Electrometry near a dielectric surface using Rydberg electromagnetically induced transparency

Electrometry near a dielectric surface is performed using Rydberg electromagnetically induced transparency. The large polarizability of high-$n$-state Rydberg atoms gives this method extreme sensitivity. We show that dipoles produced by adsorbates on the dielectric surface produce a significant electric field that responds to an applied field with a time constant of order 1 s. For transient applied fields (with a time scale of less than 1 s) we observe good agreement with calculations based on numerical solutions of Laplace’s equation using an effective dielectric constant to simulate the bulk dielectric.

Figure 1

(a) Experimental setup for electrometry using Rydberg EIT. A probe beam and counterpropagating Rydberg coupling beam are focused onto an ultracold sample of ${}^{87}$Rb atoms released from a MOT. The probe beam is scanned through resonance and detected on a fast photodiode. An electric field is produced using four rod-shaped electrodes as shown in the diagram. The measurement is carried out near a dielectric surface positioned 12.5 mm from the MOT. (b) Energy level scheme for two-photon cascade system EIT in ${}^{87}$Rb. A probe, with Rabi frequency ${\Omega }_{\mathrm{p}}$, is scanned through the 5$s$ ${}^2$$S$${}_{1/2}$ $\to$ 5$p$ ${}^2$$P$${}_{3/2}$ transition which is coupled to the 46$s$ ${}^2$$S$${}_{1/2}$ Rydberg state by ${\Omega }_{\mathrm{c}}$.

Figure 2

Probe transmission. The black lines show the transmission of a 60 nW probe beam as the detuning is scanned through resonance, in a time of 250 $\mu$s. The blue line shows the probe beam transmission in the presence of a 45 mW Rydberg coupling beam. The presence of the Rydberg coupling beam is manifest as a transparency feature, indicated by the arrows, that is superposed onto the Lorentzian absorption line shape. In (a) there is no external electric field applied by the electrodes and the EIT feature appears at zero probe detuning. In (b) the EIT feature appears shifted due to the presence of an applied electric field.

Figure 3

Energy level shift measurement of the 46$S$ Rydberg state as a function of the voltage applied to the electrodes. The voltage is applied to the electrodes throughout the duration of the experiment. In (a) the voltage is applied to electrodes ③  and ④ , in (b) to ①  and ②. The solid line is a fit to the data using Eq. (3).

Figure 4

(a) Energy level shift of the 46$S$ Rydberg state for contrasting pulse length regimes. The blue data (solid line) are the measurement of the Rydberg energy level shift where the electrode voltage pulse length tends to zero $({\tau }_{\mathrm{p}}\to 0)$. These data are fitted with a quadratic function and the corresponding electric field found from the polarizability. The dashed line shows the Rydberg energy shift where the electrode voltage is applied continuously $({\tau }_{\mathrm{p}}\to \infty )$. (b) The Rydberg energy level shift as a function of the voltage pulse length with the voltage fixed at $-$9 V.

Figure 5

Calculation of the electric field by numerically solving Laplace’s equation. (a) The geometry of the known regions of potential, where ⓐ  is free space; ⓑ  is the grounded metal bulk of the vacuum chamber; ⓒ  are the electrodes; and ⓓ is the dielectric. (b) The magnitude of the electric field without the dielectric. (c) and (d) show the electric field magnitude in the region of the electrodes without and with the dielectric, respectively. In (d) the boundary of the dielectric is indicated by the vertical dotted lines.

Figure 6

Comparison of measured Rydberg energy level shift with that corresponding to the calculated electric field. Each panel shows data for a different electrode geometry relative to the dielectric surface, where grounded electrodes are unfilled while those with an applied voltage are filled black. The dotted lines show the results of the calculated electric field when the dielectric surface is not included in the calculation. The solid lines show the case where the dielectric is included, resulting in improved agreement to the data.