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. 2025 Mar:372:107840.
doi: 10.1016/j.jmr.2025.107840. Epub 2025 Jan 23.

On the geometric phase effects on time evolution of the density matrix during modulated radiofrequency pulses

Dennis J Sorce  1 , Shalom Michaeli  2
Affiliations

On the geometric phase effects on time evolution of the density matrix during modulated radiofrequency pulses

Dennis J Sorce et al. J Magn Reson. 2025 Mar.

Abstract

In this work the effect of the geometric phase on time evolution of the density matrix was evaluated during nonadiabatic radiofrequency (RF) pulses with Sine amplitude modulation (AM) and Cosine frequency modulation (FM) functions of the RAFF (Relaxations Along a Fictitious Field) family, and the polarization between two energy level ½ spin system coupled by dipolar interaction was evaluated during the application of RF irradiation. The dependencies of the diagonal density matrix elements and the polarization on the rotational correlation times and the time during RF pulses were evaluated. The general treatment of the density matrix elements along with the polarization generated during RF pulses was unavailable thus far, and for the first time was here derived for the nonadiabatic case of the RAFF pulses. The current formalism could be extended to other AM and FM RF waveforms, including the adiabatic RF pulses which are widely used in magnetic resonance (MR). We demonstrate that the sub-geometric phases (SGP) influence the density matrix elements and thus the polarization generated during the application of RF AM and FM pulses. The corrections to describe the SGP influence of the density matrix elements developed in this work could be essential for determination of MR fundamental parameters necessary for evaluation of tissue contrasts in vivo in MRI and for protein dynamics characterization in high resolution NMR, where AM and FM RF pulses are frequently utilized.

Keywords: Density matrix; Dipolar interactions; Geometric phase; Nonadiabatic pulses.

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Conflict of interest statement

Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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References

    1. Bohm A, Mostafazadeh A, Koizumi H, Niu Q, Zwanziger J, The Geometric Phase in Quantum Systems, Springer Verlag, Berlin, Heidelberg, 2003.
    1. Berry MV, Quantal phase-factors accompanying adiabatic changes, in: Proceedings of the Royal Society of London Series a-Mathematical and Physical Sciences, 1984, pp. 45–57.
    1. Pancharatnam S, Generalized theory of interference and its applications, Proc. Indian Acad. Sci. A 44 (1956) 398–417.
    1. Suter D, Chingas GC, Harris RA, Pines A, Berry’s phase in magnetic resonance, Mol. Phys 61 (1987) 1327–1340.
    1. Suter D, Mueller KT, Pines A, Study of the Aharonov-Anandan quantum phase by NMR interferometry, Phys. Rev. Lett 60 (1988) 1218–1220. - PubMed

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