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Applied Optics

Two-dimensional microwave electric field gradient imaging using a MEMS cesium vapor cell

Rui Zhao, Junxian Ren, ZHONGHAO Li, Shuai Liu, Yunbo Shi, Zongmin Ma, Jun Tang, Jun Liu

Published Apr 27, 2026• 0 citations
Publisher

Abstract

Two-dimensional imaging of microwave electric field gradients was performed using a MEMS cesium vapor cell based on Rydberg atoms. The variations in probe laser fluorescence intensity, continuously monitored via high-sensitivity CCD imaging at 24.038 GHz, enabled detailed analysis of electromagnetically induced transparency (EIT) and Autler–Townes (AT) splitting effects. By establishing the quantitative relation between the splitting interval (Δ f ) and the electric field intensity, spatial electric field gradient distributions were accurately measured. The experimental results demonstrated a minimum detectable electric field strength of 1.22 V/m and a spatial resolution of 151.2 µm, with the measurement error in electric field strength maintained below 2%.

DOI
10.1364/ao.586993

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Two-dimensional imaging of microwave electric field gradients was performed using a MEMS cesium vapor cell based on Rydberg atoms. The variations in probe laser fluorescence intensity, continuously monitored via high-sensitivity CCD imaging at 24.038 GHz, enabled detailed analysis of electromagnetically induced transparency (EIT) and Autler–Townes (AT) splitting effects. By establishing the quantitative relation between the splitting interval (Δ f ) and the electric field intensity, spatial electric field gradient distributions were accurately measured. The experimental results demonstrated a minimum detectable electric field strength of 1.22 V/m and a spatial resolution of 151.2 µm, with the measurement error in electric field strength maintained below 2%.
In this letter, we demonstrate an approach for the measurement of microwave electric field intensity based on Rydberg electromagnetically induced transparency (EIT)– Autler Townes (AT) splitting effect using a cesium vapor MEMS cell. The atomic absorption characteristics at different pump powers were obtained experimentally, which proved the feasibility of fabricated cesium vapor MEMS cell. The dependence of EIT-AT splitting separations on the microwave electric field intensities at 23.887 GHz was investigated at room temperature, and the minimum microwave electric field was measured to be 2 V/m. This approach indicates that the prepared cesium vapor MEMS cell can be qualified for microwave electric field intensity measurement, and has tremendous potential for the development of integrating quantum microwave field intensity meters.
We demonstrate the high-resolution spatial feature measurement of microwave electric field using an cesium atomic vapor cell based on the electromagnetically induced transparency (EIT) spectrum of133Cs Rydberg atom. The microwave electric field with the frequency of 6.95 GHz couples the transition of 47D5/2→48P3/2 Rydberg states. The EIT spectrum of a 6S1/2-6P3/2-47D5/2 ladder system will split by the Autler-Townes(AT) effect under the microwave electric field. The dependence of AT splitting separation on the microwave electric fields strength is observed. Moreover, we present the imaging of the spatial feature of microwave electric field in the atomic vapor cell. The theoretical maximum spatial resolution is about λMw/430.
The geometry effect of a vapor cell on the metrology of a microwave electric field is investigated. Based on the splitting of the electromagnetically induced transparency spectra of cesium Rydberg atoms in a vapor cell, high-resolution spatial distribution of the microwave electric field strength is achieved for both a cubic cell and a cylinder cell. The spatial distribution of the microwave field strength in two dimensions is measured with sub-wavelength resolution. The experimental results show that the shape of a vapor cell has a significant influence on the abnormal spatial distribution because of the Fabry–Pérot effect inside a vapor cell. A theoretical simulation is obtained for different vapor cell wall thicknesses and shows that a restricted wall thickness results in a measurement fluctuation smaller than 3% at the center of the vapor cell.
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.
We have recently shown [Nat. Phys.8, 819 (2012)] that Alkali atoms contained in a vapor cell can serve as a highly accurate standard for microwave (MW) electric field strength as well as polarization. Here we show for the first time that Rydberg atom electromagnetically induced transparency can be used to image MW electric fields with unprecedented precision. The spatial resolution of the method is far into the subwavelength regime ∼λ/650 or 66 μm at 6.9 GHz. The electric field resolutions are similar to those we have already demonstrated ∼50 μV cm(-1). Our experimental results agree with finite element calculations of test electric-field patterns.
We have theoretically and experimentally studied the dispersive signal of the Rydberg atomic electromagnetically-induced transparency (EIT) Autler–Townes (AT) splitting spectra obtained using amplitude modulation of the microwave (MW) electric field. In addition to the two zero-crossing points interval Δf zeros, the dispersion signal has two positive maxima with an interval defined as the shoulder interval Δf sho, which is theoretically expected to be used to measure a much weaker MW electric field. The relationship of the MW field strength E MW and Δf sho is experimentally studied at the MW frequencies of 31.6 GHz and 9.2 GHz respectively. The results show that Δf sho can be used to characterize the much weaker E MW than that of Δf zeros and the traditional EIT–AT splitting interval Δf m; the minimum E MW measured by Δf sho is about 30 times smaller than that by Δf m. As an example, the minimum E MW at 9.2 GHz that can be characterized by Δf sho is 0.056 mV/cm, which is the minimum value characterized by the frequency interval using a vapor cell without adding any auxiliary fields. The proposed method can improve the weak limit and sensitivity of E MW measured by the spectral frequency interval, which is important in the direct measurement of weak E MW.