The Landau-Zener-Stückelberg-Majorana transition in the T2 ≪ T1 limit

Michael C Boucher; Peter Sun; Ivan Keresztes; Lee E Harrell; John A Marohn

doi:10.1016/j.jmr.2023.107523

The Landau-Zener-Stückelberg-Majorana transition in the T₂ ≪ T₁ limit

J Magn Reson. 2023 Sep:354:107523. doi: 10.1016/j.jmr.2023.107523. Epub 2023 Jul 14.

Authors

Michael C Boucher¹, Peter Sun¹, Ivan Keresztes¹, Lee E Harrell², John A Marohn³

Affiliations

¹ Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853, USA.
² Department of Physics and Nuclear Engineering, U.S. Military Academy, West Point, NY 10996, USA.
³ Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853, USA. Electronic address: jam99@cornell.edu.

PMID: 37625202
DOI: 10.1016/j.jmr.2023.107523

Abstract

Landau-Zener-Stückelberg-Majorana (LZSM) transitions occur between quantum states when parameters in the system's Hamiltonian are varied continuously and rapidly. In magnetic resonance, losses in adiabatic rapid passage can be understood using the physics of LZSM transitions. Most treatments of LZSM transitions ignore the T₂ dephasing of coherences, however. Motivated by ongoing work in magnetic resonance force microscopy, we employ the Bloch equations, coordinate transformation, and the Magnus expansion to derive expressions for the final magnetization following a rapid field sweep at fixed irradiation intensity that include T₂ losses. Our derivation introduces an inversion-function, Fourier transform method for numerically evaluating highly oscillatory integrals. Expressions for the final magnetization are given for low and high irradiation intensity, valid in the T₂≪T₁ limit. Analytical results are compared to numerical simulations and nuclear magnetic resonance experiments. Our relatively straightforward calculation reproduces semiquantitatively the well known LZSM result in the T₂→0 limit.

Keywords: Adiabatic rapid passage; Bloch equations; Electron spin resonance; Force-gradient detected magnetic resonance; Landau–Zener transition; Landau–Zener–Stückelberg–Majorana transition; Magnetic resonance force microscopy; Saturation.