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Physical Review Applied

Restrictions of microwave electrometry due to nonlocal interactions in Rydberg atoms

Binbin Wang, Xiao-Jun Zhang, Jin‐Hui Wu

Published Aug 12, 2024• 3 citations
Publisher

Abstract

Large dipole moments between high Rydberg states have been utilized to measure microwave electric fields based on electromagnetically induced transparency, while nonlocal Rydberg interactions are not suitably addressed yet in most relevant works. Here we adopt a mean-field superatom model to investigate the main restrictions of Rydberg microwave electrometry due to nonlocal interactions in atomic samples of appropriate densities. It is found that accurate microwave measurements can be attained in the linear regime only for dilute enough atomic samples and not too strong probe fields, which jointly determine whether Rydberg excitations are insignificant. This then leads to the critical lines of atomic density and probe intensity, below which the discrepancy between measured and real values is negligible due to vanishing Rydberg interactions, for a fixed microwave or coupling field. Our findings are instructive to identify the optimal conditions for Rydberg microwave electrometry by reaching a compromise between high precisions and high accuracies, requiring, respectively, large and small numbers of Rydberg excitations, when measuring weaker microwave fields.

DOI
10.1103/physrevapplied.22.024034

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Large dipole moments between high Rydberg states have been utilized to measure microwave electric fields based on electromagnetically induced transparency, while nonlocal Rydberg interactions are not suitably addressed yet in most relevant works. Here we adopt a mean-field superatom model to investigate the main restrictions of Rydberg microwave electrometry due to nonlocal interactions in atomic samples of appropriate densities. It is found that accurate microwave measurements can be attained in the linear regime only for dilute enough atomic samples and not too strong probe fields, which jointly determine whether Rydberg excitations are insignificant. This then leads to the critical lines of atomic density and probe intensity, below which the discrepancy between measured and real values is negligible due to vanishing Rydberg interactions, for a fixed microwave or coupling field. Our findings are instructive to identify the optimal conditions for Rydberg microwave electrometry by reaching a compromise between high precisions and high accuracies, requiring, respectively, large and small numbers of Rydberg excitations, when measuring weaker microwave fields.
This study addresses the restrictions imposed by nonlocal van der Waals (vdW) and dipole-dipole (DD) interactions on the microwave electrometry in cold Rydberg atoms driven into the four-level cascade configuration with relatively high excitation densities. Utilizing the mean-field superatom model, we examine, in particular, the effects of vdW and DD interactions on microwave-controlled transmission spectra of a probe field in the regime of electromagnetically induced transparency (EIT). In response to spectral shifts depending on such Rydberg interactions, we propose a modified formula for correctly describing the nonlinear relationship between the microwave electric field and the splitting of two EIT peaks, which could enhance the measurement accuracy. This formula also extends the lower limit set by a certain measurement accuracy into the nonlinear response region by approximately five times, effectively mitigating the restrictions imposed by vdW and DD interactions. Our findings suggest that an accurate measurement of weak microwave electric fields could be achieved under both high and low-density conditions through data correction, yet without altering the experimental method. This research provides an alternative solution for microwave electrometry in weakly interacting atomic gases and highlights its potential applications in integrated quantum devices.
With the interaction among one optical probe field and pairs of standing microwaves in the configuration of Rydberg-dressed electromagnetically induced transparency, we study theoretically the sub-microwave wavelength localization of Rydberg superatoms in two and three dimensions. Composited by an ensemble of Rydberg atoms with strong dipole–dipole interactions, a superatom can be localized within the microwave wavelength through the position-dependent atom–field interaction. By measuring the absorption spectrum from the optical probe field, a single position of Rydberg superatoms with high precision can be obtained, depending on the probe field detuning and phase shifts associated with the standing microwaves.
Atoms form the basis of precise measurement for many quantities (time, acceleration, rotation, magnetic field, etc.). Measurements of microwave frequency electric fields by traditional methods (i.e. engineered antennas) have limited sensitivity and can be difficult to calibrate properly. Highly-excited (Rydberg) neutral atoms have very large electric-dipole moments and many dipole allowed transitions in the range of 1 - 500 GHz. It is possible to sensitively probe the electric field in this range using the combination of two quantum interference phenomena: electromagnetically induced transparency and the Autler-Townes effect. This technique allows for very sensitive field amplitude, polarization, and sub-wavelength imaging measurements. These quantities can be extracted by measuring properties of a probe laser beam as it passes through a warm rubidium vapor cell. Thus far, Rydberg microwave electrometry has relied upon the absorption of the probe laser. We report on our use of polarization rotation, which corresponds to the real part of the susceptibility, for measuring the properties of microwave frequency electric fields. Our simulations show that when a magnetic field is present and directed along the optical propagation direction a polarization rotation signal exists and can be used for microwave electrometry. One central advantage in using the polarization rotation signal rather than the absorption signal is that common mode laser noise is naturally eliminated leading to a potentially dramatic increase in signal-to-noise ratio.
Atom in Rydberg state has large polarizability, large electric dipole and low ionization threshold field. It is very sensitive to electric field, therefore it can be used to measure the amplitude of electric field, especially the microwave electric field. The new developed scheme is based on quantum interference effects (electromagnetically induced transparency and Autler-Townes splitting) in Rydberg atoms. Instead of the direct amplitude measurement, this method tests the Rabi frequency value of the transmission spectrum which is determined by the microwave electric field strength and the corresponding atom nature. The minimum measured strengths of microwave electric fields are far below the standard values obtained by traditional antenna methods. Compared with the traditional methods, this new scheme has several advantages, such as self-calibration, non-perturbation to the measured field and independence of the probe length. Besides, this scheme can also be used to measure the polarization direction of microwave electric field and realize sub-wavelength imaging. Through adjusting the wavelength of coupling laser, a broadband 1-500 GHz microwave electric field measurement can be achieved. This new scheme is benefitial to conducting the continue electric field measurement and the miniaturization of the test equipment. In this paper, the researches about using Rydberg atom to measure electric field with high precision are reviewed. The basic theory and experimental techniques are introduced. Finally, we discuss a promising method of using Rydberg atom interferometer to detect the accumulated phase in the process of interaction between electric field and Rydberg atoms. This method converts amplitude measurement into phase test, which may improve the precision and sensitivity.
Precision microwave electrometry using Rydberg atoms is limited by many-body interactions at moderate or not too low excitation densities, which may result in distorted probe spectra of electromagnetically induced transparency (EIT) as predicted by mean-field superatom simulations. This nonlinearity fundamentally restricts measurement accuracy and renders the linear response formula of Autler-Townes splitting to microwave (MW) amplitude inapplicable. Here we present a machine learning (ML) framework assisted by principal component analysis (PCA) that can well overcome this difficulty by mapping distorted noisy EIT spectra directly to MW electric fields. Numerical results show that a basic PCA-assisted regression model reduces the minimal detectable MW field by a few folds as compared to both linear response formula and nonlinear least squares fitting in the interaction-dominant regime. It is of more interest that we can employ a four-class ensemble ML scheme to further reduce the minimal detectable MW field by two orders of magnitude to approach its noise-dependent physical limit and hence largely improve the measurement sensitivity. Our work transforms detrimental Rydberg interactions into beneficial spectral features, providing a practical route toward optimal sensitivity for MW quantum sensing in the nonlinear regime. Rydberg atom-based microwave electrometry is hindered by many-body interactions, distorting probe spectra and limiting measurement accuracy. Here, the authors employ a machine learning framework with principal component analysis to map distorted spectra to microwave fields, significantly enhancing sensitivity and transforming interaction challenges into advantageous spectral features for quantum sensing.
The Rydberg atom-based microwave electric field sensor has high sensitivity for weak RF-field detection. Selection of Rydberg states with larger electric dipole moment is beneficial to enhance the sensitivity, and we choose Rydberg states with its principal quantum number up to n ∼ 80. We study the probe laser transmission response to a microwave field for these chosen high Rydberg states at room temperature. It agrees well with theoretical simulation based on an optical Bloch equation with considered microwave-atom interaction and Doppler broadening effect. In our experiment, the microwave sensing sensitivity based on 85 Rb transition | 78 S 1 / 2 ⟩ → | 78 P 3 / 2 ⟩ arrives at 5.102(49) nV cm − 1 Hz − 1 / 2 at 1 kHz.