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Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento

Exact quantum-mechanical theory of spin-spin interaction and nuclear magnetic resonance

E. Conte

Published Sep 1, 1972• 0 citations
Publisher
DOI
10.1007/bf02905268

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We present an open-source software for simulation of observables in magnetic resonance experiments, including nuclear magnetic/quadrupole resonance NMR/NQR and electron spin resonance (ESR). Inspired by magnetic resonance protocols that emerged in the context of quantum information science (QIS), this software can assist experimental research in the design of new strategies for the investigation of fundamental quantum properties of materials. The package introduced here can simulate both standard NMR spectroscopic observables and the time-evolution of an interacting single-spin system subject to complex pulse sequences, i.e. quantum gates. The main purpose of this software is to facilitate the development of much needed novel NMR-based probes of emergent quantum order, which can be elusive to standard experimental probes. The software is based on a quantum mechanical description of nuclear spin dynamics in NMR/NQR experiments and has been widely tested on available theoretical and experimental results. Moreover, the structure of the software allows for basic experiments to be easily generalized to more sophisticated ones because it includes all the libraries required for the numerical simulation of generic spin systems. In order to make the program easily accessible to a large user base, we developed a user-friendly graphical interface, Jupyter notebooks, and fully-detailed documentation. Lastly, we portray several examples of the execution of the code that illustrate the prosepcts of a novel NMR paradigm, inspired by QIS, for efficient investigation of emergent phases in strongly correlated materials. Program Title: PULSEE (Program for the simULation of nuclear Spin Ensemble Evolution) CPC Library link to program files: https://doi.org/10.17632/vvv8tcb2nt.1 Developer's repository link: https://github.com/vemiBGH/PULSEE Licensing provisions: GPLv3 Programming language: Python 3 Nature of problem: Application of nuclear magnetic/quadrupole resonance techniques to study properties of materials often requires extensive spectral simulations. On the other hand, application of magnetic resonance techniques to quantum information science (QIS) involves different sets of observables. Available simulation software addresses only one of these applications: either detailed spectral simulations [1] or QIS relevant observables [2]. For this reason, NMR has not seen as much development in the condensed matter community compared to other spectroscopic techniques that combine these two approaches. Therefore, there is a need for an up-to-date and easily accessible software that can simulate an extensive set of NMR/NQR experimental observables, reproducing the behavior/response of nuclear systems with a varying degree of complexity encountered in strongly correlated quantum materials. Solution method: The open-source Python code provides an extensive set of libraries for the simulation of spin time evolution in the presence of specific interactions and reproduction of spectra; as well as other observables measured in magnetic resonance experiments; and simulations of quantum circuits and gates. The ready-to-use software features a user-friendly graphical interface, and Jupyter notebooks. F. A. Perras, C. M. Widdifield, and D. L. Bryce, “QUEST - Quadrupolar Exact Software: A fast graphical program for the exact simulation of NMR and NQR spectra for quadrupolar nuclei,” Solid State Nuclear Magnetic Resonance, vol. 45-46, pp. 36-44, (2012). D. Possa, A. C. Gaudio, and J. C. C. Freitas, “Numerical simulation of NQR/NMR: Applications in quantum computing,” Journal of Magnetic Resonance, vol. 209, pp. 250-260, (2011).

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An open quantum system is a system coupled to an environment that can describe time-irreversible dynamics through which the system evolves toward the thermal equilibrium state.We present a quantum mechanically rigorous theory in order to help the analysis of spectra obtained from the advanced nuclear magnetic resonance (NMR) and muon spin rotation, relaxation or resonance (μSR) techniques.Our approach is based on the numerically "Exact" hierarchical equations of motion (HEOM) approach, which allows us to study the reduced system dynamics for non-perturbative and non-Markovian system-bath interactions at finite temperature even under strong time-dependent perturbations.We demonstrate the present theory to analyze μSR and low-field NMR spectra, as an extension of the Kubo-Toyabe theory focusing on the effects of temperature and anisotropy of a local magnetic field on spectra, to help further the development of these experimental means.
Multiple quantum (MQ) nuclear magnetic resonance (NMR) spin dynamics are investigated analytically in infinite one-dimensional (1D) chains of spins 1/2. The representation of spin 1/2 operators with fermion field operators allows to calculate exactly the spin density operator, and hence NMR observables, under a variety of different conditions for 1D spin systems. The exact expressions are valid for all times and for a macroscopic number of coupled spins. The calculations for a 1D spin system initially at thermal equilibrium, and evolving under a 2-quantum/2-spin average dipolar Hamiltonian, in the presence of nearest-neighbor dipolar interactions yield MQ NMR spectra with 0- and 2-quantum coherences only. For a nonequilibrium initial condition with transverse magnetization, the analogous spin dynamics calculations produce MQ NMR spectra with all possible coherences of odd orders. Calculations at the level of perturbation theory, which include next-nearest-neighbor dipolar interactions, generate MQ spectra with higher even order coherences for equilibrium initial condition and evolution under a 2-quantum/2-spin propagator. Consideration of multiple spin correlations, 0-quantum coherences, and rf pulse imperfections are also presented. The relevance and implications of these theoretical results for comparison with the recent MQ NMR experiments of Yesinowski et al. on materials with quasi-one-dimensional distributions of spins, and for MQ NMR of solids in general are discussed.
We present an open-source software for simulation of observables in magnetic resonance experiments, including nuclear magnetic/quadrupole resonance NMR/NQR and electron spin resonance (ESR). Inspired by magnetic resonance protocols that emerged in the context of quantum information science (QIS), this software can assist experimental research in the design of new strategies for the investigation of fundamental quantum properties of materials. The package introduced here can simulate both standard NMR spectroscopic observables and the time-evolution of an interacting single-spin system subject to complex pulse sequences, i.e. quantum gates. The main purpose of this software is to facilitate the development of much needed novel NMR-based probes of emergent quantum order, which can be elusive to standard experimental probes. The software is based on a quantum mechanical description of nuclear spin dynamics in NMR/NQR experiments and has been widely tested on available theoretical and experimental results. Moreover, the structure of the software allows for basic experiments to be easily generalized to more sophisticated ones because it includes all the libraries required for the numerical simulation of generic spin systems. In order to make the program easily accessible to a large user base, we developed a user-friendly graphical interface, Jupyter notebooks, and fully-detailed documentation. Lastly, we portray several examples of the execution of the code that illustrate the prosepcts of a novel NMR paradigm, inspired by QIS, for efficient investigation of emergent phases in strongly correlated materials. Program Title: PULSEE (Program for the simULation of nuclear Spin Ensemble Evolution) CPC Library link to program files: https://doi.org/10.17632/vvv8tcb2nt.1 Developer's repository link: https://github.com/vemiBGH/PULSEE Licensing provisions: GPLv3 Programming language: Python 3 Nature of problem: Application of nuclear magnetic/quadrupole resonance techniques to study properties of materials often requires extensive spectral simulations. On the other hand, application of magnetic resonance techniques to quantum information science (QIS) involves different sets of observables. Available simulation software addresses only one of these applications: either detailed spectral simulations [1] or QIS relevant observables [2]. For this reason, NMR has not seen as much development in the condensed matter community compared to other spectroscopic techniques that combine these two approaches. Therefore, there is a need for an up-to-date and easily accessible software that can simulate an extensive set of NMR/NQR experimental observables, reproducing the behavior/response of nuclear systems with a varying degree of complexity encountered in strongly correlated quantum materials. Solution method: The open-source Python code provides an extensive set of libraries for the simulation of spin time evolution in the presence of specific interactions and reproduction of spectra; as well as other observables measured in magnetic resonance experiments; and simulations of quantum circuits and gates. The ready-to-use software features a user-friendly graphical interface, and Jupyter notebooks. F. A. Perras, C. M. Widdifield, and D. L. Bryce, “QUEST - Quadrupolar Exact Software: A fast graphical program for the exact simulation of NMR and NQR spectra for quadrupolar nuclei,” Solid State Nuclear Magnetic Resonance, vol. 45-46, pp. 36-44, (2012). D. Possa, A. C. Gaudio, and J. C. C. Freitas, “Numerical simulation of NQR/NMR: Applications in quantum computing,” Journal of Magnetic Resonance, vol. 209, pp. 250-260, (2011).