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arXiv:1906.07386 · Physical Review A

Architecture to achieve nuclear magnetic resonance spectroscopy with a superconducting flux qubit

Koichiro Miyanishi, Yuichiro Matsuzaki, Hiraku Toida, Kosuke Kakuyanagi, Makoto Negoro, Masahiro Kitagawa, Shiro Saito

Published May 1, 2020• 5 citations
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Abstract

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 ${10}^{21}/{\mathrm{cm}}^{3}$ (${10}^{8}$) with an accumulation time of 1 s.

DOI
10.1103/physreva.101.052303

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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≈\ensuremathμm\ensuremath{\approx}\ensuremath{\mu}\mathrm{m}\ensuremath≈\ensuremathμm) with low temperatures (\ensuremath≈mK\ensuremath{\approx}\mathrm{mK}\ensuremath≈mK) and low magnetic fields (\ensuremath≈mT\ensuremath{\approx}\mathrm{mT}\ensuremath≈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.
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.
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We present the concept of quadrature-detected zero-to-ultralow-field nuclear magnetic resonance (QD ZULF NMR). Two orthogonal sensors, atomic optically pumped magnetometers, are used to separately detect components of oscillating sample magnetization, which are then combined into a quadrature signal. This approach enables the distinction of positive and negative resonance frequencies with respect to the laboratory frame---such that absolute signs of gyromagnetic ratios can be determined. In addition, QD ZULF NMR reduces peak density and overlap compared to ZULF NMR with single-axis detection, while providing richer information about nuclear-spin dynamics. As an illustration, we present experimental JJJ-spectra for thermally polarized [13^{13}13C]-formic acid and [13^{13}13C]-methanol, compounds commonly used in ZULF NMR which represent XA and XA3_33​ spin systems, respectively. A theoretical framework describing QD ZULF NMR signals is provided.
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Advanced atomic magnetometers have made it possible to acquire nuclear magnetic resonance spectra in zero to ultralow magnetic fields. This regime carries the benefit of compact, low-cost instrumentation with reduced spin relaxation effects and the ability to probe phenomena that are inaccessible in conventional high-field experiments. A trade-off is that the resulting spectra must be interpreted using simulations that are taxing for classical computation. Working by example for small-molecule and protein spectroscopy, we demonstrate that these simulations are a promising target for fault-tolerant quantum computation. Our holistic analysis spans from input selection to the construction of explicit circuits for qubitized quantum dynamics. By maintaining parity with experimental requirements, we demonstrate how certain cases might be especially promising for early fault-tolerant architectures. Notably, valuable natural products and small proteins could be simulated with a few hundred logical qubits and less than 10 12 T gates, corresponding to days of runtime with foreseeable hardware based on spin or superconducting qubits.