Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2501.10989 · Physical Review Applied

Phase-sensitive Rydberg-atom interferometry with Floquet electromagnetically induced transparency

Yingying Han, Chun He, Peng Xu, Yanting Zhao, Tao Wang, Weidong Li

Published Jul 30, 2025• 2 citations
arXivHTMLPDF

Abstract

We design phase-sensitive Rydberg-atom interferometry by implementing Floquet electromagnetically induced transparency (FEIT). The FEIT mixes the sidebands of a Rydberg state induced by a megahertz radio frequency (rf) field and recombines them into FEIT bands. The FEIT bands act as screens to present the interference between paths with different phases, which are transitions between the sidebands and excited states. This interferometry can measure the phase of a megahertz rf field without a local rf reference field. A phase reference is supplied to the atoms via a periodic electrical signal in the FEIT. We demonstrate that the megahertz rf phase can be resolved over the full $2\ensuremath{\pi}$ range with a theoretical accuracy of ${10}^{\ensuremath{-}4}$ rad. Moreover, the rf amplitude can also be resolved with higher accuracy than with the traditional EIT-based scheme.

DOI
10.1103/2crh-5yvr

Related papers

Atomic measurements of high-intensity VHF-band radio-frequency fields with a Rydberg vapor-cell detector

Éric Paradis, Georg A. Raithel, David Alexander Anderson

We investigate and employ optical Rydberg resonances in an atomic vapor cell for measurements of high-intensity VHF-band radio frequency (rf) electric fields. An atomic vapor cell with integrated electrodes is used to generate high-intensity 50--500 MHz rf electric fields reaching $\ensuremath{\sim}5$ kV/m in a submillimeter gap. The fields are measured using Rydberg electromagnetically induced transparency as an optical readout of field-sensitive $30{D}_{J}$ and $35{D}_{J}$ Rydberg states of atoms within the gap. The rf electric field is determined by matching observed spectroscopic markers, including ac level shifts, even-harmonic rf sidebands, and rf-induced avoided crossings in the Rydberg manifold to calculated spectra derived from a nonperturbative Floquet theory. In our measurements, rf field frequencies and electric-field amplitudes are determined to an accuracy of $1.0%$ and $1.5%$, respectively. In the atom-field interaction, we observe a transition from a quantum regime, characterized by discrete even-harmonic Floquet states separated by an even multiple of the rf field frequency, into a semiclassical regime at very strong fields, in which the spectrum exhibits unresolved resonances whose strengths are smoothly modulated at a frequency of approximately five times the rf frequency. The underlying physics is explored.

Physical Review A•Jul 30, 2019•59 citations

Optical Radio-Frequency Phase Measurement With an Internal-State Rydberg Atom Interferometer

David Alexander Anderson, Rachel Sapiro, Luís F. Gonçalves +2 more

We realize and model an internal-state Rydberg atom interferometer for measurement of phase and intensity of radio-frequency (rf) electromagnetic waves. A phase reference is supplied to the atoms via a modulated laser beam, enabling atomic measurement of the rf wave's phase without a rf reference wave. The rf and optical fields give rise to closed interferometric loops within the atoms' internal Hilbert space. In our experiment, we construct interferometric loops in the state space ${6{P}_{3/2},90{S}_{1/2},91{S}_{1/2},90{P}_{3/2}}$ of cesium and employ them to measure phase and intensity of a 5-GHz rf wave in a room-temperature vapor cell. Electromagnetically induced transparency on the $6{S}_{1/2}$ to $6{P}_{3/2}$ transition serves as an all-optical interferometer probe. The rf phase is measured over a range of $\ensuremath{\pi}$, and a sensitivity of 2 mrad is achieved. Measurements of rf phase and amplitude at submillimeter optical spatial resolution are demonstrated.

arXiv:2010.13657•Physical Review Applied•Apr 11, 2022•49 citations

Closed-loop quantum interferometry for phase-resolved Rydberg-atom field sensing

Samuel Berweger, Alexandra B. Artusio‐Glimpse, Andrew P. Rotunno +5 more

Although Rydberg-atom-based electric field sensing provides key advantages over traditional antenna-based detection, it remains limited by the need for a local oscillator (LO) for low-field and phase-resolved detection. In this work, we demonstrate that closed-loop quantum interferometric schemes can be used to generate a system-internal reference that can directly replace an external LO for Rydberg field sensing. We reveal that this quantum interferometrically defined internal reference phase and frequency can be used analogously to a traditional LO for atom-based down-mixing to an intermediate frequency for lock-in phase detection. We demonstrate that this LO-equivalent functionality provides analogous benefits to an LO, including full ${360}^{\ensuremath{\circ}}$ phase resolution as well as improved sensitivity. The general applicability of this approach is confirmed by demodulating a four-phase-state signal broadcast on the atoms. Our approach may open up new sensing schemes and although the present implementation still uses an auxiliary rf field, we provide a clear path toward all-optical Rydberg-atom sensing implementations by discussing several schemes that allow for all-optical rf phase detection without the need for an external rf LO field.

Physical Review Applied•Nov 3, 2023•25 citations

Spectroscopy of cesium Rydberg atoms in strong radio-frequency fields

Yuechun Jiao, Xiaoxuan Han, Zhiwei Yang +4 more

We study Rydberg atoms modulated by strong radio-frequency (rf) fields with a frequency of 70 MHz. The Rydberg atoms are prepared in a room-temperature cesium cell, and their level structure is probed using electromagnetically induced transparency (EIT). As the rf field increases from the weak- into the strong-field regime, the range of observed rf-induced phenomena progresses from ac level shifts through increasingly pronounced and numerous rf modulation sidebands to complex state mixing and level crossings with $\mathrm{high}\ensuremath{-}l$ hydrogenlike states. Weak anharmonic admixtures in the rf field generate clearly visible modifications in the Rydberg EIT spectra. A Floquet analysis is employed to model the Rydberg spectra, and good agreement with the experimental observations is found. Our results show that all-optical spectroscopy of Rydberg atoms in vapor cells can serve as an antenna-free, atom-based, and calibration-free technique to measure rf electric fields and to analyze their higher-harmonic contents.

arXiv:1601.01748•Physical Review A•Aug 17, 2016•58 citations

Highly Sensitive Measurement of a Megahertz rf Electric Field with a Rydberg-Atom Sensor

Bang Liu, Lihua Zhang, Zong-Kai Liu +6 more

Rydberg atoms have great potential in electric field measurement and have an advantage with a large frequency bandwidth from the kHz to the THz scale. However, the sensitivity for measuring a weak MHz electric field signal is limited by the spectroscopic resolution, because the weak electric field induces only a small perturbation of the population and energy-level shift of the Rydberg atoms. Here, we report highly sensitive measurement of a weak MHz electric field using electromagnetically induced transparency with Rydberg atoms in a thermal atomic system. Using the heterodyne method on a 30-MHz electric field, we successfully measure the minimum electric field strength to be $37.3\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{V}/\mathrm{cm}$ with a sensitivity up to $\ensuremath{-}65$ dBm/Hz and a linear dynamic range over 65 dB. Additionally, we measure an amplitude-modulated signal and demodulate the signal with a fidelity over 98%. This work extends the sensitivity of atomic sensors for measuring MHz electric fields, which advances atomic electric field-sensing technology.

arXiv:2206.06576•Physical Review Applied•Jul 19, 2022•106 citations

Electromagnetically induced transparency spectra of cesium Rydberg atoms decorated by radio-frequency fields

Yulong Han, Bang Liu, Kan Zhang +3 more

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.

Acta Physica Sinica•Jan 1, 2024•1 citation
We design phase-sensitive Rydberg-atom interferometry by implementing Floquet electromagnetically induced transparency (FEIT). The FEIT mixes the sidebands of a Rydberg state induced by a megahertz radio frequency (rf) field and recombines them into FEIT bands. The FEIT bands act as screens to present the interference between paths with different phases, which are transitions between the sidebands and excited states. This interferometry can measure the phase of a megahertz rf field without a local rf reference field. A phase reference is supplied to the atoms via a periodic electrical signal in the FEIT. We demonstrate that the megahertz rf phase can be resolved over the full 2\ensuremathπ2\ensuremath{\pi}2\ensuremathπ range with a theoretical accuracy of 10\ensuremath−4{10}^{\ensuremath{-}4}10\ensuremath−4 rad. Moreover, the rf amplitude can also be resolved with higher accuracy than with the traditional EIT-based scheme.
We investigate and employ optical Rydberg resonances in an atomic vapor cell for measurements of high-intensity VHF-band radio frequency (rf) electric fields. An atomic vapor cell with integrated electrodes is used to generate high-intensity 50--500 MHz rf electric fields reaching $\ensuremath{\sim}5$ kV/m in a submillimeter gap. The fields are measured using Rydberg electromagnetically induced transparency as an optical readout of field-sensitive 30DJ30{D}_{J}30DJ​ and 35DJ35{D}_{J}35DJ​ Rydberg states of atoms within the gap. The rf electric field is determined by matching observed spectroscopic markers, including ac level shifts, even-harmonic rf sidebands, and rf-induced avoided crossings in the Rydberg manifold to calculated spectra derived from a nonperturbative Floquet theory. In our measurements, rf field frequencies and electric-field amplitudes are determined to an accuracy of 1.01.0%1.0 and 1.51.5%1.5, respectively. In the atom-field interaction, we observe a transition from a quantum regime, characterized by discrete even-harmonic Floquet states separated by an even multiple of the rf field frequency, into a semiclassical regime at very strong fields, in which the spectrum exhibits unresolved resonances whose strengths are smoothly modulated at a frequency of approximately five times the rf frequency. The underlying physics is explored.
We realize and model an internal-state Rydberg atom interferometer for measurement of phase and intensity of radio-frequency (rf) electromagnetic waves. A phase reference is supplied to the atoms via a modulated laser beam, enabling atomic measurement of the rf wave's phase without a rf reference wave. The rf and optical fields give rise to closed interferometric loops within the atoms' internal Hilbert space. In our experiment, we construct interferometric loops in the state space 6P3/2,90S1/2,91S1/2,90P3/2{6{P}_{3/2},90{S}_{1/2},91{S}_{1/2},90{P}_{3/2}}6P3/2​,90S1/2​,91S1/2​,90P3/2​ of cesium and employ them to measure phase and intensity of a 5-GHz rf wave in a room-temperature vapor cell. Electromagnetically induced transparency on the 6S1/26{S}_{1/2}6S1/2​ to 6P3/26{P}_{3/2}6P3/2​ transition serves as an all-optical interferometer probe. The rf phase is measured over a range of $\ensuremath{\pi}$, and a sensitivity of 2 mrad is achieved. Measurements of rf phase and amplitude at submillimeter optical spatial resolution are demonstrated.
Although Rydberg-atom-based electric field sensing provides key advantages over traditional antenna-based detection, it remains limited by the need for a local oscillator (LO) for low-field and phase-resolved detection. In this work, we demonstrate that closed-loop quantum interferometric schemes can be used to generate a system-internal reference that can directly replace an external LO for Rydberg field sensing. We reveal that this quantum interferometrically defined internal reference phase and frequency can be used analogously to a traditional LO for atom-based down-mixing to an intermediate frequency for lock-in phase detection. We demonstrate that this LO-equivalent functionality provides analogous benefits to an LO, including full ${360}^{\ensuremath{\circ}}$ phase resolution as well as improved sensitivity. The general applicability of this approach is confirmed by demodulating a four-phase-state signal broadcast on the atoms. Our approach may open up new sensing schemes and although the present implementation still uses an auxiliary rf field, we provide a clear path toward all-optical Rydberg-atom sensing implementations by discussing several schemes that allow for all-optical rf phase detection without the need for an external rf LO field.
We study Rydberg atoms modulated by strong radio-frequency (rf) fields with a frequency of 70 MHz. The Rydberg atoms are prepared in a room-temperature cesium cell, and their level structure is probed using electromagnetically induced transparency (EIT). As the rf field increases from the weak- into the strong-field regime, the range of observed rf-induced phenomena progresses from ac level shifts through increasingly pronounced and numerous rf modulation sidebands to complex state mixing and level crossings with $\mathrm{high}\ensuremath{-}l$ hydrogenlike states. Weak anharmonic admixtures in the rf field generate clearly visible modifications in the Rydberg EIT spectra. A Floquet analysis is employed to model the Rydberg spectra, and good agreement with the experimental observations is found. Our results show that all-optical spectroscopy of Rydberg atoms in vapor cells can serve as an antenna-free, atom-based, and calibration-free technique to measure rf electric fields and to analyze their higher-harmonic contents.
Rydberg atoms have great potential in electric field measurement and have an advantage with a large frequency bandwidth from the kHz to the THz scale. However, the sensitivity for measuring a weak MHz electric field signal is limited by the spectroscopic resolution, because the weak electric field induces only a small perturbation of the population and energy-level shift of the Rydberg atoms. Here, we report highly sensitive measurement of a weak MHz electric field using electromagnetically induced transparency with Rydberg atoms in a thermal atomic system. Using the heterodyne method on a 30-MHz electric field, we successfully measure the minimum electric field strength to be $37.3\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{V}/\mathrm{cm}$ with a sensitivity up to $\ensuremath{-}65$ dBm/Hz and a linear dynamic range over 65 dB. Additionally, we measure an amplitude-modulated signal and demodulate the signal with a fidelity over 98%. This work extends the sensitivity of atomic sensors for measuring MHz electric fields, which advances atomic electric field-sensing technology.
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.