Stabilization of the magnetic resonance position by a harmonized field

Abstract

A two-level system in a magnetic field with a periodic temporal modulation that stabilizes the position of the magnetic resonance is investigated in the density matrix formalism. An exact solution is found for the density matrix at resonance. It is shown that at resonance the probability of a spin-flip transition is independent of the form of the field, i.e., the main resonance is stable against harmonized variation of the longitudinal and transverse components of the magnetic field. The Bloch polarization vector and the geometric phase at resonance are calculated. A differential equation for the transition probability is obtained. The dependence of the time-averaged probability of a spin flip on the normalized Larmor frequency is investigated numerically for different parameters of the model. It is shown that the position of the main resonance is independent of the deformation of the field; only the width of the resonance peak changes upon deformation. The odd parametric (’multiphoton) resonance transitions are investigated. The static magnetization induced by the harmonized field is considered. This study may find application in the analysis of interference experiments, for refining the designs of magnetic spectrometers, and for controlling qubits.