Figure 1

(a) The ac polarizability and (b) dressing field induced dipole moment differences [see Eq. (1)] between the $49s_{1/2}$ and $48s_{1/2}$ states of ${}^{87}$Rb in a 1-V/cm dc field. These diverge near the zero dc-field atomic transition frequencies (labeled).Reuse & Permissions

Figure 2

(a) Zero field atomic energy levels and the microwave dressing and probe frequencies. (b) Dipole nulling effect under ideal conditions: With the application of a dressing field there is no first-order dependence of the transition energy on the dc electric field and no differential ac Stark shift at $F_{dc,0}$.Reuse & Permissions

Figure 3

(a) Experimental apparatus. (b) Sequence of applied fields. Prior to Rydberg excitation, the anti-Helmholtz coil current is ramped down and the residual magnetic field nulled using compensation coils; the coil current is switched on again once selective field ionization (SFI) is complete. This sequence is repeated at $10\mathrm{Hz}$ as the probe frequency is stepped, and the Rydberg populations are measured using SFI.Reuse & Permissions

Figure 4

(a) The $49s_{1/2}\to 48s_{1/2}$ probe transition for different microwave dressing powers and dc electric fields (labeled). At 8-dBm dressing power the spectral lines for the three different dc fields coincide, illustrating the dipole nulling effect. The dressing frequency is $38.465\mathrm{GHz}$, chosen so that the doublet has zero average ac Stark shift at $1.1\mathrm{V}/\mathrm{cm}$. (b) Observed frequencies of the $49s_{1/2}-48s_{1/2}$ probe transitions as a function of dc electric field under different dressing field conditions, illustrating the dipole nulling and enhancement effects, compared with the nondressed case. Estimated statistical errors are on the order of the symbol sizes. Also shown are the results of a Floquet diagonalization with a linearly polarized dressing field ($F_{ac}=0.13\mathrm{V}/\mathrm{cm}$ and $\omega /2\pi =38.465\mathrm{GHz}$). Since the probe is a two-photon transition, “frequency” in both (a) and (b) refers to twice the applied frequency, for correspondence with energy-level differences.Reuse & Permissions

Figure 5

(a) Arrangement of interfering (nearly) orthogonal microwave polarizations for verifying splitting is due to ellipticity. (b) Location of two lines of the $48s_{1/2}-49s_{1/2}$ doublet as a function of phase between two interfering dressing fields at $38.1\mathrm{GHz}$. The experimental data are shifted horizontally by a constant phase for best agreement with the calculation. The shading around the calculation indicates uncertainty related to variations in the transmitted amplitude through the phase shifter. Uncertainties in the measured line positions are on the order of the symbol sizes.Reuse & Permissions