Electric field diagnostics in a continuous rf plasma using Rydberg-EIT

TL;DR

This work demonstrates a non-invasive method to diagnose internal electric fields in low-pressure inductively coupled plasmas using Rydberg-EIT on trace rubidium atoms. By comparing spectra with and without plasma, the authors show efficient RF-field shielding inside the plasma and use the Holtsmark microfield distribution to extract electron density and collisional broadening from the Rydberg-EIT line shapes. The analysis employs a three-way convolution of a field-free EIT profile, Holtsmark Stark shifts, and Gaussian collisional broadening, enabling quantitative plasma characterization in the few mTorr Ar regime. The approach offers a pathway to spatio-temporal E-field mapping in plasma sheaths, dusty plasmas, and other low-field environments, with potential extensions to higher-n Rydberg states and RF-wave sensing.

Abstract

We present a non-invasive spectroscopic technique to measure electric fields in plasma, leveraging large polarizabilities and Stark shifts of Rydberg atoms. Rydberg Stark shifts are measured with high precision using narrow-linewidth lasers via Electromagnetically Induced Transparency (EIT) of rubidium vapor seeded into a continuous, inductively coupled radio-frequency (rf) plasma in a few mTorr of argon gas. Without plasma, the Rydberg-EIT spectra exhibit rf modulation sidebands caused by electric- and magnetic-dipole transitions in the rf drive coil. With the plasma present, the rf modulation sidebands vanish due to screening of the rf drive field from the plasma interior. The lineshapes of the EIT spectra in the plasma reflect the plasma's Holtsmark microfield distribution, allowing us to determine plasma density and collisional line broadening over a range of pressures and rf drive powers. The work is expected to have applications in non-invasive spatio-temporal electric-field diagnostics of low-pressure plasma, plasma sheaths, process plasma and dusty plasma.

Figures (5)

• Figure 1: (a) Schematic of the experimental setup for plasma discharge and EIT spectroscopy. An inductively coupled Ar plasma (pressure range $\sim 5$ to 50 mTorr) is generated inside the depicted domed glass cylinder by a 13.56 MHz rf source, a matching network, and a helical drive coil. Near-thermal Rb vapor, entrained into the Ar flow and the plasma discharge, is optically interrogated for Rydberg-EIT-based electric-field diagnostics. (b) Illustration of the discharge volume and EIT interrogation region. The 780-nm EIT probe (red) and 480-nm coupling laser beams (purple), combined with a dichroic mirror (D1), counter-propagate and overlap each other inside the domed glass cylinder. The transmitted EIT probe power is measured with a photodiode (PD). Both laser beams are linearly polarized parallel to the rf drive magnetic field, $B_z$. (c) Rb energy levels used in this work. The probe laser (wavelength $\lambda_p = 780$ nm) is on-resonance with the $5S_{1/2}, F=3$$\leftrightarrow$$5P_{3/2}, F'=4$ transition, while the coupling laser (wavelength $\lambda_c = 480$ nm) is scanned across a $5P_{3/2}, F'=4 \leftrightarrow nS_{1/2}$ transition for Rydberg-EIT-based plasma electric field diagnostics.
• Figure 2: (a) Fields arising from applied rf power, $P_{\text{rf}}$, at 13.56 MHz in the chamber in the absence of Ar: axial rf magnetic field $B_z$, induced rf electric field $E_{\theta}$, capacitive rf electric field $E_z$, and dc electric field $E_{dc}$ (self-bias). (b) Within Ar plasma, the rf fields are shielded due to the skin effect, leaving the stochastic microfield as the dominant field. The microfield distribution is given by the Holtsmark distribution (inset). (c) Measured Rydberg-EIT spectra (solid lines) of Rb $27S_{1/2}$ without plasma, with $P_{\text{rf}}$ indicated by the color bar. The rf drive fields create electric and magnetic rf sidebands at integer multiples of $\omega_{\text{rf}}$. Calculated spectra, shown in gray (black) dashed lines, are for EIT-beam polarizations along $z$, $B_z$ = 7.5 G (15 G), $E_{dc}$=2 V/cm (4 V/cm), and $E = \sqrt{E_\theta^2 + E_z^2}= 10~$V/cm (12 V/cm). Aside from line broadening likely caused by field inhomogeneities along the EIT probe beam, the simulated spectra are a fairly close match to experimental spectra at $P_{\text{rf}}= 8$ W (12 W). (d) Rydberg-EIT spectra in plasma with 12 mTorr of Ar. The rf-induced sidebands disappear due to the skin effect. The asymmetric line shape is due to the Rydberg-atom Stark effect in the plasma's microfields, which follow a Holtsmark distribution. The red dashed curves show our fit results obtained from fits according to Eq. \ref{['eq:all_conv']}. Identical color scaling is used in panel (c) and (d).
• Figure 3: Plasma parameters extracted from Rydberg-EIT spectra for $25S_{1/2}$, obtained by fitting based on the the three-way convolution in Eq. (\ref{['eq:all_conv']}), plotted vs $P_{\rm{rf}}$ with color-coded Ar pressure $p$. (a) Plasma density $n_e$ extracted from the Holtsmark part of the fits, assuming quasi-neutrality in the bulk ($n_e \approx n_i$). Over the $n_e$-range found, the most probable microfield ranges from 5.1 V/cm to 9.8 V/cm. At $p \gtrsim 25$ mTorr, the slopes $\Delta n_e / \Delta P_{\mathrm{rf}}$ undergo a significant increase. (b) Broadening $\gamma$ from collision-induced dephasing mechanisms. Error bars exceed statistical fit uncertainties and rather reflect confidence based on signal to noise ratio and drift in the underlying EIT spectra.
• Figure 4: Electron density from Fig. \ref{['fig:fig3']}, plotted vs Ar pressure with color-coded powers $P_{\rm{rf}}$. At $p \gtrsim 25$ mTorr, the different-colored curves spread out, reflecting the increase in $\Delta n_e / \Delta P_{\mathrm{rf}}$.
• Figure 5: Optical emission spectrum of the Ar discharge with and without Rb present. The D$_2$ line of Rb at 780 nm is well isolated from the Ar transitions, the strongest of which are labeled (Paschen notation). The Rb emission arises from the fluorescence of Rb vapor in the EIT probe laser.