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arXiv:1608.05130 · Physical Review Letters

Electron Spin Resonance at the Level of 104 Spins Using Low Impedance Superconducting Resonators

Christopher Eichler, Anthony J. Sigillito, S. A. Lyon, J. R. Petta

Published Jan 19, 2017• 111 citations
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Abstract

We report on electron spin resonance measurements of phosphorus donors localized in a 200 μm^{2} area below the inductive wire of a lumped element superconducting resonator. By combining quantum limited parametric amplification with a low impedance microwave resonator design, we are able to detect around 2×10^{4} spins with a signal-to-noise ratio of 1 in a single shot. The 150 Hz coupling strength between the resonator field and individual spins is significantly larger than the 1-10 Hz coupling rates obtained with typical coplanar waveguide resonator designs. Because of the larger coupling rate, we find that spin relaxation is dominated by radiative decay into the resonator and dependent upon the spin-resonator detuning, as predicted by Purcell.

DOI
10.1103/physrevlett.118.037701

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We report on electron spin resonance measurements of phosphorus donors localized in a 200 μm^{2} area below the inductive wire of a lumped element superconducting resonator. By combining quantum limited parametric amplification with a low impedance microwave resonator design, we are able to detect around 2×10^{4} spins with a signal-to-noise ratio of 1 in a single shot. The 150 Hz coupling strength between the resonator field and individual spins is significantly larger than the 1-10 Hz coupling rates obtained with typical coplanar waveguide resonator designs. Because of the larger coupling rate, we find that spin relaxation is dominated by radiative decay into the resonator and dependent upon the spin-resonator detuning, as predicted by Purcell.
The use of superconducting micro-resonators in combination with quantum-limited Josephson parametric amplifiers has in recent years lead to more than four orders of magnitude improvement in the sensitivity of pulsed Electron Spin Resonance (ESR) measurements. So far, the microwave resonators and amplifiers have been designed as separate components, largely due to the incompatibility of Josephson junction-based devices with even moderate magnetic fields. This has led to complex spectrometers that operate under strict environments, creating technical barriers for the widespread adoption of the technique. Here we circumvent this issue by inductively coupling an ensemble of spins directly to a weakly nonlinear microwave resonator, which is engineered from a magnetic field-resilient thin superconducting film. We perform pulsed ESR measurements with a 111~pL effective mode volume and amplify the resulting spin signal using the same device, ultimately achieving a sensitivity of 2.8×1032.8 \times 10^32.8×103 spins in a single-shot Hahn echo measurement at a temperature of 400 mK. We demonstrate the combined functionalities at fields as large as 254~mT, highlighting the technique's potential for application under more conventional ESR operating conditions.
We introduce a multilayer superconducting microwave resonator with sub-Ohm impedance optimized for high coupling strength to single electron spins. The design minimizes the magnetic far-field and therefore achieves a Purcell factor FP>1015F_P > 10^{15}FP​>1015. We show several ways to fabricate this type of resonator and present resonators with an intrinsic QQQ-factor exceeding 2⋅1042 \cdot 10^42⋅104 at the single-photon level. We further characterize these resonators in magnetic fields up to 500 mT500 \, \text{mT}500mT. Finally, we evaluate the impact of the achievable Purcell factor on single-spin detection through photon counting and dispersive readout.
The use of superconducting microresonators together with quantum-limited Josephson parametric amplifiers has enhanced the sensitivity of pulsed electron spin resonance (ESR) measurements by more than four orders of magnitude. So far, the microwave resonators and amplifiers have been designed as separate components due to the incompatibility of Josephson junction–based devices with magnetic fields. This has produced complex spectrometers and raised technical barriers toward adoption of the technique. Here, we circumvent this issue by coupling an ensemble of spins directly to a weakly nonlinear and magnetic field–resilient superconducting microwave resonator. We perform pulsed ESR measurements with a 1-pL mode volume containing 6 × 10 7 spins and amplify the resulting signals within the device. When considering only those spins that contribute to the detected signals, we find a sensitivity of 2.8 × 1 0 3 spins / Hz for a Hahn echo sequence at a temperature of 400 mK. In situ amplification is demonstrated at fields up to 254 mT, highlighting the technique’s potential for application under conventional ESR operating conditions.
We report electron spin resonance measurements of donors in silicon at millikelvin temperatures using a superconducting LC planar micro-resonator and a Josephson parametric amplifier. The resonator includes a nanowire inductor, defining a femtoliter detection volume. Due to strain in the substrate, the donor resonance lines are heavily broadened. Single-spin to photon coupling strengths up to ∼3 kHz are observed. The single shot sensitivity is 120 ± 24 spins/Hahn echo, corresponding to ≈12±3 spins /Hz for repeated acquisition.
We report electron spin resonance measurements of donors in silicon at millikelvin temperatures using a superconducting LC planar micro-resonator and a Josephson parametric amplifier. The resonator includes a nanowire inductor, defining a femtoliter detection volume. Due to strain in the substrate, the donor resonance lines are heavily broadened. Single-spin to photon coupling strengths up to ∼3 kHz are observed. The single shot sensitivity is 120 ± 24 spins/Hahn echo, corresponding to ≈12±3 spins / √Hz for repeated acquisition.
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.