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arXiv:1203.4414

Characterization of RF Inhomogeneity via NOON states

Abhishek Shukla, T. S. Mahesh

Published Mar 20, 2012• 0 citations
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Abstract

We describe a method for quantitative characterization of radio-frequency (RF) inhomogeneity using NOON states. NOON states are special multiple-quantum coherences which can be easily prepared in star-topology spin-systems. In this method we exploit the high sensitivity of the NOON states for z-rotations. As a result, Torrey oscillations with NOON states decay much faster than that of single quantum coherences. Therefore the present method requires shorter pulse durations, and enables the study of inhomogeneity at higher RF powers. To model such a inhomogeneity profile, we propose a two-parameter asymmetric Lorentzian function. The experiments are carried out in 1H channels of two different high-resolution NMR probes and the results are compared. Finally, we also extend the NOON state method to characterize the inhomogeneity correlations between two RF channels. We obtain the correlation profile between 1H and 31P channels of an NMR probe by constructing a five-parameter asymmetric-3D Lorentzian model.

DOI
10.48550/arxiv.1203.4414

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We describe a method for quantitative characterization of radio-frequency (RF) inhomogeneity using NOON states. NOON states are special multiple-quantum coherences which can be easily prepared in star-topology spin-systems. In this method we exploit the high sensitivity of the NOON states for z-rotations. As a result, Torrey oscillations with NOON states decay much faster than that of single quantum coherences. Therefore the present method requires shorter pulse durations, and enables the study of inhomogeneity at higher RF powers. To model such a inhomogeneity profile, we propose a two-parameter asymmetric Lorentzian function. The experiments are carried out in 1H channels of two different high-resolution NMR probes and the results are compared. Finally, we also extend the NOON state method to characterize the inhomogeneity correlations between two RF channels. We obtain the correlation profile between 1H and 31P channels of an NMR probe by constructing a five-parameter asymmetric-3D Lorentzian model.
A method for measuring translational diffusion constant in liquids via NOON state is described using a quantum circuit and is experimentally demonstrated using a model system. When compared with the standard single quantum method, the NOON state method requirs shorter diffusion delays and weaker gradients. These improvements depend on the on the size of the NOON state. Due to the high sensitivity of the NOON state for the changes in the local magnetic fields, this method enables studying slow diffusion and studying diffusion with limited strengths of pulsed-field-gradients.
Utilizing the highly correlated quantum NOON states of particles, we have implemented a proof-of-principle quantum thermometer using the NMR technique for measuring the variation of local magnetic field with the temperature variation. The system used was the star-topology system of hexafluorophosphate molecules and the thermometer showed a sensitivity of 85nT/oC85nT/ ^o C85nT/oC. Using the hexafluorophosphate and the trimethylphosphite spin systems, we have quantified the advantage of the quantum protocol over the classical one for measuring magnetic field. The quantum protocol showed the best performance for a time evolution in the quantum circuit of T=20msT = 20msT=20ms, where the errors in the measurement scaled as the Heisenberg limit 1/N1/N1/N.
Abstract High-fidelity control of spin ensemble dynamics is essential to many fields, spanning from quantum computing to optical, coherent, and nuclear magnetic resonance (NMR) spectroscopy and imaging (MRI). However, attaining robust and high-fidelity quantum spin operations remains an unmet challenge. Using a combination of an evolutionary algorithm and artificial intelligence, we designed time-optimal, radio frequency (RF) pulses with tunable spatial or temporal field inhomogeneity compensation and fidelity for unitary operations up to 0.9999. As a benchmark, we constructed a spin entanglement operator and a programmable quantum state creator for a weakly-coupled two-spin-1/2 system. We achieved high-fidelity transformations under multiple inhomogeneity sources. The newly designed RF pulses are more robust and less prone to imperfection than the commonly used shapes for basic liquid-state NMR experiments and reduce RF artifacts in MRI. This new strategy will enable the design of efficient quantum computing opera-tors as well as new spectroscopic and imaging techniques.
Abstract High-fidelity control of spin ensemble dynamics is essential for many research areas, spanning from quantum computing and radio-frequency (RF) engineering to NMR spectroscopy and imaging. However, attaining robust and high-fidelity spin operations remains an unmet challenge. Using an evolutionary algorithm and artificial intelligence (AI), we designed new RF pulses with customizable spatial or temporal field inhomogeneity compensation. Compared with the standard RF shapes, the new AI-generated pulses show superior performance for bandwidth, robustness, and tolerance to field imperfections. As a benchmark, we constructed a spin entanglement operator for the weakly coupled two-spin-1/2 system of 13CHCl3, achieving high-fidelity transformations under multiple inhomogeneity sources. We then generated band-selective and ultra-broadband RF pulses typical of biomolecular NMR spectroscopy. When implemented in multipulse NMR experiments, the AI-generated pulses significantly increased the sensitivity of medium-size and large protein spectra relative to standard pulse sequences. Finally, we applied the new pulses to typical imaging experiments, showing a remarkable tolerance to changes in the RF field. These AI-generated RF pulses can be directly implemented in quantum information, NMR spectroscopy of biomolecules, magnetic resonance imaging techniques for in vivo and materials sciences.
Quantum entanglement has long been recognized as an important resource for quantum sensing. In this work, we demonstrate the use of multiple-quantum solid-state NMR for quantum sensing by creating, manipulating, and detecting large clusters of correlated nuclear spins. We show that such clusters can sensitively detect pulse-width jitters in radio-frequency control fields at the level of tens of nanoseconds. By analyzing the response of high-order quantum coherences to these control-field jitters, we investigate the critical interplay between the enhanced sensitivity offered by large coherence orders, their relative distributions, and their varying susceptibility to decoherence. We further demonstrate that, even within a non-uniform distribution of coherence orders, there exists an optimal maximum coherence order that maximizes sensing efficiency. To support our interpretation, we supplement the experimental results with a simplified numerical model that estimates the corresponding quantum Fisher information. These results support the solid-state NMR platform as a valuable testbed for investigating many-body quantum metrology protocols.
Abstract Quantum systems composed of solid-state electronic spins can be sensitive detectors of narrowband magnetic fields. A prominent example is the nitrogen-vacancy (NV) center in diamond, which has been employed for magnetic spectroscopy with high spatial and spectral resolution. However, NV-diamond spectroscopy protocols are typically based on dynamical decoupling sequences, which are limited to low-frequency signals (≲ 20 MHz) due to the technical requirements on microwave (MW) pulses used to manipulate NV electronic spins. In this work, we experimentally demonstrate a high-resolution magnetic spectroscopy protocol that integrates a quantum frequency mixing (QFM) effect in a dense NV ensemble with coherently averaged synchronized readout (CASR) to provide both a wide range of signal frequency detection and sub-Hz spectral resolution. We assess the sensitivity of this QFM-CASR protocol across a frequency range of 10 MHz to 4 GHz. By measuring the spectra of multi-frequency signals near 0.6, 2.4 and 4 GHz, we demonstrate sub-Hz spectral resolution with a nT-scale noise floor for the target signal, and precise phase measurement with error <1°. Compared to state-of-the-art NV-diamond techniques for narrowband magnetic spectroscopy, the QFM-CASR protocol greatly extends the detectable frequency range, enabling applications in high-frequency radio frequency (RF) and MW signal microscopy and analysis, as well as tesla-scale nuclear magnetic resonance (NMR) spectroscopy of small samples.