Hyperpolarization and the physical boundary of Liouville space
Open Access
- 8 June 2021
- journal article
- research article
- Published by Copernicus GmbH in Magnetic Resonance
- Vol. 2 (1), 395-407
- https://doi.org/10.5194/mr-2-395-2021
Abstract
The quantum state of a spin ensemble is described by a density operator, which corresponds to a point in the Liouville space of orthogonal spin operators. Valid density operators are confined to a particular region of Liouville space, which we call the physical region and which is bounded by multidimensional figures called simplexes. Each vertex of a simplex corresponds to a pure-state density operator. We provide examples for spins , I=1, and for coupled pairs of spins-1/2. We use the von Neumann entropy as a criterion for hyperpolarization. It is shown that the inhomogeneous master equation for spin dynamics leads to non-physical results in some cases, a problem that may be avoided by using the Lindbladian master equation.
Funding Information
- Research Councils UK (EP/P009980/1)
- H2020 European Research Council (786707-FunMagResBeacons)
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