Floquet theory in solid-state nuclear magnetic resonance

Accurate measurement of one-bond H–X heteronuclear dipolar couplings in MAS solid-state NMR

“…1 In the past we have used a numbering of the average Hamiltonian starting from 0 as it was introduced by Haeberlen and Waugh [36,37]. Such a numbering leads to differences between AHT and Floquet treatments [38] where comparable terms appear in the Floquet treatment in order (n) while they appear in order (n À 1) in the AHT expansion. We have, therefore, decided to follow the convention suggested by Hohwy et al [39] and start the numbering of the AHT expansion with 1. of e. This can also be seen from a plot of the REDOR curves in Fig.…”

Detection of radio-frequency field with a single spin in diamond

“…Then we consider the first term cosðx RF t þ u 0 Þc e B RFx S x . This term induces the Bloch-Siegert shift [32] which amounts to…”

A new broadband homonuclear mixing pulse for NMR with low applied power

“…Our design method neglects the off-resonance term generated by each rotating frame construction; however, in general corrections to lowest order in the resonance offset for counter-rotating waves (for example, the BlochSiegert shift 20 ) can be found using (e.g.) average Hamiltonian theory, 21,22 the Magnus expansion, 23,24 or the Floquet expansion, 25,26 and included in the effective Hamiltonian in each constructed frame. Note that with corrections for offresonance terms, (1) can be adjusted by adding the lowest order z-and x-component corrections to ω k−1 and u k−1 , respectively.…”