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Optimising control over nuclear spin transitions

Navin Khaneja

Published Jan 1, 2024• 0 citations
Publisher

Abstract

Optimising control over nuclear spin transitionsAt specific frequencies, nuclei will absorb the energy contained in the pulses, causing their spins to flip direction.Controlling transitions between the spin states of atomic nuclei is a fundamental aspect of modern technologies as wide-ranging as medical imaging, chemical analysis, and quantum computing.

DOI
10.26904/rf-153-6854603514

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Optimising control over nuclear spin transitionsAt specific frequencies, nuclei will absorb the energy contained in the pulses, causing their spins to flip direction.Controlling transitions between the spin states of atomic nuclei is a fundamental aspect of modern technologies as wide-ranging as medical imaging, chemical analysis, and quantum computing.
The electron spin decoherence by nuclear spins in semiconductor quantum dots is caused by quantum entanglement between the electron and the nuclei. The many-body dynamics problem of the interacting nuclear spins can be solved with the pair-correlation approximation which treats the nuclear spin flip-flops as mutually independent. The nuclear spin dynamics can be controlled by simply flipping the electron spin so that the electron is disentangled from the nuclei and hence its lost coherence is restored.
The possibility of controlled direct laser-nuclear excitations is considered from a quantum control perspective. The controllability of laser-driven electric dipole and magnetic dipole transitions among pure nuclear states is analyzed. Within a set of realistic and general conditions, atomic nuclei are demonstrated to possess full state controllability. Additionally, an analysis of the nuclear state excitation probability as a function of the laser control field is conducted. This control landscape is shown to possess a generic topology, which has important physical consequences for achieving optimal nuclear state excitation with laser fields. Last, an assessment is given of the technological challenges that need to be considered when implementing direct nuclear control in the laboratory.
Solid-state nuclear magnetic resonance (NMR) has emerged as an important technique for material characterization, finding extensive applications across a diverse range of disciplines including physics, materials science, chemistry, and biology. Its utility stems from the ability to probe the local atomic environments and molecular dynamics within solid materials, which provides information on the composition of the material. In recent years, the scope of solid-state NMR has expanded into the realm of quantum information science and technology, where its abundant many-body interactions pulse control methodologies make it have significant research value and application potential. This paper offers a comprehensive overview of the research objects and theoretical underpinnings of solid-state NMR, delving into the critical nuclear spin interaction mechanisms and their corresponding Hamiltonian forms. These interactions, which include dipolar coupling, chemical shift anisotropy, and quadrupolar interactions, are fundamental to the interpretation of NMR spectra and the understanding of material properties at the atomic level. Moreover, the paper introduces typical dynamical control methods employed in the manipulation of solid-state nuclear spins. Techniques such as dynamical decoupling, which mitigates the effects of spin-spin interactions to extend coherence times, and magic-angle spinning, which averages out anisotropic interactions to yield high-resolution spectra. These methods are essential for enhancing the sensitivity and resolution of NMR experiments, enabling the extraction of detailed structural and dynamic information from complex materials. Then we introduce some recent advancements in quantum control based on solid-state NMR, such as nuclear spin polarization enhancement techniques, which include dynamic nuclear polarization (DNP) and cross polarization (CP), significantly boost the sensitivity of NMR measurements. Additionally, the control techniques of Floquet average Hamiltonians are mentioned, showcasing their role in the precise manipulation of quantum states and the realization of quantum dynamics. Finally, the paper presents a series of seminal research works that illustrate the application of solid-state NMR quantum control technologies in the field of quantum simulation. These studies demonstrate how solid-state NMR can be leveraged to simulate and investigate quantum many-body systems, providing valuable insights into quantum phase transitions, entanglement dynamics, and other phenomena relevant to quantum information science. By bridging the gap between fundamental research and practical applications, solid-state NMR continues to play a crucial role in advancing our understanding of quantum materials and technologies.
We study control of electron-nuclear spin dynamics at magnetic field strengths where the Larmor frequency of the nucleus is comparable to the hyperfine coupling strength. The quantization axis for the nuclear spin differs from the static B0{B}_{0}B0​ field direction and depends on the state of the electron spin. The quantization axis can be switched by flipping the state of electron spin, allowing for universal control of nuclear spin states. We show that by performing a sequence of flips (each followed by a suitable delay), we can perform any desired rotation of the nuclear spin, which can also be conditioned on the state of the electron spin. These operations, combined with electron spin rotations, can be used to synthesize any unitary transformation of the coupled electron-nuclear spin system. We discuss how these methods can be used for design of experiments for transfer of polarization from the electron to the nuclear spins.
The nuclear spin, which is the fundamental atomic attribute underlying the magnetic resonance imaging, is an exact two-state quantum system. Therefore, it is a suitable candidate for use as a qubit in quantum computing. The aim of this letter is to review the main equations governing the dynamics of the spin magnetic dipole moment in Magnetic Resonance Imaging. It is also shown that exposing the magnetic dipole moment to a continuous-wave results in travelling back and forth between its two energy states. It absorbs energy from its environment when going from the lower to the higher energy state, and emits the same amount of energy back when relaxing from the higher to the lower energy state. In a complete cycle, the dipole moment behaves therefor purely reactive with zero net energy exchange with its environment.