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arXiv:1512.03606 · Physical review. B./Physical review. B

Coupling erbium spins to a three-dimensional superconducting cavity at zero magnetic field

Yu‐Hui Chen, Xavier Fernandez-Gonzalvo, Jevon J. Longdell

Published Aug 10, 2016• 34 citations
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Abstract

We experimentally demonstrate the coupling at zero magnetic field of an isotopically pure erbium-doped yttrium orthosilicate crystal ($^{167}\mathrm{Er}:\mathrm{YSO}$) to a three-dimensional superconducting cavity with a $Q$ factor of ${10}^{5}$. 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.

DOI
10.1103/physrevb.94.075117

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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 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.
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.
Microwave-to-optical quantum transducers are essential for entangling remote superconducting qubits. Among the available transduction platforms, ensembles of Er3+^{3+}3+ and Yb3+^{3+}3+ ions doped into solids have emerged as leading candidates. While external magnetic fields are needed to split the Zeeman levels of erbium ions and enable a microwave--qubit interface, superconducting qubits suffer decoherence in such fields. In contrast, ytterbium ions exhibit zero-first-order Zeeman transitions and large hyperfine splittings at zero magnetic field (when doped into inorganic crystals). Owing to its long optical and spin coherence times, Yb:YSO has been widely used as a quantum memory, yet its potential for quantum transduction remains largely unexplored. Investigating this material could enable the integration of quantum memory and transduction in a single platform. Here, we demonstrate microwave-to-optical transduction in the continuous-wave regime using a 5\,ppm doped Yb:YSO crystal. The internal transduction efficiency is 2×10−82\times10^{-8}2×10−8 with a bandwidth of 200\,kHz, achieved using a 3D loop-gap microwave resonator (LGR) and a single-pass optical configuration. We explore all the ground states that form a V-type three-level system with the first and second optical excited states and assert the use of the ground state, which provides the highest efficiency and isolated optical transition. We further establish strong spin-microwave coupling from avoided crossing measurements. With a strong microwave drive to saturate the spin transition, we estimate the spin population pumped into the excited state, close to the simulated value. Finally, we calculate target parameter values for maximum efficiency with our system and suggest using 50\,ppm doped Yb:YSO crystal. With the calculated target parameters, the internal transduction efficiency is predicted to reach up to 10−410^{-4}10−4 in the current LGR.
Erbium-doped crystals provide a promising platform for integration with other quantum systems, offering telecom-band optical and microwave spin transitions with long coherence times for quantum memory and transduction applications. In order to construct efficient hybrid quantum systems, it is challenging but necessary to realize strong coupling between erbium spins and other microwave photons. Here, we design and construct a high-quality-factor three-dimensional loop-gap microwave resonator for wide-range electron spin resonance detection. We achieved strong coupling with a strength of 85.1 MHz at 100 mK. Our results demonstrate a viable hybrid quantum system, paving the way for integrated networks that combine optical communication with microwave quantum computing.
A quantum coherent interface between optical and microwave photons can be used as a basic building block within a future quantum information network. The interface is envisioned as an ensemble of rare-earth ions coupled to a superconducting resonator, allowing for coherent transfer between optical and microwave photons. Towards this end, we have realized a hybrid device coupling a Er3+-doped Y2SiO5 crystal in a superconducting coplanar waveguide cavity. We observe a collective spin coupling of 4 MHz and a spin linewidth of down to 75 MHz.
Spin echoes in the ground and an optically excited state of 167^{167}167Er3+^{3+}3+:Y2_22​SiO5_55​ at near-zero magnetic fields using Raman heterodyne spectroscopy
Erbium-167-doped yttrium orthosilicate is an ideal candidate for a microwave-addressed quantum memory due to its telecom wavelength optical transition and hyperfine structure with and without an applied magnetic field. However, to date there has been little investigation in coherence times for transitions around zero magnetic field, or for hyperfine structure other than from the ground state. Through the use of Raman heterodyne spectroscopy, we have identified transitions at zero magnetic field with a small dependence on field that are suitable for detecting spin echoes for both the ground and excited state. We measured coherence times of transitions at 879.4 MHz and 896.7 MHz as 370 μ\muμs and 1.4 ms respectively at 3.2 K. This is a 100-fold increase in coherence time compared to previous measurements at the same dopant concentration and 200 times greater than the even isotopes of erbium-doped yttrium orthosilicate previously used to demonstrate a microwave memory.