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Applied Optics

Sensitive detection of radio-frequency field phase with interacting dark states in Rydberg atoms

Lidan Lin, Yuan He, Zheng Yin, Dehua Li, Zhengmao Jia, Yuefeng Zhao, Bing Chen, Yandong Peng

Published Jan 18, 2022• 5 citations
Publisher

Abstract

An efficient scheme of phase measurement of a radio-frequency (RF) field is proposed by interacting dark states. Under the condition of electromagnetically induced transparency (EIT), the four-level Rydberg atom exhibits two windows. Compared with the transmission spectrum on resonance, the linewidths of absorption peaks off resonance are very narrow due to the interaction of double dark states. It is interesting to find that the distance of absorption peaks shifts approximately linearly with the phase of an RF field, which can be used to measure the RF field phase. Simulation results show that the linewidth of an absorption peak can be narrowed by more than one order of magnitude, and a narrow linewidth improves the detectable minimum phase difference by more than six times. It helps to reduce analyzation complexity and increase sensing resilience. The dependence of phase measurement on the control field and RF field is also investigated.

DOI
10.1364/ao.449918

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An efficient scheme of phase measurement of a radio-frequency (RF) field is proposed by interacting dark states. Under the condition of electromagnetically induced transparency (EIT), the four-level Rydberg atom exhibits two windows. Compared with the transmission spectrum on resonance, the linewidths of absorption peaks off resonance are very narrow due to the interaction of double dark states. It is interesting to find that the distance of absorption peaks shifts approximately linearly with the phase of an RF field, which can be used to measure the RF field phase. Simulation results show that the linewidth of an absorption peak can be narrowed by more than one order of magnitude, and a narrow linewidth improves the detectable minimum phase difference by more than six times. It helps to reduce analyzation complexity and increase sensing resilience. The dependence of phase measurement on the control field and RF field is also investigated.
Abstract A scheme for measuring microwave (MW) electric (E) fields is proposed based on bichromatic electromagnetically induced transparency (EIT) in Rydberg atoms. A bichromatic control field drives the excited state transition, whose absorption shows three EIT windows. When a MW field drives the Rydberg transition, the EIT windows split and six transmission peaks appear. It is interesting to find that the peak-to-peak distance of transmission spectrum is sensitive to the MW field strength, which can be used to measure MW E-field. Simulation results show that the measurement accuracy could be increased by about 4 times, and the minimum detectable strength of the MW E-field may be improved by about 3 times compared with the common EIT scheme. After the Doppler averaging, the minimum detectable MW E-field strength is about 5 times larger than that without Doppler effect. Also, we investigate other effects on the sensitivity of the system.
We demonstrate the use of multiple atomic-level Rydberg-atom schemes for continuous frequency detection of radio-frequency (RF) fields. Resonant detection of RF fields by electromagnetically induced transparency and Autler-Townes (AT) splitting in Rydberg atoms is typically limited to frequencies within the narrow bandwidth of a Rydberg transition. By applying a second field resonant with an adjacent Rydberg transition, far-detuned fields can be detected through a two-photon resonance AT splitting. This two-photon AT splitting method is several orders of magnitude more sensitive than off-resonant detection using the Stark shift. We present the results of various experimental configurations and a theoretical analysis to illustrate the effectiveness of this multiple level scheme. These results show that this approach allows for the detection of frequencies in a continuous band between resonances with adjacent Rydberg states.
An enhanced measurement of the microwave electric (MW E) field by using intracavity Rydberg atoms is proposed. Based on electromagnetically induced transparency (EIT), the intracavity atomic system exhibits two EIT windows, resulting in two narrow peaks in the cavity transmission. The peak-to-peak distance is sensitive to MW fields and can be used to probe MW E-field strength. Simulation results show that the detectable minimum strength of the MW fields is nearly eight times smaller than that without a cavity. Due to cavity coupling, the transmission spectrum is greatly narrowed, which improves the measurement resolution substantially. The numerical results show that the spectrum resolution is increased by more than 20 times. Furthermore, the cavity-enhanced measurement scheme seems to be robust against the changes in the control field strength and shows a broadband tunability.
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.
The large electric dipole moment of the Rydberg atom allows for strong coupling with weak electric fields, and is widely used in electric field measurements because of its reproducibility, precision and stability. The combination of Rydberg atoms and electromagnetically induced transparency (EIT) technology has been used for detecting and characterizing radio-frequency (RF) electric fields. In this work, by selecting probe light (852 nm), dressed light (1470 nm), and coupled light (780 nm), the Rydberg state (49P3/2) of Cs atom is prepared by using a three-photon excitation scheme through using all-infrared light excitation of Rydberg atoms. We experimentally observe the EIT spectra of the Rydberg states decorated by radio-frequency electric fields, which optically detects Rydberg atoms. The effect of the amplitude and frequency of the RF electric field on the spectrum is explored in light of changes in the EIT spectrum. The results show that in the region of weak electric field, only the ac Stark energy shift and spectral broadening occur. As the electric field is further enhanced, the sideband phenomenon occurs in both the primary peak and secondary peak of the EIT. In the region of strong field, the Rydberg energy level produces a series of Floquet states with higher-order terms, as well as state shifting and mixing, resulting in asymmetry in the spectra of the EIT sideband peaks. The effect of frequency on the shielding effect of the Cs vapor cell is further discussed based on the shift of the main peak of the EIT. The demodulation of the electric field in a range of 50 Hz–1 kHz with a fidelity of 95% is achieved by modulating the low-frequency electric field to the RF electric field. The results can provide valuable references for spectral detection and traceable measurements of low-frequency electric fields.
The radio-frequency modulated electromagnetically induced transparency (EIT) in a ladder three-level system with Rydberg state is studied. Under the influence of a fast radio-frequency field, the EIT peak splits into a series of sidebands. When attaching a power-frequency electric field directly to the fast radio-frequency field, the odd-order sidebands of the Rydberg-EIT oscillate sensitively with the power-frequency field. The oscillation frequency is equal to twice the power frequency; the oscillation amplitude is monotonically increasing with the amplitude of the power-frequency field when the change of Stark-shift is smaller than the radio frequency. Our work paves the way for measurement of power-frequency electric field based on Rydberg atoms.