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Magnus expansion paradoxes in the study of equilibrium magnetization and entanglement in multi-pulse spin locking

 a,  a,  b
a Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, Moscow Region, Russian Federation
b Department of Physics, Brown University, Providence, Rhode Island, USA

Divergence of the Magnus expansion leads to paradoxes in the spin dynamics of solid-state NMR and in quantum informatics. This review presents results on quasi-equilibrium magnetization in a system of dipole--dipole (DD) coupled spins at times T2tT in multiple pulse spin locking (T2 is the transverse spin relaxation time, and T is the rotating-frame spin-lattice relaxation time). It is shown how the contradictions between the results obtained with the Magnus expansion and experimental data can be removed. Systems of two and three DD coupled spins in multi-pulse spin locking are considered and the entanglement evolution is investigated using both the Magnus expansion and the exact solution obtained. The critical temperature for an entangled state is also found.

Text can be downloaded in Russian. English translation is available here.
Keywords: Floquet theorem, Floquet Hamiltonian, Magnus expansion, Magnus paradox, multi-pulse spin locking, average Hamiltonian theory, concurrence, quantum entanglement
PACS: 03.65.−w, 03.67.Mn, 76.60.−k (all)
DOI: 10.3367/UFNe.2016.02.037753
URL: https://ufn.ru/en/articles/2016/6/g/
Citation: Kuznetsova E I, Fel’dman É B, Feldman D E "Magnus expansion paradoxes in the study of equilibrium magnetization and entanglement in multi-pulse spin locking" Phys. Usp. 59 577–582 (2016)
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Received: 29th, February 2016, 4th, February 2016

Оригинал: Кузнецова Е И, Фельдман Э Б, Фельдман Д Э «Парадоксы ряда Магнуса при исследовании равновесной намагниченности и запутанности в многоимпульсном спиновом локинге» УФН 186 647–653 (2016); DOI: 10.3367/UFNr.2016.02.037753

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