Atom-Based Vector Microwave Electrometry Using Rubidium Rydberg Atoms in a Vapor Cell

It is clearly important to pursue atomic standards for quantities like electromagnetic fields, time, length, and gravity. We have recently shown using Rydberg states that Rb atoms in a vapor cell can serve as a practical, compact standard for microwave electric field strength. Here we demonstrate for the first time that Rb atoms excited in a vapor cell can also be used for vector microwave electrometry by using Rydberg-atom electromagnetically induced transparency. We describe the measurements necessary to obtain an arbitrary microwave electric field polarization at a resolution of 0.5°. We compare the experiments to theory and find them to be in excellent agreement.

Figure 1

(a) Level diagram showing all 52 possible states addressed by the experiment. The arrows indicate allowed excitations for the $\sigma$-polarized probe and coupling beams and $\pi$-polarized MWs. The $54P_{3/2}$ states are shown above the $53D_{5/2}$ states for simplicity. On the right, the corresponding effective four-level system is shown. (b) Theoretical line shapes resulting from a three-level (black) and four-level (red) system.

Figure 2

Theoretical (a) and experimental (b) results for the illustrative polarization cases described in the text: probe laser, coupling laser, and MWs $\widehat{x}$ polarized (black); probe and coupling laser $\widehat{y}$ polarized and MWs $\widehat{x}$ polarized (blue); probe and coupling lasers ${\sigma }^{+}$ polarized and MWs $\widehat{z}$ polarized (red). The additional line broadening observed in the experiment is due to the MWs being inhomogeneous over the extent of the vapor cell. The effect resulted from the positioning of the antenna that was required to avoid unwanted reflections in our laboratory. The slight asymmetry in the data is due to a small amount of ionization. This effect did not significantly affect our measurements but can be reduced by driving the Rydberg transition with higher Rabi frequency. Our experiment is limited by the amount of blue laser power available.

Figure 3

Schematic view of the setup including the cell in the foreground and the test antenna in the background. The laser propagation direction (red), the polarization of the two laser beams (blue), and an arbitrary polarization direction of the MW (magenta) are shown together with the relevant angles between them as described in the main text. The shadows are the projections onto the $\widehat{x}\mathrm{\text{−}}\widehat{y}$ plane on the left and the $\widehat{x}\mathrm{\text{−}}\widehat{z}$ plane in the back.

Figure 4

Probe laser transmission on resonance for different angles between the laser polarizations and the MW electric field vector. The vertical error bars for the experimental points are due to statistical errors in the measured peak height while the horizontal error bars are due to systematic uncertainty in $\xi$. Fifty-two-state theoretical results (solid lines) with $\pm 1°$ uncertainty in $\zeta$ (dotted lines). The curves for $1-(E_{\parallel }/|\overrightarrow{E}|{)}^2=1-{cos}^2(\xi ){sin}^2(\zeta )$ are also shown (dashed lines). The probe transmission is normalized such that the maximum theoretical transmission is 1. The deviation of the points with larger $\zeta$ around $\xi =0°$ is due to polarization impurities in the laser and MW beams. The angular resolution of $\sim 0.5°$ is derived from a least squares fit of each trace to the theory. A three-direction measurement would yield reduced resolution as three different measurements must be combined.