  Non-resonant dressing fields can make the transition frequency between two
circular Rydberg states insensitive to second order variations in the dc
electric field. Perturbation theory can be used to establish the required
dressing field amplitude and frequency. The same perturbative approach may be
used to understand removal of the first order dependence of the transition
frequency on electric field about a bias dc electric field [Hyafil et al. Phys.
Rev. Lett., v. 93, 103001 (2004)]. The directional alignment of the dressing
and dc fields is critical in determining the electric field sensitivity of the
dressed transition frequencies. This sensitivity is significantly larger for
circular Rydberg states compared to low-angular momentum Rydberg states of Rb.
