Spin Diffusion of Correlated Two-Spin States in a Dielectric Crystal

Abstract

Reciprocal space measurements of spin diffusion in a single crystal of calcium fluoride (CaF2) have been extended to dipolar ordered states. The experimental results for the component of the spin diffusion rate parallel to the external field are D(parallel)(D)=29+/-3x10(-12) cm(2)/s for the [001] direction and D(parallel)(D)=33+/-4x10(-12) cm(2)/s for the [111] direction. The measured diffusion rates for dipolar order are faster than those for Zeeman order and are considerably faster than predicted by simple theoretical models. It is suggested that constructive interference in the transport of the two-spin states is responsible for this enhancement. As expected, the anisotropy in the diffusion rates is observed to be significantly less for dipolar order compared to the Zeeman case.

Hydrodynamic approach to coherent nuclear-spin transport

“…a = 2.73 × 10 −8 cm for the Fluorines in CaF 2 , and L ∼ 0.1 cm, k −1 ∼ 10 −4 cm in the experiments. The realization of such states is discussed in detail by Boutis et al 4 In practice, k is parallel to the external magnetic field, and transport is measured in the same direction.…”

“…3,4 Assumption (2) is more subtle, as it rests on the validity of the ergodic hypothesis, which has received much attention recently in the context of lattice spin systems in dimensions 1 -3. 18,19,20,21,22 As discussed below, we believe that it may not be valid for the diffusion of energy.…”

“…18,19,20,21,22 As discussed below, we believe that it may not be valid for the diffusion of energy. Experimentally, spin diffusion has been measured by observing the relaxation of initial states varying sinusoidally in real space with a given wavevector k. 3,4 Such spatially-inhomogeneous states are represented mathematically as perturbations on the infinite temperature equilibrium state, ρ ∞ = 1/2 N , where N is the number of spins. We have…”

NMR Quantum Information Processing

“…In an early demonstration of the capability to explore many body dynamics in spin systems, solid state NMR techniques have been used to directly measure the rate of spin diffusion of Zeeman and dipolar energy in a single crystal of calcium fluoride [113,114]. As seen from the Hamiltonian above, these are both constants of the motion and are independently conserved.…”

Implementation of State Transfer Hamiltonians in Spin Chains with Magnetic Resonance Techniques

“…Transport in complex many-body spin systems has been widely studied as it manifests itself as spin diffusion [76,108,109]. In a solid, diffusive behaviour driven by the naturally occurring secular dipolar Hamiltonian arises from energy-conserving flip-flops of anti-aligned spin pairs, which produce a dynamics analogous to a random walk.…”