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Applied Physics Letters

Kilohertz-range electric field calibration in an alkali vapor cell using time-averaged Stark shifts

M. J. Lim, Marc Cervantes, Cameron Brady, Shawn McPoyle, John Simmermon

Published Jul 31, 2023• 12 citations
Publisher

Abstract

We present a model-independent experimental method for calibrating the amplitude of a low-frequency electric field in an alkali vapor cell. Three-photon excitation to a Rydberg state in atomic rubidium produces an electromagnetically induced transparency (EIT) signal that is sensitive to low-frequency fields originating outside the cell. We superpose the measured shape of the EIT resonance in the presence of an electric field with the expected line shape, obtained by numerically time-averaging the effect of the DC-Stark shift. The value of the fractional field amplitude transmission, caused by Faraday screening by the metallic rubidium layer on the cell interior, is a direct result of this comparison. A transmission spectrum is obtained by making measurements between 0 and 100 kHz, which demonstrates high-pass filtering behavior described by two cutoff frequencies. Independently, finite-element simulation provides supporting evidence of the accuracy of the measurement, which is responsive to the nonuniform alkali distribution on the vapor cell wall. In combination with recent advances in the sensitivity of low-frequency electrometry, this may improve absolute, free-space measurements of weak, low-frequency electric fields that are of interest in basic and applied research.

DOI
10.1063/5.0153752

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We present a model-independent experimental method for calibrating the amplitude of a low-frequency electric field in an alkali vapor cell. Three-photon excitation to a Rydberg state in atomic rubidium produces an electromagnetically induced transparency (EIT) signal that is sensitive to low-frequency fields originating outside the cell. We superpose the measured shape of the EIT resonance in the presence of an electric field with the expected line shape, obtained by numerically time-averaging the effect of the DC-Stark shift. The value of the fractional field amplitude transmission, caused by Faraday screening by the metallic rubidium layer on the cell interior, is a direct result of this comparison. A transmission spectrum is obtained by making measurements between 0 and 100 kHz, which demonstrates high-pass filtering behavior described by two cutoff frequencies. Independently, finite-element simulation provides supporting evidence of the accuracy of the measurement, which is responsive to the nonuniform alkali distribution on the vapor cell wall. In combination with recent advances in the sensitivity of low-frequency electrometry, this may improve absolute, free-space measurements of weak, low-frequency electric fields that are of interest in basic and applied research.
Rydberg-assisted atomic electrometry using alkali-metal atoms contained inside a vacuum environment for detecting external electric fields at frequencies below a few kilohertz has been quite challenging due to the low-frequency electric-field-screening effect that is caused by the alkali-metal atoms adsorbed on the inner surface of the container. We report a very slow electric-field-screening phenomenon with a time scale up to the order of seconds on a rubidium-vapor cell that is made of monocrystalline sapphire. Using this sapphire rubidium-vapor cell with an optically induced, internal bias electric field, we demonstrate vapor-cell-based, low-frequency atomic electrometry that responds to the electric field strength linearly. Limited by the given experimental conditions, this demonstrated atomic electrometer uses an active volume of 11mm311\phantom{\rule{0.2em}{0ex}}{\mathrm{mm}}^{3}11mm3 and delivers a spectral noise floor of around 0.34mV/mHz0.34\phantom{\rule{0.2em}{0ex}}\mathrm{mV}/\mathrm{m}\phantom{\rule{0.1em}{0ex}}\sqrt{\mathrm{Hz}}0.34mV/mHz​ and a 3-dB low cutoff frequency of around 770 Hz inside the vapor cell. This work investigates a regime of vapor-cell-based atomic electrometry that was seldom studied before, which may enable more applications that use atomic electric-field-sensing technology.
The high polarizability of Rydberg atoms enables the multi-parameters measurement of electromagnetic fields. In this paper, we report on an atomic antenna based on Rydberg atoms in a room temperature vapor cell. The EIT is a destructive interference spectroscopy with a narrow linewidth and can be used to detect small electric fields through Autler-Townes splitting or Stark shifts. In our experiments, we employ cascade-type two-photon excitation electromagnetically induced transparency (EIT) spectroscopy to measure the shift of the Rydberg energy level. We introduce a low-frequency electric field (~kHz frequency) using a built-in electrode technique in the cesium cell. The interaction between the Rydberg atom and electric field induces the Stark shifts, where the amplitude of the electric field is converted into corresponding two-photon detuning by the EIT effect. Furthermore, the amplitude of the low-frequency electric field is converted into an intensity signal of EIT probe beam. Under weak field conditions, it is an approximate linear relationship between EIT transmission signal and input electric field amplitude, enabling measurement of waveform, amplitude, and frequency. We have demonstrated optical measurements of low-frequency electric field using Rydberg atoms. By increasing the power of probe beam and coupling beam, the EIT can increase the response bandwidth from ~MHz to hundreds of MHz. This provides a scalable approach for measuring high-frequency electric fields.
Significant progress has been made in atom-based measurements of length, time, gravity and electromagnetic fields in recently years. Rydberg atom-based microwave electric field measurement, using electromagnetically induced transparency (EIT) in room temperature alkali-metal vapors, has been extensively investigated and aroused the broad interest. This approach may establish a new standard for the measurements of microwave (MW) and radio frequency (RF) electric fields.In this review, we describe the work on a new method of measuring electric fields based on quantum interference by using either cesium or rubidium atoms contained in a dielectric vapor cell. Rydberg atoms with principal quantum number n >>1 have large direct current (DC) polarizabilities and microwave transition dipole moments, thereby making them extremely sensitive to external electric fields. Using the Rydberg three-level EIT to detect the level splitting and shift that is induced by the external field, we can realize a rapid and robust self-calibration method of measuring the electric field in a frequency range from 0.01 GHz to 1000 GHz. For the MW electric field (frequency range > 1 GHz), the MW field causes the Rydberg states to split, known as an Autler-Townes splitting (A-T) effect when the applied microwave can resonate with adjacent Rydberg states. The MW coupled A-T splitting is proportional to the applied electric field strength, from which the field strength is measured. Using the EIT window, a high sensitivity of 3 μV·cm-1·Hz-1/2 and small electric field of 1 μV/cm are expected to be achieved with a modest setup, and the limitations of the sensitivity are also addressed in the review. For the RF field at frequency mj EIT lines, and avoided crossings formed with the fine-structure levels of equal mj and different J's, which is used to calibrate and measure the RF field amplitude. On the other hand, the dependence of the EIT-line strength on the RF field polarization provides a fast and robust polarization measurement of RF fields based on matching experimental data with a theoretical simulation. The measurements of minimum strengths and sensitivity of RF fields based on Rydberg atoms are one order magnitude below the values obtained by traditional antenna methods. The atom-based field measurement paves the way for determining fields through calibration-free, invariable atomic properties and miniaturization. We also propose its various potential applications in the future.
Rydberg-assisted atomic electrometry with thermal vapors offers a promising approach for detecting external electric fields. However, this technique presents significant challenges for measuring low frequencies due to the effects of metal-alkali atoms adsorbed on the interior surface of the vacuum chamber. In this work, we apply high-contrast Rydberg electromagnetically induced transparency (EIT) spectroscopy to systematically investigate these effects, including the influence of laser power and electric field strength. We demonstrate the ability to measure electric field frequencies ranging from 10 Hz to 1 MHz. Additionally, this study identifies a fundamental limit for data capacity in such measurements. Furthermore, we propose a method for precise Stark shift measurements by locking the coupling laser to Zeeman-split Rydberg EIT peaks. Using the Zeeman shift in a reference cell as a stable frequency reference, we are able to track Stark-induced shifts in a science cell and confirm excellent agreement with theoretical predictions. These results provide valuable insights for future precision measurement techniques and field sensing applications based on Rydberg atom systems.
We demonstrate the measurement of super low-frequency electric field using Rydberg atoms in an atomic vapor cell with inside parallel electrodes, thus overcoming the low-frequency electric-field-screening effect at frequencies below a few kHz. Rydberg electromagnetically induced transparency (EIT) spectra involving 52 D 5/2 state is employed to measure the signal electric field. An auxiliary DC field is applied to improve the sensitivity. A DC Stark map is demonstrated, where the utilized 52 D 5/2 exhibits m j = 1/2, 3/2, 5/2 Stark shifts and splittings. The m j = 1/2 state is employed to detect the signal field because of its larger polarizability than that of m j = 3/2, 5/2. Also, we show that the strength of the spectrum is dependent on the angle between the laser polarizations and the electric field. With optimization of the applied DC field to shift the m j = 1/2 Rydberg energy level to a high sensitivity region and the laser polarizations to obtain the maximum m j = 1/2 signal, we achieve the detection of the signal electric field with a frequency of 100 Hz down to 214.8 µ V/cm with a sensitivity of 67.9 µ V cm −1 Hz −1/2 , and the linear dynamic range is over 37 dB. Our work extends the measurement frequency of Rydberg sensors to super low frequency with high sensitivity, which has the advantages of high sensitivity and miniaturization for receiving super low frequency.
We report on the measurement of Stark shifted energy levels of 87 Rb Rydberg atoms in static electric fields by means of electromagnetically induced transparency (EIT). Electric field strengths of up to 500 V cm −1 , ranging beyond the classical ionization threshold, were applied using electrodes inside a glass cell with rubidium vapour. Stark maps for principal quantum numbers n = 35 and n = 70 have been obtained with high signal-to-noise ratio for comparison with results from ab initio calculations following the method described in (Zimmerman et al 1979 Phys. Rev. A 20 2251 ), which was originally only verified for states around n = 15. We also calculate the dipole matrix elements between low-lying states and Stark shifted Rydberg states to give a theoretical estimate of the relative strength of the EIT signal. The present work significantly extends the experimental verification of this numerical method in the range of both high principal quantum numbers and high electric fields with an accuracy of up to 2 MHz.