Spin Dressed Relaxation and Frequency Shifts from Field Imperfections

Critical dressing, the simultaneous dressing of two spin species to the same effective Larmor frequency, is a technique that can, in principle, improve the sensitivity to small frequency shifts. The benefits of spin dressing and thus critical dressing are achieved at the expense of generating a large (relative to the holding field $B_{0}$,) homogeneous oscillating field. Due to inevitable imperfections of the fields generated, the benefits of spin dressing may be lost from the additional relaxation and noise generated by the dressing field imperfections. In this analysis the subject of relaxation and frequency shifts are approached with simulations and theory. Analytical predictions are made from a new quasi-quantum model that includes gradients in the holding field $B_{0}=\omega _{0}/\gamma$ and dressing field $B_{1}=\omega _{1}/\gamma$ where $B_{1}$ is oscillating at frequency $\omega$. The results are compared with a Monte Carlo simulation coupled with a 5$^{\text{th}}$ order Runge-Kutta integrator. Comparisons of the two methods are presented as well as a set of optimized parameters that produce stable critical dressing at a range for oscillating frequencies $\omega ,$ as well as pulsed frequency modulation parameters for maximum sensitivity.