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arXiv:1507.03739 · Applied Physics Letters

High cooperativity coupling between a phosphorus donor spin ensemble and a superconducting microwave resonator

Christoph W. Zollitsch, Kai Müller, David P. Franke, Sebastian T. B. Goennenwein, Martin S. Brandt, Rudolf Groß, Hans Huebl

Published Oct 5, 2015• 40 citations
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Abstract

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.

DOI
10.1063/1.4932658

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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.
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.
Realisation of strong coupling between a superconducting microwave resonator and an ensemble of phosphorus donor spins, contained in an isotopically purified silicon host crystal. Investigation of the dynamical properties of the coupled system at mK temperatures and ultra-low microwave powers. The relaxation and coherence times of the coupled system were extracted by pulsed microwave spectroscopy, with the result that the hybrid system's coherence time is enhanced compared to the uncoupled spin system.
We report strong coupling between an ensemble of nitrogen-vacancy center electron spins in diamond and a superconducting microwave coplanar waveguide resonator. The characteristic scaling of the collective coupling strength with the square root of the number of emitters is observed directly. Additionally, we measure hyperfine coupling to (13)C nuclear spins, which is a first step towards a nuclear ensemble quantum memory. Using the dispersive shift of the cavity resonance frequency, we measure the relaxation time of the NV center at millikelvin temperatures in a nondestructive way.
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.
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.
We report measurements made at millikelvin temperatures of a superconducting coplanar waveguide resonator (CPWR) coupled to a sphere of yttrium-iron garnet. Systems hybridising collective spin excitations with microwave photons have recently attracted interest for their potential quantum information applications. In this experiment the non-uniform microwave field of the CPWR allows coupling to be achieved to many different magnon modes in the sphere. Calculations of the relative coupling strength of different mode families in the sphere to the CPWR are used to successfully identify the magnon modes and their frequencies. The measurements are extended to the quantum limit by reducing the drive power until, on average, less than one photon is present in the CPWR. Investigating the time-dependent response of the system to square pulses, oscillations in the output signal at the mode splitting frequency are observed. These results demonstrate the feasibility of future experiments combining magnonic elements with planar superconducting quantum devices.