On effect of stability of magnetic resonance position by harmonized field

The formalism of density matrix in a two level system is used to study the time-periodic modulation of the magnetic field stabilizating the magnetic resonance position. An exact solution for density matrix at resonance is found. It is shown that the fundamental resonance is stable with respect to consistent variations of longitudinal and transversal magnetic fields. A differential equation for the transition probability is obtained. The dependence of time-averaged spin flip probability on the normalized Larmor frequency was numerically researched in different parameter regimes with account of dissipation and decoherence. It is shown that the position of the main resonance is independent of field deformation and dissipation; only the width of resonance line changes upon field deformation and dissipation. The odd parametric (multi-photon) resonance transitions is studied. Static magnetization induced by time-periodic modulated magnetic field is considered. The results of the investigation may be useful for analysis of interference experiments, improvement of magnetic spectrometers and in the field of quantum computing manipulation of q-bits