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arXiv:2108.02463 · Physical Review A

Polarizing electron spins with a superconducting flux qubit

Shingo Kukita, Hideaki Ookane, Yuichiro Matsuzaki, Yasushi Kondo

Published Jan 28, 2022• 1 citation
arXivHTMLPDF

Abstract

Electron-spin resonance is a useful tool to investigate properties of materials in magnetic fields where high spin polarization of target electron spins is required in order to obtain high sensitivity. However, the smaller the magnetic fields becomes, the more difficult it is to obtain high polarization by thermalization. Here, we propose to employ a superconducting flux qubit (FQ) to polarize electron spins actively. We have to overcome a large energy difference between the FQ and electron spins for efficient energy transfer among them. For this purpose, we adopt a spin-lock technique on the FQ where the Rabi frequency associated with the spin-locking can match the resonance (Larmor) one of the electron spins. We find that adding dephasing on the spins is beneficial to obtain high polarization of them, because otherwise the electron spins are trapped in dark states that cannot be coupled with the FQ. We show that our scheme can achieve high polarization of electron spins in realistic experimental conditions.

DOI
10.1103/physreva.105.012613

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Electron-spin resonance is a useful tool to investigate properties of materials in magnetic fields where high spin polarization of target electron spins is required in order to obtain high sensitivity. However, the smaller the magnetic fields becomes, the more difficult it is to obtain high polarization by thermalization. Here, we propose to employ a superconducting flux qubit (FQ) to polarize electron spins actively. We have to overcome a large energy difference between the FQ and electron spins for efficient energy transfer among them. For this purpose, we adopt a spin-lock technique on the FQ where the Rabi frequency associated with the spin-locking can match the resonance (Larmor) one of the electron spins. We find that adding dephasing on the spins is beneficial to obtain high polarization of them, because otherwise the electron spins are trapped in dark states that cannot be coupled with the FQ. We show that our scheme can achieve high polarization of electron spins in realistic experimental conditions.
We use a superconducting flux qubit for the sensing application of electron spin resonance (ESR) spectroscopy.The superconducting flux qubit is a highly sensitive magnetometer with micrometer-scale spatial resolution.The sensitivity of our spectrometer is 400 spins/√Hz, and the sensing volume is 0.05 pL.This high sensitivity and high spatial resolution enable us to investigate a small number of electron spins in a microscale area.The spectrometer also obtains a wider ESR spectrum range with twoparameter (frequency and magnetic field) scanning.This enables us to refine the material parameters.
Superconducting circuits are promising components for future quantum information technologies such as quantum computing, quantum simulation, and quantum sensing. Superconducting quantum interference devices (SQUIDs) and superconducting flux qubits can be used as a sensitive magnetic field sensor to detect local electron spin resonance (ESR). These types of sensor are characterized by good sensitivity and high spatial resolution for electron spins. In fact, we have achieved a sensitivity of 20 spins/Hz\sqrt{\text {Hz}}Hz​ with a sensing volume of 6 fl combining a flux qubit and qubit readout using a Josephson bifurcation amplifier. As a demonstration, we measured the ESR spectrum of erbium electron spins in a Y2_{2}2​SiO5_{5}5​ crystal and nitrogen vacancy centers in diamond. In both cases, we obtained reasonable electron spin parameters by fitting a simulation to the spectrum. In this way, we proved superconducting circuits to be promising magnetic field sensors for evaluating the properties of solid materials.
Abstract Interest is growing in the development of quantum sensing based on the principles of quantum mechanics, such as discrete energy levels, quantum superposition, and quantum entanglement. Superconducting flux qubits are quantum two-level systems whose energy is sensitive to a magnetic field. Therefore, they can be used as high-sensitivity magnetic field sensors that detect the magnetization of a spin ensemble. Since the magnetization depends on temperature and the magnetic field, the temperature can be determined by measuring the magnetization using the flux qubit. In this study, we demonstrated highly sensitive temperature sensing with high spatial resolution as an application of a magnetic field sensor using the quantum coherence of a superconducting flux qubit. By using a superconducting flux qubit to detect the temperature dependence of the polarization ratio of electron spins in nano-diamond particles, we succeeded in measuring the temperature with a sensitivity of 1.3 µKµ Hz − 1 at T = 9.1 mK in the submicrometer range.
We report on electron spin resonance spectroscopy measurements using a superconducting flux qubit with a sensing volume of 6 fl. The qubit is read out using a frequency-tunable Josephson bifurcation amplifier, which leads to an inferred measurement sensitivity of about 20 spins in a 1 s measurement. This sensitivity represents an order of magnitude improvement when compared to flux-qubit schemes using a direct current-superconducting quantum interference device switching readout. Furthermore, noise spectroscopy reveals that the sensitivity is limited by flicker (1/f) flux noise.
We theoretically analyze the performance of the nuclear magnetic resonance (NMR) spectroscopy with a superconducting flux qubit (FQ). Such NMR with the FQ is attractive because of the possibility to detect the relatively small number of nuclear spins in a local region ($\ensuremath{\approx}\ensuremath{\mu}\mathrm{m}$) with low temperatures ($\ensuremath{\approx}\mathrm{mK}$) and low magnetic fields ($\ensuremath{\approx}\mathrm{mT}$), in which other types of quantum sensing schemes cannot easily be accessed. A sample containing nuclear spins is directly attached on the FQ, and the FQ is used as a magnetometer to detect magnetic fields from the nuclear spins. Especially, we consider two types of approaches to NMR with the FQ. One of them is to use spatially inhomogeneous excitations of the nuclear spins, which are induced by a spatially asymmetric driving with radio-frequency (rf) pulses. Such an inhomogeneity causes a change in the dc magnetic flux penetrating a loop of the FQ, which can be detected by a standard Ramsey measurement on the FQ. The other approach is to use a dynamical decoupling on the FQ to measure ac magnetic fields induced by Larmor precession of the nuclear spins. In this case, neither a spin excitation nor a spin polarization is required since the signal comes from fluctuating magnetic fields of the nuclear spins. We calculate the minimum detectable density (number) of the nuclear spins for the FQ with experimentally feasible parameters. We show that the minimum detectable density (number) of the nuclear spins with these approaches is around 1021/cm3{10}^{21}/{\mathrm{cm}}^{3}1021/cm3 (108{10}^{8}108) with an accumulation time of 1 s.
State of the art quantum sensing experiments targeting frequency measurements or frequency addressing of nuclear spins require one to drive the probe system at the targeted frequency. In addition, there is a substantial advantage to performing these experiments in the regime of high magnetic fields, in which the Larmor frequency of the measured spins is large. In this scenario we are confronted with a natural challenge of controlling a target system with a very high frequency when the probe system cannot be set to resonance with the target frequency. In this contribution we present a set of protocols that are capable of confronting this challenge, even at large frequency mismatches between the probe system and the target system, both for polarization and for quantum sensing.