Static dc electric field orientation effects on two-photon Rydberg EIT

TL;DR

This work demonstrates vector electrometry of a dc electric field using polarization-dependent two-photon Rydberg EIT in rubidium. By rotating the laser polarizations relative to the field, the authors show that the amplitudes of Stark-split EIT resonances depend sensitively on the field orientation, enabling reconstruction of the field direction in addition to magnitude. They develop a semi-analytical dipole-moment model and corroborate it with full density-matrix simulations, achieving good agreement for the strongest resonances, and they extend the method to spatially resolved, fluorescence-based field mapping with a biased wire. The results indicate a viable route to vector electric-field sensing relevant for quantum sensing, electron-beam characterization, and plasma diagnostics, while also outlining limitations and directions for more complete modeling. Theoretical and experimental alignment suggests that simultaneous analysis of resonance frequencies and amplitudes can yield robust vector electrometry using Rydberg EIT with accessible infrastructure.

Abstract

We examine the influence of a static dc electric field on Electromagnetically Induced Transparency (EIT) resonances that involve highly excited Rydberg states. Our focus is on how these resonances are altered when the relative orientation between the laser polarization and the external electric field vectors are varied. We experimentally demonstrate characteristic variations in the amplitude of the Stark-split EIT resonances, which can be explained by the selection rules in various geometries. We also present a simplified semi-analytical model that closely resembles the experimental observations. We use these findings to obtain information about the spatially inhomogeneous electric field, produced by a biased wire, using EIT fluorescence measurements that agrees with the expected angular dependencies. These results suggest that simultaneous analysis of frequency shifts and amplitudes of Rydberg EIT resonances may enable vector electrometry of electrostatic fields, necessary for many quantum sensing applications.

Figures (4)

• Figure 1: (a) Simplified energy level configuration of $^{85}$Rb used to observe two-photon EIT resonances. The 780 nm probe laser is on resonance with the $5S_{1/2}\rightarrow 5P_{3/2}$ transition. The 480 nm coupling laser is scanned across the $5P_{3/2}\rightarrow nD_{5/2}$ transition with frequency detuning $\Delta_c$. Dashed lines depict Stark splitting of the Rydberg $nD_{5/2}$ level into $|m_J|=1/2,3/2,5/2$ sublevels as the static electric field strength increases. (b) Allowed transitions for optical field polarized parallel (solid) or perpendicular (dashed) to the dc electric field for a simplified fine structure of involved atomic levels. (c) Examples of EIT spectra in the absence of electric field (black), with electric field E applied perpendicular (magenta) and parallel (green) to both laser polarizations ($\mathcal{E}$).
• Figure 2: (a) Experimental arrangement for uniform electric field measurements. The electric field E points along the $x$-direction when a voltage $V_0$ is applied to the top capacitor plate. The laser beams counter-propagate along the $z$ direction, and their polarization orientations are defined by angles $\phi_r$ and $\phi_b$, formed between the laser polarization vectors $\mathcal{E}_r$ and $\mathcal{E}_b$ with the $\hat{y}$ axis. (b) Experimentally measured peak areas of $|m_J|$ EIT peaks as functions of independently varying laser polarizations. (c) Experimentally measured dependence of all three peak areas on the angle between the electric field and the laser polarization when $\mathcal{E}_r$ and $\mathcal{E}_b$ are matched, i.e. $\phi_r = \phi_b$ ($\phi_{r,b}$). (d-g) Corresponding theoretical EIT area values calculated using the semi-analytical atomic model (d,e) or by solving exact numerical interaction Hamiltonian (f,g).
• Figure 3: Fluorescence based electric field magnitude measurements. (a-c) Electric field magnitude reconstruction as the wire is displaced a distance $\Delta y$ from the lasers. A retractable wire in our Rb vacuum chamber creates a spatially varying electric field when a voltage $V_0$ is applied. In the diagram of the wire with respect to the lasers, the darker red and blue lines indicate the laser fluorescence region monitored by the camera, $\theta_E = \theta_{a,b,c}$ denote the electric field variation with respect to the $z$-axis in each position of the probe and $\phi_E$ indicate angles with respect to the $x$- axis. Underneath these diagrams, the black and white color maps are recorded fluorescence spectra for laser polarization orientation where the $m_{\pm5/2}$ peak is minimized. Solid lines show reconstructed peak positions of the 46D${}_{5/2}$$|m_j|$ = 5/2, 3/2 and 1/2 and dashed red lines are the peak positions of the 46D${}_{3/2}$ levels. Finally, at the bottom we show the spatially reconstructed electric field magnitude for each position of the wire with respect to the lasers.
• Figure 4: Variation of $\theta_E$ and $\phi_E$ for different $\Delta y$ wire displacements. The different $\Delta \theta_{a,b,c}$ correspond to the different angular variations we show in Fig. \ref{['fig:fluorescenceMagnitude']}. (a1) Experimental $m_{\pm1/2}$ peak area for different wire $\Delta y$-positions, monitored with fluorescence at $\Delta z$ = 0 mm. Error bars are an average of pixels from the center $\pm0.25$ mm. (b1) Experimental $m_{\pm1/2}$ peak area for different wire $\Delta y$-positions with a fixed polarization when $m_{\pm5/2}$ peak is minimum. (a2) Modeled $m_{\pm1/2}$ peak area for different wire $\Delta y$-positions. (b2) Modeled $m_{\pm1/2}$ peak area for different wire $\Delta y$-positions with a fixed polarization when the $m_{\pm5/2}$ peak is at a minimum.