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arXiv:1207.6039 · Physical Review Letters

High Cooperativity in Coupled Microwave Resonator Ferrimagnetic Insulator Hybrids

Hans Huebl, Christoph W. Zollitsch, Johannes Lotze, Fredrik Hocke, Moritz Greifenstein, Achim Marx, Rudolf Groß, Sebastian T. B. Goennenwein

Published Sep 20, 2013• 900 citations
arXivHTMLPDF

Abstract

We report the observation of strong coupling between the exchange-coupled spins in a gallium-doped yttrium iron garnet and a superconducting coplanar microwave resonator made from Nb. The measured coupling rate of 450 MHz is proportional to the square root of the number of exchange-coupled spins and well exceeds the loss rate of 50 MHz of the spin system. This demonstrates that exchange-coupled systems are suitable for cavity quantum electrodynamics experiments, while allowing high integration densities due to their spin densities of the order of one Bohr magneton per atom. Our results furthermore show, that experiments with multiple exchange-coupled spin systems interacting via a single resonator are within reach.

DOI
10.1103/physrevlett.111.127003

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•Jul 14, 2015•0 citations
We report the observation of strong coupling between the exchange-coupled spins in a gallium-doped yttrium iron garnet and a superconducting coplanar microwave resonator made from Nb. The measured coupling rate of 450 MHz is proportional to the square root of the number of exchange-coupled spins and well exceeds the loss rate of 50 MHz of the spin system. This demonstrates that exchange-coupled systems are suitable for cavity quantum electrodynamics experiments, while allowing high integration densities due to their spin densities of the order of one Bohr magneton per atom. Our results furthermore show, that experiments with multiple exchange-coupled spin systems interacting via a single resonator are within reach.
Abstract Hybridizing collective spin excitations and a cavity with high cooperativity provides a new research subject in the field of cavity quantum electrodynamics and can also have potential applications to quantum information. Here we report an experimental study of cavity quantum electrodynamics with ferromagnetic magnons in a small yttrium-iron-garnet (YIG) sphere at both cryogenic and room temperatures. We observe for the first time a strong coupling of the same cavity mode to both a ferromagnetic-resonance (FMR) mode and a magnetostatic (MS) mode near FMR in the quantum limit. This is achieved at a temperature ~22 mK, where the average microwave photon number in the cavity is less than one. At room temperature, we also observe strong coupling of the cavity mode to the FMR mode in the same YIG sphere and find a slight increase of the damping rate of the FMR mode. These observations reveal the extraordinary robustness of the FMR mode against temperature. However, the MS mode becomes unobservable at room temperature in the measured transmission spectrum of the microwave cavity containing the YIG sphere. Our numerical simulations show that this is due to a drastic increase of the damping rate of the MS mode.
We investigate the coupling of an ensemble of phosphorus donors in an isotopically purified 28Si host lattice interacting with a superconducting coplanar waveguide resonator. The microwave transmission spectrum of the resonator shows a normal mode splitting characteristic for high cooperativity. The evaluated collective coupling strength geff is of the same order as the loss rate of the spin system γ, indicating the onset of strong coupling. We develop a statistical model to describe the influence of temperature on the coupling strength from 50 mK to 3.5 K and find a scaling of the coupling strength with the square root of the number of thermally polarized spins.
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.
Coplanar microwave resonators made of 330 nm-thick superconducting YBa2Cu3O7 have been realized and characterized in a wide temperature (T, 2–100 K) and magnetic field (B, 0–7 T) range. The quality factor (QL) exceeds 104 below 55 K and it slightly decreases for increasing fields, remaining 90% of QL(B=0) for B = 7 T and T = 2 K. These features allow the coherent coupling of resonant photons with a spin ensemble at finite temperature and magnetic field. To demonstrate this, collective strong coupling was achieved by using di(phenyl)-(2,4,6-trinitrophenyl)iminoazanium organic radical placed at the magnetic antinode of the fundamental mode: the in-plane magnetic field is used to tune the spin frequency gap splitting across the single-mode cavity resonance at 7.75 GHz, where clear anticrossings are observed with a splitting as large as ∼82 MHz at T = 2 K. The spin-cavity collective coupling rate is shown to scale as the square root of the number of active spins in the ensemble.
As the field of superconducting quantum technology progresses beyond single-qubit control, scalable and multifunctional quantum architectures become increasingly vital. A central challenge is integrating fast, controllable superconducting circuits with components that offer longer coherence, richer physics, or new functionalities. Hybrid quantum systems, where superconducting microwave resonators interface with semiconducting or magnetic subsystems, have the capabilities to fulfil this need, yet they face significant engineering obstacles. Conventional superconducting resonator designs struggle under magnetic field biasing and electrostatic gating, both of which are essential for coupling to spin-based, semiconductor, or magnonic elements.This thesis explores solutions to these bottlenecks through the development of magnetic-field-resilient coplanar stripline (CPS) resonators based on thin-film NbTiN. These resonators retain a stable resonance frequency in in-plane magnetic fields up to 1T, can have high kinetic inductance and offer broad geometrical tunability, enabling strong and ultrastrong coupling to charge- and spin-based quantum systems. In the superconducting–semiconductor domain, we demonstrate high-impedance CPS resonators inductively coupled to Josephson junctions hosting Andreev bound states (ABSs), revealing both coherent pair transitions and single-quasiparticle excitations near the ultrastrong coupling regime. This opens the door to fast, gate-tunable qubits based on microscopic ABSs, distinct from conventional macroscopic qubit architectures, and lays the groundwork for spin–photon hybridisation, non-perturbative light–matter interactions, and parity-based quantum logic.In parallel, this work investigates rare-earth iron garnet (ReIG) ferrimagnetic insulators as low-loss spin-wave media compatible with superconducting devices. In sputtered thin-film thulium iron garnet (TmIG) with perpendicular magnetic anisotropy, we observe deterministic spin-orbit torque switching and multiple magnetisation polarity reversals. These properties showcase the attractiveness of TmIG both for low-dissipation magnonic information transport and as magnetic interfaces for superconducting hybrid devices. Taken together, the results of this thesis establish materials, device concepts, and measurement strategies for novel classes of hybrid quantum systems that combine robust superconducting circuitry, electrostatically tunable semiconductor excitations, and industry-scalable magnetic elements and pave the way for next-generation hybrid quantum systems. More broadly, they provide concrete routes to overcoming limitations of existing hybrid platforms and advance the development of versatile, low-dissipation quantum technologies.
We investigate the coupling of an ensemble of phosphorus donors in an isotopically purified 28^{28}28Si host lattice interacting with a superconducting coplanar waveguide resonator. The microwave transmission spectrum of the resonator shows a normal mode splitting characteristic for high cooperativity. The evaluated collective coupling strength geffg_{\mathrm{eff}}geff​ is of the same order as the loss rate of the spin system γ\gammaγ, indicating the onset of strong coupling. We develop a statistical model to describe the influence of temperature on the coupling strength from 50 mK50\,\mathrm{mK}50mK to 3.5 K3.5\,\mathrm{K}3.5K and find a scaling of the coupling strength with the square root of the number of thermally polarized spins.