- Open Access
Bridging gaps in Rydberg rf receivers using modulation-transfer bandwidth enhancement
Phys. Rev. Applied 26, 034013 – Published 8 September, 2026
DOI: https://doi.org/10.1103/y9dt-gs85
Abstract
We optimize theoretically and experimentally the performances of the recently demonstrated modulation transfer protocol [D.-A. Trinh et al., Modulation transfer protocol for Rydberg rf receivers, Appl. Phys. Lett. 125, 154001 (2024)] aiming at extending the bandwidth of quantum rf receivers based on hot Rydberg atoms. This optimization relies on tuning the parameters of the phase modulation of the coupling beam, which is converted by the nonlinear response of the atoms into an amplitude modulation of the probe beam. We develop a theoretical model to optimize both the modulation frequency and the modulation amplitude of the coupling beam, thereby maximizing the atomic response. Once optimized, the sensitivity to detuned rf fields of this modulation transfer protocol is measured and compared with that of the conventional protocol. This comparison shows that the new protocol permits a strong increase in the detection bandwidth. Indeed, it outperforms the usual one as soon as the rf signal to be measured is detuned by more than a few MHz. We illustrate the capability of this modulation transfer protocol to enhance the detection bandwidth by showing experimentally how it permits bridging the gap between two Rydberg transitions separated by 166 MHz. In all cases, the experimental results are in good agreement with the simulations.
Physics Subject Headings (PhySH)
Article Text
References (40)
- D. Budker and M. Romalis, Optical magnetometry, Nat. Phys. 3, 227 (2007).
- R. Finkelstein, S. Bali, O. Firstenberg, and I. Novikova, A practical guide to electromagnetically induced transparency in atomic vapor, New J. Phys. 25, 035001 (2023).
- J. A. Sedlacek, A. Schwettmann, H. Kübler, R. Löw, T. Pfau, and J. P. Shaffer, Microwave electrometry with Rydberg atoms in a vapour cell using bright atomic resonances, Nat. Phys. 8, 819 (2012).
- C. L. Holloway, J. A. Gordon, S. Jefferts, A. Schwarzkopf, D. A. Anderson, S. A. Miller, N. Thaicharoen, and G. Raithel, Broadband Rydberg atom-based electric-field probe for SI-traceable, self-calibrated measurements, IEEE Trans. Antennas Propag. 62, 6169 (2014).
- H. Q. Fan, S. Kumar, H. Kübler, and J. P. Shaffer, Dispersive radio frequency electrometry using Rydberg atoms in a prism-shaped atomic vapor cell, J. Phys. B 49, 104004 (2016).
- M. T. Simons, A. H. Haddab, J. A. Gordon, and C. L. Holloway, A Rydberg atom-based mixer: Measuring the phase of a radio frequency wave, Appl. Phys. Lett. 114, 114101 (2019).
- D. Anderson, R. Sapiro, L. Gonçalves, R. Cardman, and G. Raithel, Optical radio-frequency phase measurement with an internal-state Rydberg atom interferometer, Phys. Rev. Appl. 17, 044020 (2022).
- M. Jing, Y. Hu, J. Ma, H. Zhang, L. Zhang, L. Xiao, and S. Jia, Atomic superheterodyne receiver based on microwave-dressed Rydberg spectroscopy, Nat. Phys. 16, 911 (2020).
- J. A. Sedlacek, A. Schwettmann, H. Kübler, and J. P. Shaffer, Atom-based vector microwave electrometry using rubidium Rydberg atoms in a vapor cell, Phys. Rev. Lett. 111, 063001 (2013).
- Y. Wang, F. Jia, J. Hao, Y. Cui, F. Zhou, X. Liu, J. Mei, Y. Yu, Y. Liu, J. Zhang, F. Xie, and Z. Zhong, Precise measurement of microwave polarization using a Rydberg atom-based mixer, Opt. Express 31, 10449 (2023).
- A. K. Robinson, N. Prajapati, D. Senic, M. T. Simons, and C. L. Holloway, Determining the angle-of-arrival of a radio-frequency source with a Rydberg atom-based sensor, Appl. Phys. Lett. 118, 114001 (2021).
- Y. Yan, J. Yuan, L. Zhang, L. Xiao, S. Jia, and L. Wang, Three-dimensional location system based on an L-shaped array of Rydberg atomic receivers, Opt. Lett. 48, 3945 (2023).
- Y.-Y. Jau and T. Carter, Vapor-cell-based atomic electrometry for detection frequencies below 1 kHz, Phys. Rev. Appl. 13, 054034 (2020).
- B. Liu, L.-H. Zhang, Z.-K. Liu, Z.-Y. Zhang, Z.-H. Zhu, W. Gao, G.-C. Guo, D.-S. Ding, and B.-S. Shi, Highly sensitive measurement of a megahertz rf electric field with a Rydberg-atom sensor, Phys. Rev. Appl. 18, 014045 (2022).
- M. J. Lim, M. Cervantes, C. Brady, S. McPoyle, and J. Simmermon, Kilohertz-range electric field calibration in an alkali vapor cell using time-averaged Stark shifts, Appl. Phys. Lett. 123, 051106 (2023).
- R. C. Brown, B. Kayim, M. A. Viray, A. R. Perry, B. C. Sawyer, and R. Wyllie, Very-high- and ultrahigh-frequency electric-field detection using high angular momentum Rydberg states, Phys. Rev. A 107, 052605 (2023).
- S. Chen, D. J. Reed, A. R. MacKellar, L. A. Downes, N. F. A. Almuhawish, M. J. Jamieson, C. S. Adams, and K. J. Weatherill, Terahertz electrometry via infrared spectroscopy of atomic vapor, Optica 9, 485 (2022).
- D. A. Anderson and G. Raithel, Continuous-frequency measurements of high-intensity microwave electric fields with atomic vapor cells, Appl. Phys. Lett. 111, 053504 (2017).
- J. Hu, H. Li, R. Song, J. Bai, Y. Jiao, J. Zhao, and S. Jia, Continuously tunable radio frequency electrometry with Rydberg atoms, Appl. Phys. Lett. 121, 014002 (2022).
- J. Yao, Q. An, Y. Zhou, K. Yang, F. Wu, and Y. Fu, Sensitivity enhancement of far-detuned rf field sensing based on Rydberg atoms dressed by a near-resonant RF field, Opt. Lett. 47, 5256 (2022).
- H. Li, J. Hu, J. Bai, M. Shi, Y. Jiao, J. Zhao, and S. Jia, Rydberg atom-based AM receiver with a weak continuous frequency carrier, Opt. Express 30, 13522 (2022).
- M. T. Simons, A. B. Artusio-Glimpse, C. L. Holloway, E. Imhof, S. R. Jefferts, R. Wyllie, B. C. Sawyer, and T. G. Walker, Continuous radio-frequency electric-field detection through adjacent Rydberg resonance tuning, Phys. Rev. A 104, 032824 (2021).
- K. Ouyang, Y. Shi, M. Lei, and M. Shi, Continuous broadband microwave electric field measurement in Rydberg atoms based on the DC stark effect, Appl. Phys. Lett. 123, 264001 (2023).
- J. He, Q. Liu, Z. Yang, Q. Niu, X. Ban, and J. Wang, Noise spectroscopy with a Rydberg ensemble in a hot atomic vapor cell, Phys. Rev. A 104, 063120 (2021).
- D.-A. Trinh, K. V. Adwaith, M. Branco, Aénor Rouxel, S. Welinski, P. Berger, F. Goldfarb, and F. Bretenaker, Modulation transfer protocol for Rydberg RF receivers, Appl. Phys. Lett. 125, 154001 (2024).
- N. Šibalić, J. D. Pritchard, C. S. Adams, and K. J. Weatherill, ARC: An open-source library for calculating properties of alkali Rydberg atoms, Comput. Phys. Commun. 220, 319 (2017).
- V. Wong, R. S. Bennink, A. M. Marino, R. W. Boyd, C. R. Stroud, and F. A. Narducci, Influence of coherent Raman scattering on coherent population trapping in atomic sodium vapor, Phys. Rev. A 70, 053811 (2004).
- M. Ducloy and D. Bloch, Theory of degenerate four-wave mixing in resonant Doppler-broadened media. - II. Doppler-free heterodyne spectroscopy via collinear four-wave mixing in two- and three-level systems, J. Phys. France 43, 57 (1982).
- D. J. McCarron, S. A. King, and S. L. Cornish, Modulation transfer spectroscopy in atomic rubidium, Meas. Sci. Technol. 19, 105601 (2008).
- D. Sun, C. Zhou, L. Zhou, J. Wang, and M. Zhan, Modulation transfer spectroscopy in a lithium atomic vapor cell, Opt. Express 24, 10649 (2016).
- T. Preuschoff, M. Schlosser, and G. Birkl, Optimization strategies for modulation transfer spectroscopy applied to laser stabilization, Opt. Express 26, 24010 (2018).
- M. J. Lim, S. McPoyle, and M. Cervantes, Modulation transfer spectroscopy of a four-level ladder system in atomic rubidium, Opt. Commun. 522, 128651 (2022).
- R. P. Abel, A. K. Mohapatra, M. G. Bason, J. D. Pritchard, K. J. Weatherill, U. Raitzsch, and C. S. Adams, Laser frequency stabilization to excited state transitions using electromagnetically induced transparency in a cascade system, Appl. Phys. Lett. 94, 071107 (2009).
- A. K. Robinson, A. B. Artusio-Glimpse, M. T. Simons, and C. L. Holloway, Atomic spectra in a six-level scheme for electromagnetically induced transparency and Autler-Townes splitting in Rydberg atoms, Phys. Rev. A 103, 023704 (2021).
- H. Fan, S. Kumar, J. Sheng, J. P. Shaffer, C. L. Holloway, and J. A. Gordon, Effect of vapor-cell geometry on rydberg-atom-based measurements of radio-frequency electric fields, Phys. Rev. Appl. 4, 044015 (2015).
- A. P. Rotunno, C. L. Holloway, N. Prajapati, S. Berweger, A. B. Artusio-Glimpse, R. Brown, M. Simons, A. K. Robinson, B. N. Kayim, M. A. Viray, J. F. Jones, B. C. Sawyer, R. Wyllie, T. Walker, R. W. Ziolkowski, S. R. Jefferts, S. Geibel, J. Wheeler, and E. Imhof, Investigating electromagnetically induced transparency spectral lineshape distortion due to non-uniform fields in Rydberg-atom electrometry, J. Appl. Phys. 134, 084401 (2023).
- E. Li, J. Yao, D. Yu, J. Xi, and J. Chicharo, Optical phase shifting with acousto-optic devices, Opt. Lett. 30, 189 (2005).
- N. Schlossberger, N. Prajapati, S. Berweger, A. P. Rotunno, A. B. Artusio-Glimpse, M. T. Simons, A. A. Sheikh, E. B. Norrgard, S. P. Eckel, and C. L. Holloway, Rydberg states of alkali atoms in atomic vapour as SI-traceable field probes and communications receivers, Nat. Rev. Phys. 6, 606 (2024).
- H. Fan, S. Kumar, J. Sedlacek, H. Kübler, S. Karimkashi, and J. P. Shaffer, Atom based RF electric field sensing, J. Phys. B 48, 202001 (2015).
- S. Kumar, H. Fan, H. Kübler, J. Sheng, and J. P. Shaffer, Atom-based sensing of weak radio frequency electric fields using homodyne readout, Sci. Rep. 7, 42981 (2017).