hybrid quantum system for applications including spin-assisted transducers and memories. The coupling strength between spins of rare earth ions and the microwave photons is characterized by the cooperativity. Here we report an ultra-high cooperativity C∼C \simC∼ 650 between rare earth spins and a planar superconducting microwave resonator that features a highly uniform magnetic field for harnessing the strong anisotropic coupling strength of erbium doped yttrium orthosilicate. This cooperativity rivals that from a bulk dielectric resonator and paves a path for efficiently coupling of spins with microwave photons on an integrated platform.
Yttrium orthosilicate ( \nY \n2 \nSi \nO \n5 \n, or YSO) has proved to be a convenient host for rare-earth ions used in demonstrations of microwave quantum memories and optical memories with microwave interfaces and shows promise for coherent microwave-optical conversion owing to its favorable optical and spin properties. The strong coupling required by such microwave applications could be achieved using superconducting resonators patterned directly on \nY \n2 \nSi \nO \n5 \n and hence we investigate here the use of \nY \n2 \nSi \nO \n5 \n as an alternative to sapphire or silicon substrates for superconducting-hybrid-device fabrication. A \nNb \nN \n resonator with frequency 6.008 GHz and low-power quality factor \nQ \n≈ \n400 \n000 \n is fabricated on a \nY \n2 \nSi \nO \n5 \n substrate doped with isotopically enriched \n145 \nNd \n. Measurements of dielectric loss yield a loss tangent \ntan \n \nδ \n= \n4 \n× \n10 \n− \n6 \n, comparable to that of sapphire. Electron spin resonance (ESR) measurements performed using the resonator show the characteristic angular dependence expected from the anisotropic \n145 \nNd \n spin and the coupling strength between the resonator and the electron spins is in the high-cooperativity regime ( \nC \n= \n30 \n). These results demonstrate that \nY \n2 \nSi \nO \n5 \n is an excellent substrate for low-loss, high- \nQ \n microwave resonators, especially in applications for coupling to optically accessible rare-earth spins.
Rare-earth ions (REIs) in solid hosts have important applications in the storage and conversion of quantum information at optical and microwave frequencies. Yttrium orthosilicate is a widely used host for REIs, with excellent optical properties, but its compatibility with superconducting resonators and circuits for quantum technology is not known. This study uses Y2{}_{2}2​SiO5{}_{5}5​ directly as a substrate for superconducting devices, revealing dielectric losses comparable to those of sapphire. This enables fabrication of high-quality microwave devices coupled to optically accessible rare-earth spins, pointing to applications in quantum storage and microwave-to-optical conversion.
Engineering and understanding microwave resonators is essential for the efficient electron-spin control and readout in electron-spin-resonance (ESR) spectroscopy. This work, focused on superconducting planar microresonators, presents finite-element simulations modeling the spin-photon coupling rate, in quantitative agreement with experimental data. Three resonator designs are optimized to address spectroscopy applications in $\ensuremath{\mu}$m-thick samples, with one exhibiting notably good magnetic field homogeneity at microwave frequencies.
We experimentally demonstrate the coupling at zero magnetic field of an isotopically pure erbium-doped yttrium orthosilicate crystal (167Er:YSO^{167}\mathrm{Er}:\mathrm{YSO}167Er:YSO) to a three-dimensional superconducting cavity with a QQQ factor of 105{10}^{5}105. A tunable loop-gap resonator is used and its resonance frequency is tuned to observe the hyperfine transitions of the erbium sample. The observed spectrum differs from what is predicted by the published spin Hamiltonian parameters. The narrow cavity linewidth also enables the observation of asymmetric line shapes for these hyperfine transitions. Such a broadly tunable superconducting cavity (from 1.6 to 4.0 GHz in the current design) is a promising device for building hybrid quantum systems.
Interfacing photonic and solid-state qubits within a hybrid quantum architecture offers a promising route towards large scale distributed quantum computing. Ideal candidates for coherent qubit interconversion are optically active spins, magnetically coupled to a superconducting resonator. We report on an on-chip cavity QED experiment with magnetically anisotropic Er(3+)∶Y2SiO5 crystals and demonstrate collective strong coupling of rare-earth spins to a lumped element resonator. Moreover, the electron spin resonance and relaxation dynamics of the erbium spins are detected via direct microwave absorption, without the aid of a cavity.