# Sensitivity Improvement and Determination of Rydberg Atom-Based Microwave Sensor

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theory and Experimental Setup

## 3. Results

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Gallagher, T.F.; Safinya, K.A.; Gounand, F.; Delpech, J.F.; Sandner, W.; Kachru, R. Resonant Rydberg-atom—Rydberg-atom collisions. Phys. Rev. A
**1982**, 25, 1905–1917. [Google Scholar] [CrossRef] - Deb, A.B.; Kjærgaard, N. Radio-over-fiber using an optical antenna based on Rydberg states of atoms. Appl. Phys. Lett.
**2018**, 112, 211106. [Google Scholar] [CrossRef] - Holloway, C.L.; Simons, M.T.; Kautz, M.D.; Haddab, A.H.; Gordon, J.A.; Crowley, T.P. A quantum-based power standard: Using Rydberg atoms for a SI-traceable radio-frequency power measurement technique in rectangular waveguides. Appl. Phys. Lett.
**2018**, 113, 094101. [Google Scholar] [CrossRef] - Sedlacek, J.A.; Schwettmann, A.; Kübler, H.; Löw, R.; Pfau, T.; Shaffer, J.P. Microwave electrometry with Rydberg atoms in a vapour cell using bright atomic resonances. Nat. Phys.
**2012**, 8, 819–824. [Google Scholar] [CrossRef] - Simons, M.T.; Gordon, J.A.; Holloway, C.L. Fiber-coupled vapor cell for a portable Rydberg atom-based radio frequency electric field sensor. Appl. Opt.
**2018**, 57, 6456–6460. [Google Scholar] [CrossRef] - Simons, M.T.; Haddab, A.H.; Gordon, J.A.; Holloway, C.L. Applications with a Rydberg Atom-based Radio Frequency Antenna/Receiver. In Proceedings of the 2019 International Symposium on Electromagnetic Compatibility—EMC EUROPE, Barcelona, Spain, 2–6 September 2019; pp. 885–889. [Google Scholar]
- Song, Z.; Liu, H.; Liu, X.; Zhang, W.; Zou, H.; Zhang, J.; Qu, J. Rydberg-atom-based digital communication using a continuously tunable radio-frequency carrier. Opt. Express
**2019**, 27, 8848–8857. [Google Scholar] [CrossRef] [Green Version] - Liao, K.Y.; Tu, H.T.; Yang, S.Z.; Chen, C.J.; Liu, X.H.; Liang, J.; Zhang, X.D.; Yan, H.; Zhu, S.L. Microwave electrometry via electromagnetically induced absorption in cold Rydberg atoms. Phys. Rev. A
**2020**, 101, 053432. [Google Scholar] [CrossRef] - Zhang, L.; Jia, Y.; Jing, M.; Guo, L.; Zhang, H.; Xiao, L.; Jia, S. Detuning radio-frequency electrometry using Rydberg atoms in a room-temperature vapor cell. Laser Phys.
**2019**, 29, 035701. [Google Scholar] [CrossRef] - Jia, F.D.; Liu, X.B.; Mei, J.; Yu, Y.H.; Zhang, H.Y.; Lin, Z.Q.; Dong, H.Y.; Zhang, J.; Xie, F.; Zhong, Z.P. Span shift and extension of quantum microwave electrometry with Rydberg atoms dressed by an auxiliary microwave field. Phys. Rev. A
**2021**, 103, 063113. [Google Scholar] [CrossRef] - Simons, M.T.; Artusio-Glimpse, A.B.; Holloway, C.L.; Imhof, E.; Jefferts, S.R.; Wyllie, R.; Sawyer, B.C.; Walker, T.G. Continuous radio-frequency electric-field detection through adjacent Rydberg resonance tuning. Phys. Rev. A
**2021**, 104, 032824. [Google Scholar] [CrossRef] - Meyer, D.H.; Kunz, P.D.; Cox, K.C. Waveguide-Coupled Rydberg Spectrum Analyzer from 0 to 20 GHz. Phys. Rev. Appl.
**2021**, 15, 014047. [Google Scholar] [CrossRef] - Peng, Y.D.; Wang, J.L.; Li, C.; Lu, X.; Qi, Y.H.; Yang, A.H.; Wang, J.Y. Enhanced microwave electrometry with intracavity anomalous dispersion in Rydberg atoms. Opt. Quantum Electron.
**2020**, 52, 120. [Google Scholar] [CrossRef] - Holloway, C.L.; Gordon, J.A.; Jefferts, S.; Schwarzkopf, A.; Anderson, D.A.; Miller, S.A.; Thaicharoen, N.; Raithel, G. Broadband Rydberg Atom-Based Electric-Field Probe for SI-Traceable, Self-Calibrated Measurements. IEEE Trans. Antenna Propag.
**2014**, 62, 6169–6182. [Google Scholar] [CrossRef] [Green Version] - Simons, M.T.; Haddab, A.H.; Gordon, J.A.; Novotny, D.; Holloway, C.L. Embedding a Rydberg Atom-Based Sensor Into an Antenna for Phase and Amplitude Detection of Radio-Frequency Fields and Modulated Signals. IEEE Access
**2019**, 7, 164975–164985. [Google Scholar] [CrossRef] - Fan, H.Q.; Kumar, S.; Daschner, R.; Kubler, H.; Shaffer, J.P. Subwavelength microwave electric-field imaging using Rydberg atoms inside atomic vapor cells. Opt. Lett.
**2014**, 39, 3030–3033. [Google Scholar] [CrossRef] [Green Version] - Gordon, J.A.; Holloway, C.L.; Schwarzkopf, A.; Anderson, D.A.; Miller, S.; Thaicharoen, N.; Raithel, G. Millimeter wave detection via Autler-Townes splitting in rubidium Rydberg atoms. Appl. Phys. Lett.
**2014**, 105, 024104. [Google Scholar] [CrossRef] [Green Version] - Holloway, C.L.; Gordon, J.A.; Schwarzkopf, A.; Anderson, D.A.; Miller, S.A.; Thaicharoen, N.; Raithel, G. Sub-wavelength imaging and field mapping via electromagnetically induced transparency and Autler-Townes splitting in Rydberg atoms. Appl. Phys. Lett.
**2014**, 104, 244102. [Google Scholar] [CrossRef] [Green Version] - Sedlacek, J.A.; Schwettmann, A.; Kubler, H.; Shaffer, J.P. Atom-based vector microwave electrometry using rubidium Rydberg atoms in a vapor cell. Phys. Rev. Lett.
**2013**, 111, 063001. [Google Scholar] [CrossRef] [Green Version] - Simons, M.T.; Gordon, J.A.; Holloway, C.L.; Anderson, D.A.; Miller, S.A.; Raithel, G. Using frequency detuning to improve the sensitivity of electric field measurements via electromagnetically induced transparency and Autler-Townes splitting in Rydberg atoms. Appl. Phys. Lett.
**2016**, 108, 174101. [Google Scholar] [CrossRef] [Green Version] - Fan, H.; Kumar, S.; Sedlacek, J.; Kübler, H.; Karimkashi, S.; Shaffer, J.P. Atom based RF electric field sensing. J. Phys. B At. Mol. Opt. Phys.
**2015**, 48, 202001. [Google Scholar] [CrossRef] - Jing, M.; Hu, Y.; Ma, J.; Zhang, H.; Zhang, L.; Xiao, L.; Jia, S. Atomic superheterodyne receiver based on microwave-dressed Rydberg spectroscopy. Nat. Phys.
**2020**, 16, 911–915. [Google Scholar] [CrossRef] - Anderson, D.A.; Sapiro, R.E.; Raithel, G. An Atomic Receiver for AM and FM Radio Communication. IEEE Trans. Antenna Propag.
**2021**, 69, 2455–2462. [Google Scholar] [CrossRef] [Green Version] - Holloway, C.; Simons, M.; Haddab, A.H.; Gordon, J.A.; Anderson, D.A.; Raithel, G.; Voran, S. A Multiple-Band Rydberg Atom-Based Receiver: AM/FM Stereo Reception. IEEE Antenna Propag. Mag.
**2021**, 63, 63–76. [Google Scholar] [CrossRef] - Song, Z.; Zhang, W.; Liu, X.; Zou, H.; Zhang, J.; Jiang, Z.; Qu, J. Quantum-Based Amplitude Modulation Radio Receiver Using Rydberg Atoms. In Proceedings of the 2018 IEEE Globecom Workshops, Abu Dhabi, United Arab Emirates, 9–13 December 2018; pp. 1–6. [Google Scholar]
- Abi-Salloum, T.Y. Electromagnetically induced transparency and Autler-Townes splitting: Two similar but distinct phenomena in two categories of three-level atomic systems. Phys. Rev. A
**2010**, 81, 053836. [Google Scholar] [CrossRef] - Petrosyan, D.; Otterbach, J.; Fleischhauer, M. Electromagnetically induced transparency with Rydberg atoms. Phys. Rev. Lett.
**2011**, 107, 213601. [Google Scholar] [CrossRef] [PubMed] - Simons, M.T.; Haddab, A.H.; Gordon, J.A.; Holloway, C.L. Waveguide-integrated Rydberg Atom-based RF Field Detector for Near-field Antenna Measurements. In Proceedings of the 2019 Antenna Measurement Techniques Association Symposium, San Diego, CA, USA, 6–11 October 2019; pp. 1–4. [Google Scholar]
- Holloway, C.L.; Simons, M.T.; Gordon, J.A.; Dienstfrey, A.; Anderson, D.A.; Raithel, G. Electric field metrology for SI traceability: Systematic measurement uncertainties in electromagnetically induced transparency in atomic vapor. J. Appl. Phys.
**2017**, 121, 233106. [Google Scholar] [CrossRef] [Green Version] - Kumar, S.; Fan, H.; Kubler, H.; Sheng, J.; Shaffer, J.P. Atom-Based Sensing of Weak Radio Frequency Electric Fields Using Homodyne Readout. Sci. Rep.
**2017**, 7, 42981. [Google Scholar] [CrossRef] - Zou, H.; Song, Z.; Mu, H.; Feng, Z.; Qu, J.; Wang, Q. Atomic Receiver by Utilizing Multiple Radio-Frequency Coupling at Rydberg States of Rubidium. Appl. Sci.
**2020**, 10, 1346. [Google Scholar] [CrossRef] [Green Version] - Valente, P.; Failache, H.; Lezama, A. Temporal buildup of electromagnetically induced transparency and absorption resonances in degenerate two-level transitions. Phys. Rev. A
**2003**, 67, 013806. [Google Scholar] [CrossRef] [Green Version] - Li, Y.Q.; Xiao, M. Transient properties of an electromagnetically induced transparency in three-level atoms. Opt. Lett.
**1995**, 20, 1489–1491. [Google Scholar] [CrossRef] - Zi-Shan, X.; Han-Mu, W.; Zeng-Li, B.; Hong-Ping, L. Transient electromagnetically induced transparency spectroscopy of 87Rb atom in buffer gas. Chin. Phys. B
**2021**. [Google Scholar] [CrossRef] - Gea-Banacloche, J.; Li, Y.; Jin, S.; Xiao, M. Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: Theory and experiment. Phys. Rev. A
**1995**, 51, 576–584. [Google Scholar] [CrossRef] [PubMed] - Sibalic, N.; Pritchard, J.D.; Adams, C.S.; Weatherill, K.J. ARC: An open-source library for calculating properties of alkali Rydberg atoms. Comput. Phys. Commun.
**2017**, 220, 319–331. [Google Scholar] [CrossRef] - Liu, X.; Jia, F.; Zhang, H.; Mei, J.; Yu, Y.; Liang, W.; Zhang, J.; Xie, F.; Zhong, Z. Using amplitude modulation of the microwave field to improve the sensitivity of Rydberg-atom based microwave electrometry. AIP Adv.
**2021**, 11, 085127. [Google Scholar] [CrossRef] - Chopinaud, A.; Pritchard, J.D. Optimal State Choice for Rydberg-Atom Microwave Sensors. Phys. Rev. Appl.
**2021**, 16, 024008. [Google Scholar] [CrossRef] - Robinson, A.K.; Artusio-Glimpse, A.B.; Simons, M.T.; Holloway, C.L. Atomic spectra in a six-level scheme for electromagnetically induced transparency and Autler-Townes splitting in Rydberg atoms. Phys. Rev. A
**2021**, 103, 023704. [Google Scholar] [CrossRef]

**Figure 1.**Experimental setup and its concerned four-energy-level diagram. The coupling (${\lambda}_{c}=480$ nm) and probe (${\lambda}_{p}=780$ nm) beams counter-propagate through a Rb vapor cell, forming a ladder-type EIT with upper Rydberg states coupled further by microwave RF. It is emitted by a horn antenna, serving as a local RF electric field oscillator (LO). The probe beam passing through an Rb cell and a dichroic mirror (DM) is detected by a photodiode (PD). The probe beam is frequency-locked to $|{5}^{2}{\mathrm{S}}_{1/2},\mathrm{F}=3\rangle \to |{5}^{2}{\mathrm{P}}_{3/2},\mathrm{F}=3\rangle $ transition via an integrated saturated absorption spectroscopy (SAS) unit of ${}^{85}\mathrm{Rb}$ atoms. The coupling beam scans across transition $|{5}^{2}{\mathrm{P}}_{3/2}\rangle \to |{70}^{2}{\mathrm{S}}_{1/2}\rangle $ and can also be frequency-locked to this transition via a Pound-Drever-Hall technique (PDH) based on an ultra-stable cavity on demand.

**Figure 2.**(

**a**) Theoretical simulation of the probe transmittancy by scanning the coupling laser based on the optical Bloch equation at various RF strengths, (

**b**) the probe transmittancy dependent on the RF strength at zero coupling detuning and its derivative depicting its RF-optical gain. The point A in (

**b**) and B in (

**c**) corresponds to the maximum gain where the RF strength is $2\pi \times 7$ MHz.

**Figure 3.**(

**a**) Probe optical transmission response on the applied RF power at various probe laser powers. (

**b**) At the optimized RF power of −10 dBm and coupling laser intensity of 420 $\mathrm{mW}$, the optical signal increases linearly with the probe laser intensity, but (

**c**) the AT-spectral linewidth also almost linearly increases. An optimized probe laser power should keep a balance between them.

**Figure 4.**(

**a**) Probe optical transmission response on the applied RF power at various coupling laser powers. (

**b**) At the optimized RF power of −10 dBm and probe laser intensity of 100 $\mathsf{\mu}\mathrm{W}$, the optical signal increases linearly with coupling laser intensity, while (

**c**) the AT-spectral linewidth nearly unchanged.

**Figure 5.**(

**a**) Typical AT-splittings due to the RF induced interaction between the adjacent Rydberg states at different RF powers. (

**b**) Measurements of the local RF E-field ${E}_{L}$ (black square) by EIT-AT spectra versus the square root of the output power, $\sqrt{{P}_{RF}}$, and its linear fit (red line) by formula ${E}_{L}=\alpha \sqrt{{P}_{RF}}$ with parameter determined as $\alpha =43.16\left(64\right)\phantom{\rule{3.33333pt}{0ex}}{\mathrm{Vm}}^{-1}/{\mathrm{W}}^{1/2}$.

**Figure 6.**The measurement of optical response of MW at different RF powers varying from $-14$ to $-4$ dBm (

**a1**,

**b1**,

**c1**,

**d1**,

**e1**) and the dynamical signal extraction (

**a2**,

**b2**,

**c2**,

**d2**,

**e2**). The laser powers are fixed at the optimized intensities. When the RF power increases up −10 dBm, the response has a large amplitude and nearly gets saturated, implying an optimized RF power.

**Figure 7.**The measurement of optical response of MW at different RF frequency detunings (

**left**) and its dynamical signal extraction (

**right**) at various LO field power (a) -12 dBm, (b) -10 dBm and (c) -4 dBm. A moderate detuning can increase the dynamical signal. The laser powers are fixed at the optimized intensities.

**Figure 8.**The maximum dynamical signal response dependent on the RF detunings at different MW RF powers in Figure 6, where obvious optimization can be determined.

**Figure 9.**Theoretical simulation of the dynamical optical response for the RF detuning. (

**a**,

**b**) are the probe transparency signal under the 1 kHz modulation at zero and −6 MHz RF detuning, respectively. Their dynamic optical response extractions are shown in (

**c**,

**d**), where a little increase in signal can be obtained by RF detuning.

**Figure 10.**The optical dynamical response at two RF detuning frequencies but all other parameters fixed at the optimized values. The applied amplitude modulation intensity decreases from (

**a**) ${E}_{mod}=860\left(13\right)\phantom{\rule{4pt}{0ex}}\mathsf{\mu}\mathrm{V}/\mathrm{cm}$ down to (

**b**) ${E}_{mod}=6.88\left(10\right)\phantom{\rule{4pt}{0ex}}\mathsf{\mu}\mathrm{V}/\mathrm{cm}$ at LO RF field resonance until approaching the lowest visual perceptible threshold. (

**a’**,

**b’**) correspond to the case of LO RF detuning of −6 MHz.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Cai, M.; Xu, Z.; You, S.; Liu, H.
Sensitivity Improvement and Determination of Rydberg Atom-Based Microwave Sensor. *Photonics* **2022**, *9*, 250.
https://doi.org/10.3390/photonics9040250

**AMA Style**

Cai M, Xu Z, You S, Liu H.
Sensitivity Improvement and Determination of Rydberg Atom-Based Microwave Sensor. *Photonics*. 2022; 9(4):250.
https://doi.org/10.3390/photonics9040250

**Chicago/Turabian Style**

Cai, Minghao, Zishan Xu, Shuhang You, and Hongping Liu.
2022. "Sensitivity Improvement and Determination of Rydberg Atom-Based Microwave Sensor" *Photonics* 9, no. 4: 250.
https://doi.org/10.3390/photonics9040250