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Molecular Physics

Bounds on spin dynamics tightened by permutation symmetry application to coherence transfer in I2S and I3S spin systems

Niels Chr. Nielsen, Thomas Schulte‐Herbrüggen, Ole W. Sørensen

Published Aug 20, 1995• 24 citations
Publisher

Abstract

The effect of spin permutation symmetry on the maximum achievable efficiency of coherence transfer between pairs of Hermitian or non-Hermitian spin operators is investigated. It is shown that spin permutation symmetry may tighten significantly the quantum mechanical bounds hitherto known to apply for coherence transfer processes. This feature is demonstrated for the heteronuclear coherence transfer processes S x → F x , S - → F - and 2F z S x → F x , 2F z S - → F - (F = Σ n i=1 I i ) in I2S and I3S (n = 2,3) spin-1/2 systems. The bounds arising from permutation symmetry apply for non-selective multidimensional NMR experiments.

DOI
10.1080/00268979500101771

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The effect of spin permutation symmetry on the maximum achievable efficiency of coherence transfer between pairs of Hermitian or non-Hermitian spin operators is investigated. It is shown that spin permutation symmetry may tighten significantly the quantum mechanical bounds hitherto known to apply for coherence transfer processes. This feature is demonstrated for the heteronuclear coherence transfer processes S x → F x , S - → F - and 2F z S x → F x , 2F z S - → F - (F = Σ n i=1 I i ) in I2S and I3S (n = 2,3) spin-1/2 systems. The bounds arising from permutation symmetry apply for non-selective multidimensional NMR experiments.
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We report a general bound for the efficiency of polarization or coherence transfer between quantized states under unitary transformations. This bound is more general than the so-called universal bound on spin dynamics [O. W. S\o{}rensen, J. Magn. Reson. 86, 435 (1990)] that applies only to transformations between Hermitian states. The new bound on transfer efficiency under unitary transformations between general non-Hermitian operators depends exclusively on the singular values of the matrix representations of these operators.
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Experiments in coherent spectroscopy correspond to control of quantum-mechanical ensembles guiding them from initial to final target states. The control inputs (pulse sequences) that accomplish these transfers should be designed to minimize the effects of relaxation and to optimize the sensitivity of the experiments. For example in Nuclear Magnetic Resonance (NMR) spectroscopy, a question of fundamental importance is what is the maximum efficiency of polarization or coherence transfer between coupled spins in the presence of relaxation. Furthermore, what is the optimal pulse sequence which achieves this efficiency? This letter is a continuation of our previous work on the above problems. Here, we attempt to answer these questions for an Ising spin chain, under the presence of transverse relaxation. The methods presented in this paper are expected to find applications not only in coherent spectroscopy but also in quantum information processing.
Quantum systems in contact with a thermal environment experience coherent and incoherent dynamics. These drive the system back toward thermal equilibrium after an initial perturbation. The relaxation process involves the reorganization of spin state populations and the decay of spin state coherences. In general, individual populations and coherences may exhibit different relaxation time constants. Particular spin configurations may exhibit exceptionally long relaxation time constants. Such spin configurations are known as long-lived spin order. The existence of long-lived spin order is a direct consequence of the symmetries of the system. For nuclear spin systems, rotational and permutational symmetries are of fundamental importance. Based on the Schur-Weyl duality theorem, we describe a theoretical framework for the study of rotational and permutational dual-symmetries in the context of long-lived spin order. Making use of the proposed formalism, we derive refined bounds on the number on long-lived spin populations and coherences for systems exhibiting rotational-permutational dual-symmetries.