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Optics Express

Theoretical analysis of an electrometer based on microwave-dressed Rydberg atoms using a quantum interferometer

Dong Zhang, Minwei Shi, Ding Huang, Yiquan Yang, Wei Du, Shuhe Wu, Guzhi Bao, Weiping Zhang

Published Jan 16, 2025• 2 citations
Publisher

Abstract

Rydberg atoms have demonstrated exceptional capabilities in the precise sensing microwave (MW) fields. Previous studies on Rydberg atom-based electrometers (RAEs) have predominantly focused on absorption measurements. Recently, phase-sensitive RAEs employing Mach-Zehnder interferometer (MZI) have been demonstrated, though their performance remains constrained by the standard quantum limit (SQL). In this study, we combine RAEs with advanced quantum interferometrics to enhance MW field sensing. Within the framework of electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting, the noise of our enhanced electrometer is suppressed below the photon shot noise (PSN) in measuring light dispersion through microwave-dressed atoms, when utilizing phase squeezed states. In our theory, the optimal sensitivity of the MW field can reach 1.36 × 10 −11 V/m/Hz 1/2 with a dressed MW field strength of 2.4 × 10 −4 V/m within a balanced SU(1,1) interferometer.

DOI
10.1364/oe.545812

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Rydberg atoms have demonstrated exceptional capabilities in the precise sensing microwave (MW) fields. Previous studies on Rydberg atom-based electrometers (RAEs) have predominantly focused on absorption measurements. Recently, phase-sensitive RAEs employing Mach-Zehnder interferometer (MZI) have been demonstrated, though their performance remains constrained by the standard quantum limit (SQL). In this study, we combine RAEs with advanced quantum interferometrics to enhance MW field sensing. Within the framework of electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting, the noise of our enhanced electrometer is suppressed below the photon shot noise (PSN) in measuring light dispersion through microwave-dressed atoms, when utilizing phase squeezed states. In our theory, the optimal sensitivity of the MW field can reach 1.36 × 10 −11 V/m/Hz 1/2 with a dressed MW field strength of 2.4 × 10 −4 V/m within a balanced SU(1,1) interferometer.
Rydberg atoms have shown remarkable performance in sensing microwave fields. The sensitivity of such an electrometer based on optical readout of the atomic ensemble has been demonstrated to approach the photon-shot-noise limit. However, the sensitivity cannot be promoted infinitely by increasing the power of the probe light due to the increased collision rates and power broadening. Compared with classical light, the use of quantum light may lead to a better sensitivity with a lower number of photons. In this paper, we exploit entanglement in a microwave-dressed Rydberg electrometer to suppress the fluctuation of noise. The results show a sensitivity enhancement that beats the shot-noise limit in both cold- and hot-atom schemes. Through optimizing the transmission of the optical readout, our quantum advantage can be maintained with differing absorptive indexes of the atomic vapor, which makes it possible to apply a quantum light source in the absorptive electrometer.
Rydberg atoms have been shown remarkable performance in sensing microwave field. The sensitivity of such an electrometer based on optical readout of atomic ensemble has been demonstrated to approach the photon-shot-noise limit. However, the sensitivity can not be promoted infinitely by increasing the power of probe light due to the increased collision rates and power broadening. Compared with classical light, the use of quantum light may lead to a better sensitivity with lower number of photons. In this paper, we exploit entanglement in a microwave-dressed Rydberg electrometer to suppress the fluctuation of noise. The results show a sensitivity enhancement beating the shot noise limit in both cold and hot atom schemes. Through optimizing the transmission of optical readout, our quantum advantage can be maintained with different absorptive index of atomic vapor, which makes it possible to apply quantum light source in the absorptive electrometer.
We have shown that Rydberg states can be used for high-sensitivity, absolute sensing of microwave (MW) electric fields. We achieved a sensitivity of 3 μVcm-1Hz-1/2 for two read-out strategies. Depending on the spectral resolution of the read-out, either the MW induced transmission line frequency splitting, the Autler-Townes regime, or a change in the on-resonant absorption, the amplitude regime, can be used to determine the MW electric field. Results using a Mach-Zehnder interferometer and frequency modulated spectroscopy both achieve similar photon shot noise limited sensitivity. In addition, we have also explored amplitude modulation and the displacement of a probe laser beam due to index of refraction changes in a prism shaped vapor cell. These latter methods were not able to achieve photon shot noise limited performance. Fundamental limits to the sensitivity of the Rydberg atom-based MW electric field sensing have been addressed, but it is important to clarify the differences between noise in different parts or subsystems of the sensor. Shot noise in the probe laser usually dominates the projection noise of the atoms participating in the measurement of the MW electric field because of the desire to operate at low effective Rydberg atom densities in order to avoid collisional dephasing and ionization.
We have shown that Rydberg atoms can be used for high-sensitivity, absolute sensing of radio frequency (RF) electric fields. We achieved a sensitivity of 3 μVcm-1Hz-1/2 for two read-out strategies. Results using a Mach-Zehnder interferometer2 and frequency modulated spectroscopy both achieve similar photon shot noise limited sensitivity. Fundamental limits to the sensitivity of the Rydberg atom-based RF electric field sensing have been addressed. Depending on the spectral resolution of the read-out, either the RF induced transmission line frequency splitting, the Autler-Townes regime, or a change in the on-resonant absorption, the amplitude regime, can be used to determine the RF electric field. Here, we present theoretical results of a 3-photon read-out scheme which enables the Autler-Townes regime of Rydberg atom-based RF electrometry to be extended to lower RF electric field strengths. We show that the residual Doppler shifts can, in principle, be reduced to ~11.8 kHz, on the order of the Rydberg atom natural lindewidths, using the approach.
We demonstrate the use of an auxiliary microwave field to extend the bandwidth sensitivity of Rydberg-atom-based microwave electrometry. Electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting in Rydberg atom microwave electrometry provide advantageous sensitivity for the resonant detection of microwave (MW) fields because the Stark shift of the target Rydberg state takes the linear form of AT splitting. However, the sensitivity is reduced by several orders of magnitude for detuned MW fields because the Stark shift of the target Rydberg state depends on a weak nonlinear effect. We show that the auxiliary microwave field with appropriate Rabi frequency or detuning could shift the atomic energy levels to bring a particular Rydberg-Rydberg transition of interest for microwave sensing into resonance with the target microwave field. Using the atomic superheterodyne method, we verified the general method that regulates Rydberg energy levels using an auxiliary microwave field. The experimental results of this study confirm that this technique works efficiently for detecting microwave fields detuned by up to 100 MHz from resonance with the field-free Rydberg-Rydberg transition used for sensing. The measurement sensitivity of the detuned target field is increased by a factor of 10 compared with that achieved without the application of the auxiliary dressing field.
The Rydberg-based microwave detection is an all-optical technology that uses the strong coherent interaction between Rydberg atoms and microwave field. Different from the traditional microwave meter, the Rydberg atomic sensing is a new-type microwave detector that transforms the microwave spectrum into a coherent optical spectrum, and arouses increasingly the interests due to its high sensibility. For this kind of sensor, the coherence effect induced by coupling atoms with microwave plays a key role, and the decoherence may reduce the sensitivity. A multi-level Rydberg atomic scheme with optimized quantum coherence, which enhances both the bandwidth and the sensitivity for 4 GHz microwave sensing, is demonstrated experimentally in this work. The enhanced quantum coherence of Rydberg electromagnetically induced transparency (EIT) and microwave induced Autler-Townes (AT) splitting in EIT windows are shown using optical pumping at D1 line. The enhanced sensitivity at 3.4 GHz with 0.3 GHz bandwidth can be realized, based on the enhanced EIT-AT spectrum. The experimental results show that in the stepped Rydberg EIT system, the spectral width of EIT and microwave field EIT-AT can be narrowed by optical pumping (OP), so the sensitivity of microwave electric field measurement can be improved. After optimizing the EIT amplitude and adding single-frequency microwaves, the sensitivity of the microwave electric field measurement observed by the AT splitting interval is improved by 1.3 times. This work provides a reference for utilizing atomic microwave detection.