Multichannel, ultra-wideband Rydberg electrometry with an optical frequency comb

Domain: physics
Published: 2025-12-07
Editorial outcome: minor_revision

Abstract
While Rydberg atoms have shown tremendous potential to serve as accurate and sensitive detectors of microwaves and millimeter waves, their response is generally limited to a single, narrow frequency band around a chosen transition. As a result, their potential to serve as agile and wideband electromagnetic receivers has not been fully realized. Here we demonstrate the use of a mid-infrared, frequency agile optical frequency comb as the coupling laser for three-photon Rydberg atom electrometry. This approach allows for rapid switching between as many as seven individual Rydberg states, allowing for multichannel detection across a frequency range from 1 GHz to 40 GHz. The generality and flexibility of this method for wideband multiplexing is anticipated to have transformative effects in the field of Rydberg electrometry, paving the way for advanced information coding, arbitrary signal detection, and the simultaneous detection of ultra-broadband radio frequency radiation.

Introduction
Rydberg atoms have become ubiquitous in quantum-based technologies, including entangled ions and atoms for quantum computing, efficient microwave-to-optical conversion, and electric field sensing. Rydberg atoms offer large tuning bandwidths that range from DC to terahertz 1–5 and are highly sensitive to electric field variation and detection 6–15 as well as allowing for direct conversion 16–18 and phase sensing 7,8,19,20. However, unlike classical receivers that continuously monitor the entire spectrum of operation, the instantaneous bandwidth of Rydberg atom sensors is generally limited to tens of MHz around a selected carrier tone 8,17,21–24.

Typical sensitive field measurements utilize the resonant Autler–Townes (AT) effect to observe the response of the selected Rydberg state to external fields 4,25. The AT effect occurs when a field resonant with two states of the atoms perturbs and splits each of these energy levels, causing an observable change in the absorption signal of a probe laser. The probe laser is combined with a coupling laser and possible dressing lasers chosen to excite the atoms and readout the selected Rydberg state. The splitting frequency of this state is directly proportional to the magnitude of the radio frequency (RF) electric field given the dipole moment of the resonant RF transition. In this case, slow, coarse laser tuning by several nanometers is required to cover the full RF reception range 26. Complicated Rydberg engineering techniques can be employed to increase the RF bandwidth, but still does not bridge the gap for continuous measurements or multichannel detection of several incoming RF signals 27,28.

An alternative to the AT effect, the off-resonant Stark shift offers a near continuous tuning capability throughout the RF spectrum 5,29,30, however, with dramatically reduced sensitivity. Under the Stark shift condition, the RF field is far detuned (>100 MHz) from the resonance frequency between the two Rydberg states. Rather than inducing a splitting, this off-resonant field shifts the selected Rydberg state, and the frequency of this shift is proportional to the magnitude of the RF electric field squared times the polarizability of the state. A notable concern with this configuration is that information from multiple RF fields can be transferred onto a single probe laser, thus, generally leading to inseparable signals and limiting the total bandwidth of the system. For example, digital television antennas receive RF waves ranging from 50 MHz to 700 MHz and carry information with 6 MHz of modulation bandwidth. By demodulating the carrier after reception, several signals can be received and readout at the same time. However, with the off-resonant Stark shifting approach, these signals would be inseparable.

A major claim of Rydberg atom sensors has been their capacity for broadband sensing from DC to frequencies in the THz. However, current Rydberg sensors are only capable of achieving this through slow laser tuning and subsequent laser relocking. There is no published method to overcome the limited tuning capabilities of Rydberg atom sensors. Here, we have developed a method to remove this limitation that allows for the rapid preparation of up to seven different Rydberg states, with the potential for simultaneous operation in the future. These new capabilities pave the way towards advanced, broadband communication protocols, a long standing promise of Rydberg sensors that can be enabled by optical frequency combs.

Optical frequency combs have been transformative in wide-ranging fields such as time transfer, astronomy, and remote sensing 31,32. These advancements have largely leveraged the exquisite frequency accuracy that combs can provide as well as their wide spectral bandwidths. However, their low power per comb tooth (generally microwatts or even nanowatts) has proven limiting in some applications 33. Recently, we have demonstrated a new approach for spectral translation of electro-optic frequency combs using an optical parametric oscillator (OPO) 33,34. Critically, this method allows for highly coherent spectral translation from the near-infrared to the important mid-infrared spectral region with exceptionally high powers per comb tooth. Further, the resulting frequency combs are frequency-agile in that their comb spacing can be rapidly changed by adjusting the applied RF.

Here we utilize this frequency-agile optical frequency comb as the coupling laser in a three-photon Rydberg electrometry instrument, allowing for the rapid preparation of as many as seven Rydberg states. Further, we demonstrate that these seven individual states can provide orthogonal (i.e., independent) RF channels, which can allow for rapid and sensitive detection of a multitude of RF tones across a range from 1 GHz to 40 GHz, a range which was limited only by our available RF sources and antennas.

Results
The multi-state Rydberg receiver described here relies upon three-photon excitation to generate and probe Rydberg states in cesium (Cs) atoms 35,36 as shown in Fig. 1. This three-photon configuration leads to reduced Doppler broadening due to the wavelengths of the three optical fields and theoretically a higher maximum sensitivity 35. Importantly, we note that the methods described here are equally applicable to more traditional two-photon approaches 37–40.

The coherent multi-photon process known as electromagnetically-induced absorption (EIA) allows for probing highly excited Rydberg states with higher precision than other methods such as ionization 26,41,42, electron beam ionization 42, and direct absorption 18. In the present three-photon process a 895 nm probe laser, a 636 nm dressing laser, and a 2235 nm coupling optical frequency comb are used in a successive excitation up to the Rydberg state(s) of interest, thus generating a coherent ensemble of atoms. The EIA is a result of this coherence, and the readout of the probe laser is a measure of the coherence between the ground state and the first excited state. The dressing and coupling laser modify this coherence through their interactions with the 9S intermediate state and the Rydberg state. This projection allows for measurements of Rydberg state(s) of interest by measuring the probe laser transmission. Similarly, modification of the Rydberg state by an RF field also affects the probe laser transmission.

We utilized an OPO to produce the frequency-agile, mid-infrared optical frequency comb 33,34 which served as the coupling laser (see Fig. 2). To generate this optical frequency comb, the 1068 nm OPO seed laser was first passed through a dual-drive Mach-Zehnder modulator 43. An optical frequency comb is produced with a comb spacing of 18 GHz by driving both sides of the modulator with an 18 GHz RF tone. This comb spacing was selected to roughly match the separation of the selected Rydberg states shown in Fig. 1b. The comb tooth amplitudes were then flattened by adjusting the phase shift and RF power between the two arms of the Mach-Zehnder modulator. The comb was then optically amplified to 10 W before serving as the pump laser for a singly resonant, continuous-wave OPO.

Because only the signal beam is resonant within the OPO cavity, the optical frequency comb on the pump beam was efficiently and coherently transferred onto the mid-infrared idler beam 33,34. Critically, this approach allows for the generation of a high power, frequency-agile comb, where the comb spacing and span are entirely flexible and can be set to well match an arbitrary set of Rydberg levels. In addition, the output comb can be tuned over a spectral range between 2200 nm and 4000 nm. For the present measurements, it was tuned to 2235 nm, where the comb had a total power >2 W and seven strong comb teeth which had an average power per tooth near 300 mW. This power per comb tooth was more than sufficient to allow for multi-state Rydberg preparation.

The optical frequency comb coupling laser was then combined with the 895 nm probe laser and passed through a 133 Cs filled vapor cell. The 636 nm dressing laser was counter-propagated through the cell to reduce the Doppler effect. The transmitted probe beam was then spectrally filtered (to remove the coupling light) and measured on a balanced photodiode, allowing for near shot-noise-limited detection.

As an initial demonstration, we scanned the OPO pump laser (and thus the entire coupling optical frequency comb) over a range of 4 GHz to excite each Rydberg state individually, as shown in Fig. 3a. The detuning of each state corresponds to the energy difference between the nearest comb tooth and the state in question (as defined in Table 1). The peaks in the spectrum show the seven Rydberg states which can be prepared by the optical frequency comb coupling laser. We note that the reverse configuration can also be performed. By locking the coupling laser and tuning the comb spacing 44, we could achieve fast switching between the distinct Rydberg states and employ a variety of demodulation schemes to receive information from the various frequency channels. While the comb spacing could theoretically be switched at gigahertz rates, the atomic lifetime of the intermediate state limits such switching to tens of MHz.

Armed with this multi-state readout, we can utilize this approach to observe a wide range of effects on the multitude of Rydberg states (see Fig. 1c) being probed. For example, we demonstrated the independent response of selected states to applied RF fields, the splitting of the Rydberg state resonances for calibration purposes, and even a Stark shift when the applied field is strong enough. Figure 3b shows the Autler–Townes splitting as the RF field strength is increased. We determined the field strength by extracting the splitting using the AT effect 4,

E = 2\pi\hbar\Delta_{meas} / \wp_{i,j} (1)

where \hbar is the reduced Planck constant, E is the electric field, \Delta_{meas} is the measured Rydberg state splitting, and \wp_{i,j} is the transition dipole moment between the two Rydberg states. For example, at -5 dBm of applied RF, we observe a splitting of 30 MHz. The transition dipole moment for this transition is 2480 e a_0, where e is the electron charge and a_0 is the Bohr radius. For this case, the field measured by the atoms was 0.95 V/m.

Figure 3b shows that as the field strength is decreased, we see the AT splitting decrease until the two peaks combine. As the splitting decreases the broadening from inhomogeneous fields also decreases 15. We are able to reduce the field down to 69 mV/m and still observe splitting. As the field is increased to large values (approaching 1 V/m) we can see that the splitting becomes so large that the split peaks can become difficult to observe. This is generally not limiting in Rydberg sensors, as there are techniques to minimize the inhomogeneities that cause broadening at strong fields and weak field measurements are not limited by these effects.

We note that if a modulated signal is used alongside lock-in detection (in order to reduce low-frequency noise), we can expect over two orders of magnitude improvement in the minimum detectable field 45. This would lead to an estimated sensitivity near 700 \mu V m^{-1} Hz^{-1/2}. However, this is far from a fundamental limitation for this sensor, as increased optical power would lead to corresponding increases in sensitivity.

We can also observe avoided crossings as the frequency of the applied RF is scanned (see Fig. 3c). The expected AT behavior with RF detuning is observed, in that there are three main effects on the observed splitting of the electromagnetically induced transparency (EIT) signal 46: (1) the two peaks of the EIT signal are asymmetric, (2) the separation between the two AT peaks increases with RF detuning, and (3) one peak is pulled to the zero detuning location of the coupling laser. In this case, the splitting is proportional to the generalized Rabi frequency,

\Delta_{meas} = \sqrt{\Omega_{RF}^2 + \Delta_{RF}^2} (2)

where \Omega_{RF} is proportional to the field strength, \Delta_{RF} is the detuning of the RF frequency from the atomic resonance, and \Delta_{meas} is the measured splitting. We can use these avoided crossings to identify the location of the different RF Rydberg transitions. A central peak can be observed in this figure and this peak is a result of the relative polarization of the RF and optical fields. The discrepancy between Fig. 3b, c is due to the fact that they were taken on separate days and the polarization of the coupling laser may have been different. In general, we align the optical fields such that the polarization is vertically aligned relative to the table. The RF are similarly vertically polarized as well. However, with variations in mounts and optics on the table, reflections of the RF radiation could provide horizontally aligned polarization components causing the central peak to appear.

The unique broadband nature of the present method becomes apparent when different RF fields are applied to the atoms. For these measurements, we used three horn antennas to apply RF fields ranging from 1 GHz to 40 GHz. The lower RF bound was set by the atomic transitions between states in this region of the Rydberg manifold while the upper bound was set by the available RF sources and antennas. We note that the use of higher frequency RF sources and antennas should allow for a significantly wider measurable RF range.

For these measurements, we applied RF frequencies over 40-MHz-wide ranges which were centered on Rydberg transitions between 1 GHz and 40 GHz (see Fig. 4). For example, the first column in Fig. 4 shows the response of the seven states to a field ranging from 1.440 GHz to 1.480 GHz. A complete table of each of the different transition frequencies we can access is given in the Supplementary Table S1. For each column in Fig. 4 we highlight the panel where we expect a response to the RF field. We observed avoided crossings caused by the mixing of the optically excited Rydberg states and the Rydberg state coupled by the RF field 47.

The fits shown in the highlighted panels map the response of the Rydberg state energies using the generalized Rabi in Eq. (2). The energy of each dressed state present in AT splitting is given by the sum and difference of the generalized Rabi frequency and the detuning of the RF frequency from the atomic resonance,

\Delta_{\pm} = \Delta_{RF} \pm \sqrt{\Omega_{RF}^2 + \Delta_{RF}^2} / 2 (3)

where \Delta_{\pm} is the shift for each dressed state in MHz. From each highlighted panel, we extract the transmission for each given RF frequency and fit the data to find the energy of the two dressed states. We fit the dressed state energy separation as a function of RF detuning to obtain the fits seen. These fits can also be used to determine the strength of the RF field present at the atoms.

Importantly, since each of the transition frequencies in this section of the Rydberg manifold are separated by over 50 MHz (i.e., significantly greater than the <10 MHz response bandwidth of a given Rydberg state), a single RF frequency is expected to only interact with a single Rydberg state, thus allowing for complete orthogonality. Experimentally, this is what we observe, where the measured response to the RF fields in a multitude of different frequency bands up to 40 GHz exhibits no observable crosstalk between Rydberg states. This orthogonality condition is critical for communication protocols such as frequency hopping shared spectrum (FHSS) and orthogonal frequency domain multiplexing (OFDM).

FHSS is a protocol that relies on frequency-agile sensors that can quickly switch between frequency bands to avoid jamming or perform signal interception. However, the bands are generally limited by the bandwidth of the antenna being utilized for reception to, at most, a few gigahertz. Critically, with the present frequency comb-based approach, it should be possible to switch between vastly different operational bands and therefore significantly improve the performance of this protocol for Rydberg sensing. FHSS does not require simultaneous measurements but instead relies on rapid switching between different bands that contain segments of the full spectrum of information. With fast tuning of the comb teeth and the orthogonality of the channels, we should be able to demonstrate this protocol with our current system. Furthermore, we could cover a range of frequencies that normally require at least 5 different antennas and sets of mixers to receive and analyze.

OFDM is another protocol that relies upon spreading information over several frequency bands simultaneously. In this way, information is simultaneously sent over multiple carriers, and each carrier must be separately demodulated. While the FHSS protocol can be achieved by utilizing Stark shifting measurements, OFDM requires that all carriers be received simultaneously and typically have the same base-band modulation (i.e., the carriers must be separable). In the case that a single probe readout were used in conjunction with Stark shifting measurements, all of the base bands would interfere. This is where the present frequency comb method would separate the RF carriers for simultaneous broadband detection. While the system demonstrated here cannot presently perform this protocol, it paves the way for this enhanced capability.

We note that a major advantage of the present approach over traditional, classical implementations of OFDM and FHSS is the capability of sensing over multiple bands. For a classical antenna, the measurement band is limited, and the antenna is typically engineered to accept specific frequencies with matching circuits in order to optimize performance at a particular frequency. This leads to measurement bands which are normally limited to within 1 GHz of the center. Rydberg atoms allow for measurements over vastly different bands separated by nearly 40 GHz in the present demonstration, and nearly 1 THz in the future. This represents a paradigm shift from classical receivers and opens the door for new methods of secure communication.

While the RF channels are connected to separate Rydberg states and therefore, to avoid cross-talk, this information is projected onto a single probe laser. This will result in a mixing of the different RF channels. To avoid this, we must incorporate a comb onto the probe and dressing lasers to match the energy difference of the comb teeth of the coupling laser and the Rydberg states of interest. However, we are concerned with the information being mixed through the narrow-band 9S intermediate state.

In future work, we will place a comb on the coupling laser in a more traditional two-photon system. In addition, we can place a comb on the probe laser 48 to compensate the energy, giving us access to the full Doppler width. The probe would have a comb that matches the detunings present on the scan of the coupling laser. This approach would allow for simultaneous state preparation and the protocols such as OFDM.

Further, the present approach provides a pathway toward a dramatic increase in the response bandwidth of Rydberg atoms sensors. By using simultaneous state readout (such as OFDM) in concert with our optical frequency comb-based approach, we should be able to demonstrate a bandwidth that scales with the number of comb teeth 49. With our current demonstration, it should be possible to demonstrate 100 MHz of bandwidth if we incorporate the nP_{1/2} states.

The use of an optical frequency comb as the coupling laser for Rydberg electrometry enables rapid and orthogonal measurements over a range of states and therefore radio frequencies. The increased capabilities made possible by this approach are expected to have an extensive impact on communications and sensing. We note that a classical receiver would require numerous different antennas and substantial down-conversion hardware to receive the same signals that this comb-enabled Rydberg receiver can readily record. Further, for the present demonstration, we recorded radio frequencies from 1 GHz to 40 GHz; however, extending this range to 100 GHz is readily possible, whereby the direct conversion nature of Rydberg atoms is anticipated to be truly enabling as telecommunications continue to push the limits of existing electronic hardware.

Methods
Laser stabilization
The 895 nm probe laser frequency was stabilized using saturated absorption spectroscopy to the 6S_{1/2}, F=4 \rightarrow 6P_{1/2}, F=3 transition. A portion of the 895 nm probe and the 636 nm dressing lasers were utilized to generate a two-photon EIT. The 636 nm dressing laser was tuned and locked to the 6P_{1/2}, F=3 \rightarrow 9S_{1/2}, F=4 transition using the two-photon EIT. The 2235 nm coupling laser was free running and scanned over 4 GHz to access the various Rydberg states prepared by the optical frequency comb.

Laser parameters
The size of the probe, dressing, and coupling lasers were set to 750 \mu m, 800 \mu m, and 820 \mu m, respectively. The power of the probe, dressing, and coupling lasers were fixed to 1.5 \mu W, 11 mW, and 1 W, respectively. All powers were measured before the cell. The corresponding Rabi rates for the probe, dressing, and coupling are then 2\pi \times 700 kHz, 2\pi \times 8 MHz, and 2\pi \times 2.6 MHz, respectively. The powers of the probe and dressing lasers were stabilized using acousto-optic modulators. The power output of the coupling laser was not directly stabilized, but the fiber amplifier for the OPO pump was stabilized internally. The polarization of each of the lasers was set to be linear and vertical (relative to the optical table). The coupling laser polarization was optimized in order to minimize the central peak that forms from transitions not accessible by the RF fields.

Comb parameters
To produce the mid-infrared optical frequency comb we first generated an near-infrared frequency comb, which utilized an external-cavity diode laser (ECDL) as its source. The ECDL output was injected into a dual-drive Mach-Zehnder modulator (MZM). An 18 GHz signal generated by a RF source was split and each side was amplified to near 0.5 W before being sent to each side of the MZM. One side of the MZM had a 3 dB RF attenuator placed on it to achieve a flatter comb 43. The output of the MZM was an optical frequency comb with seven strong teeth which were spaced by 18 GHz. This comb was then amplified to 10 W by a fiber amplifier before being injected into a commercial, singly resonant, continuous-wave optical parametric oscillator (OPO). The OPO efficiently and coherently transfers the optical frequency comb to 2235 nm with an output power of more than 2 W 33,34.

Radio frequency parameters
To supply RF radiation to the atoms, we utilized three different horn antennas. An ETS 3115 antenna was used to cover 1 GHz to 18 GHz, we used a Narda 638 standard gain horn to cover 18 GHz to 26.5 GHz, and a Narda 637 standard gain horn to cover 26.5 GHz to 40 GHz (Certain equipment, instruments, software, or materials are identified in this paper in order to specify the experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement of any product or service by NIST, nor is it intended to imply that the materials or equipment identified are necessarily the best available for the purpose). For the frequency scans, the power of the RF source for the 1 GHz to 18 GHz was fixed to 5 dBm, and the powers of the sources from 18 GHz to 40 GHz were fixed to 10 dBm. The difference was to optimize the visibility of the response between the two ranges. Each of the microwave horns were placed so that their polarization was linear and vertical (relative to the optical table).

Data acquisition
We scanned the coupling laser over 4 GHz at a scan rate of 30 Hz. We acquired 5 samples as the RF frequency or power was changed. The oscilloscope sampling rate was 2.5 GSa/s, making the frequency separation between points in the spectra 60 Hz in laser frequency. This is substantially below the linewidth and avoids electronic artifacts that can broaden the spectrum. In post-processing, we overlapped the data by using the 75P_{1/2} state since we did not scan over any resonant frequencies for that state.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Rydberg technologies are one of the most recent sensing modalities to emerge from developments in quantum technologies\nand are rapidly advancing – both in terms of technical performance and in their ability to be deployed in the field. As the\nauthors point out, Rydberg sensors currently exhibit a narrow instantaneous bandwidth that, in certain scenarios, may limit\ntheir performance. Thus, efforts to extend the instantaneous bandwidth are welcome developments. This manuscript focuses\non the novel use of an optical frequency comb as one of the excitation lasers in a three-photon Rydberg excitation scheme.\nTechnologies that sense the electromagnetic field multiple, diverse fields, including telecoms, astronomy, medical\ntechnology and materials characterisation. This work develops hardware that could potentially be deployed in a large subset\nof these fields. Of particular focus in this work is its potential use in communications, particularly those using FHSS and\nOFDM protocols. Implementation of these protocols is not my area of expertise, but I believe I will be of significant interest to\nthat community.\nMethodology and detail:\nData analysis based on EIA spectroscopy of Cs Rydberg states with principal quantum numbers around n = 75. The use of\nelectromagnetically-induced absorption for such purposes is a well-established approach, and the spectra featured in the\nmanuscript are convincing. The methods section contains sufficient information for the work to be reproduced but would\nbenefit from the inclusion of information about the light polarisation of each beam (for completeness).\nMy primary question regarding the manuscript is around the claim of simultaneous operation. For example, in the abstract:\n“This approach allows us to simultaneously prepare as many as seven individual Rydberg states”, if I have understood the\nmanuscript correctly, then each Rydberg state is prepared during a single sweep of the frequency of the coupling laser,\nwhich is done at a rate of 30 Hz, i.e. not simultaneously. Related to this point is whether FHSS and OFDM are compatible\nwith detection at this rate or whether further innovation is required. Clarification around this point would be appreciated.\nI have collected more minor comments by directly commenting on the pdf as I personally find this the most convenient way to\nreceive feedback. Please let me know if any questions are unclear.\nBest wishes,\nMark", "reviewer_2": "The manuscript by Prajapati and coworkers describe an optical scheme to measure RF waves in a range from 1 to 40 GHz\nby sensing modifications in the EIT in a Rydberg atoms cell. The scheme relies on a three-photon excitation stair where the\nupper pumping stage is provided by a mid-infrared frequency comb. The latter is generated from a near-infrared electro-optic\nfrequency comb, which is shifted to the MIR through a commercial CW OPO. This setup provides a comb pump which is\ntunable, frequency agile and robust. Through this scheme, the authors show the possibility to probe many different states of\nthe Rydberg manifold and thus sensitive, broadband RF detection.\nThe work presented is original and likely to be of interest not only in the field of Rydberg electrometry, but also for\ntelecommunications, for manipulation of neutral atoms and related fields. The proposed new technique is likely to bring a\nsignificant impact in these fields and beyond.\nThe methodology used in the work is sound and the results generally support the claims, except for one main point, which is\nthe first one I describe below. Moreover, in my opinion a few other points require clarification before I can recommend the\nmanuscript for publication:\n1. my main concern is the following: the authors state three times that they \"demonstrate [...] SIMULTANEOUS detection of a\nmultitude of RF tones\" (this verbatim is one of the statements, capitalization is mine). It seems to me that all the data\npresented in the manuscript (i.e. Figs. 3 and 4) is obtained by slowly scanning the whole comb by about 4 GHz at a rate of\nbe feasible, while I don't understand how simultaneous detection of multiple states (more than 2) could be achieved.\nThrough demodulation of the recorded probe signal? Or am I mistaken and all panels in the same column in Fig. 4 are\nmeasured simultaneously?\n2. In Figs. 2b and 2c the same transition is studied. Why the resonances occur at different comb detuning? From Fig. 2b I\nwould expect to see the splitting around -1670 MHz, not -1600.\n3. In Fig. 4, panel 73 P3/2 @ 30 GHz, what is the reason for the central resonance (the horizontal yellow line)?\n4. Methods/data acquisition: (this is related to point 1., maybe I am missing some important point about the measurement)\nwhy a 2.5 GSa/s sampling, if you measure EIT with a scan of the comb pump laser of 30 Hz? Is there a demodulation in\npost-processing that I'm missing?\nApart from these, I have a few minor remarks:\n* In the introduction, the authors explain the limitations of exploiting the resonant AT effect or non-resonant Stark shift for\nbroadband detection. Since these techniques are used as benchmarks in the Discussion, I would suggest to expand the\nparagraphs in the introduction by briefly explaining the phenomena and how they are usually employed in Rydberg\nelectrometry (e.g. mention typical measurement schemes) for the non-expert reader.\n* After \"Because only the signal beam is resonant within the OPO cavity, the optical frequency comb on the pump beam was\nefficiently and coherently transferred on to the mid-infrared idler beam\", please insert a reference to the relevant paper.\n* Table S1 is actually Figure A1.\n* \"By locking the coupling laser and tuning the comb spacing and tooth amplitudes\" can you address single tooth\namplitudes? Why would you need to do this, to equalize the response of different probed levels?", "reviewer_3": "Long and co-workers use a remarkable frequency comb (300 mW per tooth at 2.2 microns!) to demonstrate a Rydberg\nmicrowave receiver that can be quickly tuned to any number of Autler-Townes resonances. The experimental results confirm\nthe basic ideas and the discussion and analysis make a strong case that the method will be efficacious for various\ncommunication modes.\nWhat is curious to me are the extremely large RF levels that are detected in the experiment. THey state, \"Further, we\ndemonstrate that the seven individual states can provide orthogonal RF channels, allowing for simultaneous and highly\nsensitive detection of a multitude of RF tones\". Perhaps the wording is carefully saying that the only thing they have actually\ndone is show the orthogonality, and that with future work it could become highly sensitive. Because the sensitivity\ndemonstrated here is actually very unimpressive, the mentioned field being ~1 V/m, many orders of magnitude higher than\ntypical Rydberg sensor sensitivities. I understand that the real argument for this method is that a comparable classical\ntechnology would require an array of antennas, so perhaps it is not the sensitivity that is the issue. Nevertheless, the fields\nthey used are very large. Also curious is the remark, in passing, that the balanced detector was operating at shot noise limits.\nIf shot noise detection is necessary to detect 1 V/m, I am doubtful that the sensitivity of this scheme is sufficient for it to have\nthe impact suggested by the authors. Furthermore, I doubt that the complexity of a (very cool) state of the art OPO frequency\ncomb system is less than a classical antenna array.\nThus, while I admire the experiment being reported here, a sensitivity analysis is a key missing feature."}, "author_response": "Reviewer 1:\nData analysis based on EIA spectroscopy of Cs Rydberg states with principal quantum numbers around n\n= 75. The use of electromagnetically-induced absorption for such purposes is a well-established approach,\nand the spectra featured in the manuscript are convincing.\nThe methods section contains sufficient information for the work to be reproduced but would benefit from\nthe inclusion of information about the light polarisation of each beam (for completeness).\nEach of the lasers had linear polarization and were vertically polarized. The radiofrequency sources\nwere also set to have vertical polarization. We have added the following statement into the Laser\nParameters section: “The polarization of each of the lasers was set to be linear and vertical (relative\nto the optical table). The coupling laser polarization was optimized in order to minimize the central\npeak that forms from transitions not accessible by the RF fields.”\nIn addition, we added the following to the Radiofrequency Parameters section: “Each of the\nmicrowave horns were placed so that their polarization was linear and vertical (relative to the optical\ntable).”\nMy primary question regarding the manuscript is around the claim of simultaneous operation. For example,\nin the abstract:\n“This approach allows us to simultaneously prepare as many as seven individual Rydberg states”, if I have\nunderstood the manuscript correctly, then each Rydberg state is prepared during a single sweep of the\nfrequency of the coupling laser, which is done at a rate of 30 Hz, i.e. not simultaneously.\nWe thank the reviewer for this important point. We agree with the reviewer that the present approach\ndoes not currently allow for simultaneous Rydberg state preparation. However, the present method\nis fully amenable to rapid switching and provides a clear pathway towards simultaneous state\npreparation.\nWe have made changes to the manuscript to highlight and clarify this important point. We no longer\nstate that we have demonstrated simultaneous state preparation, but now note that we have\ndemonstrated the capability for rapid switching between Rydberg states (by changing the\nradiofrequency that drives the electro-optic frequency comb). In addition, we note that the present\napproach could be adapted for simultaneous state preparation in a two-photon configuration. By\nplacing combs on both the probe and coupling lasers, one could readily perform simultaneous,\nmultichannel detection.\nRelated to this point is whether FHSS and OFDM are compatible with detection at this rate or whether\nfurther innovation is required. Clarification around this point would be appreciated.\nWe have clarified this point in the manuscript. The frequency comb’s rapid switching is compatible\nwith FHSS.\nRegarding OFDM, while the present approach does not support OFDM, the two-photon\nconfiguration described above would be compatible with OFDM. This point is now described in detail\nin the manuscript. We thank the reviewer for bringing this to our attention.\nI have collected more minor comments by directly commenting on the pdf as I personally find\nthis the most convenient way to receive feedback. Please let me know if any questions are\nunclear.\nI did not receive a copy of the pdf with the reviews. Please let us know if there are further\ncomments which were not addressed in the current version of the manuscript.\nReviewer 2:\nThe methodology used in the work is sound and the results generally support the claims, except for one\nmain point, which is the first one I describe below. Moreover, in my opinion a few other points require\nclarification before I can recommend the manuscript for publication:\nMy main concern is the following: the authors state three times that they \"demonstrate [...]\nSIMULTANEOUS detection of a multitude of RF tones\" (this verbatim is one of the statements,\ncapitalization is mine). It seems to me that all the data presented in the manuscript (i.e. Figs. 3 and 4) is\nobtained by slowly scanning the whole comb by about 4 GHz at a rate of 30 Hz, so no simultaneous\ndetection (nor fast switching) is demonstrated here. I agree that fast switching should in principle\nbe feasible, while I don't understand how simultaneous detection of multiple states (more than 2) could be\nachieved. Through demodulation of the recorded probe signal? Or am I mistaken and all panels in the same\ncolumn in Fig. 4 are measured simultaneously?\nWe thank the reviewer for this important point. We agree with the reviewer that the present approach\ndoes not currently allow for simultaneous Rydberg state preparation. However, the present method\nis fully amenable to rapid switching and provides a clear pathway towards simultaneous state\npreparation.\nWe have made changes to the manuscript to highlight and clarify this important point. We no longer\nstate that we have demonstrated simultaneous state preparation, but now note that we have\ndemonstrated the capability for rapid switching between Rydberg states (by changing the\nradiofrequency that drives the electro-optic frequency comb).\nIn addition, we note that the present approach could be adapted for simultaneous state preparation\nin a two-photon configuration. By placing combs on both the probe and coupling lasers, one could\nreadily perform simultaneous, multichannel detection.\nWe have also clarified the discussion regarding the FHSS and OFDM protocols. The rapid switching\nwhich the present method enables is compatible with FHSS. Regarding OFDM, while the present\napproach does not support OFDM, the two-photon configuration described above would be\ncompatible with OFDM. This point is now described in detail in the manuscript. We thank the\nreviewer for bringing this to our attention.\nIn Figs. 2b and 2c the same transition is studied. Why the resonances occur at different comb detuning?\nFrom Fig. 2b I would expect to see the splitting around -1670 MHz, not -1600.\nThe reviewer is correct. The zero was slightly offset on the two days the data was acquired, leading\nto a difference in this offset. While the frequency scale was established using the atomic resonance\nlines, the lines themselves were adjusted and aligned using a cavity reference. The frequency offset\ncorrection was done manually since the splitting of the lines was independent of the offset. The\naccurate value for the state should be roughly -1665 MHz based on the calculation. However, the\ncalculation of the atomic lines is not always perfect and can deviate from the actual atomic resonance.\nHere we see that the value for this resonance is roughly -1620 MHz. The percent error on this is less\nthan 3 %. For this demonstration, this is sufficient. In future studies, we can explore the deviations\nfrom the calculated values more thoroughly and whether the deviations arise from theory or\ninaccuracies in the laser scan and comb clock. We have also added the measured values for the\ndifferent peaks and the percent error associated with each of these to Table 1.\nIn Fig. 4, panel 73 P3/2 @ 30 GHz, what is the reason for the central resonance (the horizontal yellow\nline)?\nThis line is due to the polarization of the RF relative to the lasers. If the polarization is mismatched,\nthere will be magnetic sublevels that do not shift in response to the RF. However, this will only be seen\nfor P→S transitions and not P→D transitions of the RF field (as shown in\nhttps://arxiv.org/pdf/2503.17997, shown below). We utilized several horns with slight variations in\nangles relative to the atoms. This likely caused variations in the polarization that are most obvious in\nthe high frequency horn. For example, the 30 GHz transition for 73P is to an S state, while the 35\nGHz transition for the panel for 75P is a transition to a D state, and we do not see the central peak.\nWhile we set the polarizations of the horns and lasers to minimize this peak, reflections and scattering\nof the RF can cause the peak to appear and be strong.\nWe have added the following text to the manuscript: “A central peak can be observed in this figure\nand this peak is a result of the relative polarization of the RF and optical fields.”\nMethods/data acquisition: (this is related to point 1., maybe I am missing some important point about the\nmeasurement) why a 2.5 GSa/s sampling, if you measure EIT with a scan of the comb pump laser of 30 Hz?\nIs there a demodulation in post-processing that I'm missing?\nThe 2.5 GSa/s is from the oscilloscope that we use to obtain the traces. There is no post-processing.\nThe total number of points in the spectrum below is (2.5GSa/s)/30Hz=80×106. This leads to a\nfrequency resolution of 60 Hz. This ensured that we are not undersampling the atomic lines, which\nwould cause artificial broadening. To clarify, we have added the following sentences to the\nmanuscript: “The oscilloscope sampling rate was 2.5 GSa/s, making the frequency separation\nbetween points in the spectra 60 Hz in laser frequency. This is substantially below the linewidth and\navoids electronic artifacts that can broaden the spectrum.”\nApart from these, I have a few minor remarks:\n* In the introduction, the authors explain the limitations of exploiting the resonant AT effect or non-\nresonant Stark shift for broadband detection. Since these techniques are used as benchmarks in the\nDiscussion, I would suggest to expand the paragraphs in the introduction by briefly explaining the\nphenomena and how they are usually employed in Rydberg electrometry (e.g. mention typical\nmeasurement schemes) for the non-expert reader.\nWe thank the reviewer for this suggestion. We have added the following into the introduction:\n“The AT effect occurs when a field resonant with two states of the atoms perturbs and splits each of\nthese energy levels, causing an observable change in the absorption signal of a probe laser. The probe\nlaser is combined with a coupling laser and possible dressing lasers chosen to excite the atoms and\nreadout the selected Rydberg state. The splitting frequency of this state is directly proportional to the\nmagnitude of the radiofrequency (RF) electric field given the dipole moment of the resonant RF\ntransition.”\nAnd\n“Under the Stark shift condition, the RF field is far detuned (>100 MHz) from the resonance\nfrequency between the two Rydberg states. Rather than inducing a splitting, this off-resonant field\nshifts the selected Rydberg state, and the frequency of this shift is proportional to the magnitude of\nthe RF electric field squared times the polarizability of the state.”\n* After \"Because only the signal beam is resonant within the OPO cavity, the optical frequency comb on\nthe pump beam was efficiently and coherently transferred on to the mid-infrared idler beam\", please insert\na reference to the relevant paper.\nWe have added a pair of relevant references.\n* Table S1 is actually Figure A1.\nThis has been corrected. The Appendix table is now referred to as Table A1 throughout the\nmanuscript.\n* \"By locking the coupling laser and tuning the comb spacing and tooth amplitudes\" can you address\nsingle tooth amplitudes? Why would you need to do this, to equalize the response of different probed\nlevels?\nHere we referring to the ability to rapidly change the comb spacing in order to rapidly switch between\ndifferent Rydberg states. This would enable protocols such as FHSS. The amplitude portion of that\nstatement indicated that we can change the number of comb teeth (but not single tooth amplitudes).\nWe could, for instance, reduce the number of comb teeth for use in the rapid switching case. This is\na small point and made the sentence less clear, as a result we removed the reference to “tooth\namplitudes.”\nReviewer 3:\nLong and co-workers use a remarkable frequency comb (300 mW per tooth at 2.2 microns!) to demonstrate\na Rydberg microwave receiver that can be quickly tuned to any number of Autler-Townes resonances. The\nexperimental results confirm the basic ideas and the discussion and analysis make a strong case that the\nmethod will be efficacious for various communication modes.\nWhat is curious to me are the extremely large RF levels that are detected in the experiment. They state,\n\"Further, we demonstrate that the seven individual states can provide orthogonal RF channels, allowing\nfor simultaneous and highly sensitive detection of a multitude of RF tones\". Perhaps the wording is carefully\nsaying that the only thing they have actually done is show the orthogonality, and that with future work it\ncould become highly sensitive.\nBecause the sensitivity demonstrated here is actually very unimpressive, the mentioned field being ~1 V/m,\nmany orders of magnitude higher than typical Rydberg sensor sensitivities. I understand that the real\nargument for this method is that a comparable classical technology would require an array of antennas, so\nperhaps it is not the sensitivity that is the issue. Nevertheless, the fields they used are very large. Also\ncurious is the remark, in passing, that the balanced detector was operating at shot noise limits. If shot noise\ndetection is necessary to detect 1 V/m, I am doubtful that the sensitivity of this scheme is sufficient for it to\nhave the impact suggested by the authors. Furthermore, I doubt that the complexity of a (very cool) state of\nthe art OPO frequency comb system is less than a classical antenna array.\nWe thank the reviewer; this is a very important distinction. The sensitivity was not evaluated for this\nsystem. When we state that we can achieve highly sensitive detection, it is because the three-photon\nsystem has a Doppler canceling that the two-photon systems do not and can achieve very narrow\nlines. So, in the sentence where we state “highly sensitive detection”, we have added “theoretically”\nto avoid ambiguity of the measurement. The standard two-photon system can achieve 5\n𝛍𝐕𝐦−𝟏𝐇𝐳−𝟏/𝟐 sensitivity. This is achieved by using a mixer approach with the atoms and looking at\nthe beat-note on a spectrum analyzer. We have not taken that step. In out paper titled “Investigation-\nof-fluorescence-versus-transmission”\n(https://pubs.aip.org/avs/aqs/article/6/3/034401/3302129/Investigation-of-fluorescence-versus-\ntransmission), we have demonstrated sensitivity in three-photon system down to 8 𝛍𝐕𝐦−𝟏𝐇𝐳−𝟏/𝟐 for\nfluorescence measurements and 30 𝛍𝐕𝐦−𝟏𝐇𝐳−𝟏/𝟐 for EIA based measurements. Because we are\nsplitting our power into 7 channels, we decrease out power for each mode by the same factor. There\nis a scaling of the Rabi rate to the sensitivity of the system. If we locked our laser and performed\nheterodyne detection, we would expect our sensitivity in this system to be worse than 300\n𝛍𝐕𝐦−𝟏𝐇𝐳−𝟏/𝟐 . However, this is not the objective of the paper, as it is something that can be overcome\nwith more laser power as opposed to a limitation of the atoms. The core result we wish to highlight in\nthis publication is that multiband detection of this level traditionally requires 5 different horn\nantennas. We achieved this with a single receiver.\nWe add the following statement to emphasize this:\n“However, we can substantially reduce the field strength and still observe splitting. In past three-\nphoton EIA/EIT systems involving these lasers, we have demonstrated sensitivity down to 30\n𝛍𝐕𝐦−𝟏𝐇𝐳−𝟏/𝟐 [45]. Since the sensitivity of the sensor scales with the power in the coupling laser, we\ncan extrapolate that previous sensitivity to the present comb approach (where the use of a comb\nreduces the coupling laser power probing a given state) to be near 300 𝛍𝐕𝐦−𝟏𝐇𝐳−𝟏/𝟐 ."}, {"round": 2, "reviewer_comments": {"reviewer_1": "Dear authors,\nThank you for taking my comments on board and for updating and improving the manuscript. I think it is stronger as a result.\nI apologise that you didn’t receive all my previous comments, which were directly on the PDF. I will forward these to the\neditor again. I see that almost all of them have already been covered in the updated version. I will leave the remainder with\nyou to implement as you see fit.", "reviewer_2": "The authors have addressed all the points raised by me and other referees. I thus suggest the publication of the manuscript.", "reviewer_3": "The authors have responded to my observations about the extremely poor sensitivity in this system by adding remarks about\nextrapolating their previous single-channel results with heterodyne to detection to the multi-channel comb configuration\ndiscussed in the paper. While I can't argue with their logic, reading it while simultaneously looking at their Fig 4 data really\nstrains credulity. If it weren't for the dashed fit lines, I'm not sure I could identify the signal in some of the channels. At 1 V/m!\nThe motivations driving Rydberg RF sensors are accuracy and sensitivity. For accuracy, befitting the core mission of NIST, I\ndon't care about the sensitivity. But this paper is all about the \"potential to serve as agile and wideband electromagnetic\nreceivers\". Receivers are all about sensitivity. A key point to any advance in the technology is that it has to preserve the\nsensitivity; it really doesn't matter what new methodologies are presented if they sacrifice the sensitivity.\nIn my view, the authors failure to demonstrate their advertised 300 microV/cm/sqrt(Hz) sensitivity labels this work as\nincremental. They've got to show that the multiplexing preserves the sensitivity, otherwise I'm just not interested. I'm\nguessing that the reason they didn't do this is that it is complicated, both experimentally and in analysis, to add the 7 local\noscillators. But that's what a real system would have to do. This is an ongoing challenge for sensor arrays, which this\nessentially is. If a new capability adds too much complexity, it will remain a curiousity and not really advance the field."}, "author_response": "Response to Reviewers\nReviewer #1:\nDear authors,\nThank you for taking my comments on board and for updating and improving the manuscript. I\nthink it is stronger as a result. I apologize that you didn’t receive all my previous comments,\nwhich were directly on the PDF. I will forward these to the editor again. I see that almost all of\nthem have already been covered in the updated version. I will leave the remainder with you to\nimplement as you see fit.\nWe thank the reviewer for their careful reading of our manuscript and are pleased to hear\nthat they believe that it was significantly stronger. We have read through the PDF which\nwas sent and believe that all suggested changes have been incorporated into the current\nmanuscript.\nReviewer #2:\nThe authors have addressed all the points raised by me and other referees. I thus suggest the\npublication of the manuscript.\nWe are pleased to hear that the reviewer views the manuscript as suitable for publication.\nWe thank them for their careful reading of paper and believe that it has been significantly\nstrengthened by this process.\nReviewer #3:\nThe authors have responded to my observations about the extremely poor sensitivity in this\nsystem by adding remarks about extrapolating their previous single-channel results with\nheterodyne to detection to the multi-channel comb configuration discussed in the paper. While I\ncan't argue with their logic, reading it while simultaneously looking at their Fig 4 data really\nstrains credulity. If it weren't for the dashed fit lines, I'm not sure I could identify the signal in\nsome of the channels. At 1 V/m!\nWe thank the reviewer for this note as it reveals an aspect of the manuscript which was\npreviously unclear. Importantly, as the applied field increases to large strengths it causes\nsuch a high degree of splitting that the spectra appear to vanish. This can be seen in Figure\n3b, as the applied field increases to large values the split feature loses intensity (the figure is\nreproduced below). Thus, decreasing the field strength has the effect of moving the peaks\ntogether, not reducing their strength.\nAs further evidence of this effect, we plot three spectra below for different field values. At\n0.069 V/m we can observe a weak splitting. The splitting becomes both larger and more\napparent as we move to 0.675 V/m, until becoming difficult to observe due to the large\nsplitting at 2.11 V/m.\n250\n0.069484 V/m\n0.67527 V/m\n2.1172 V/m\n200\n)\ns\nt\ni\nn\nU\nb . 150\nr\nA\n(\nA\nI\nE\n100\n50\n-1680 -1660 -1640 -1620 -1600 -1580 -1560\nCoupling Laser Detuning (MHz)\nAs a result, the signal is more prominent at lower fields, which is the regime where\nsensitivity is generally quantified. To clarify this point and avoid confusion, we have\nadjusted figure 3(b) to give the calibrated value for the field rather than the power of the\nRF source. We have added parts of this discussion to the manuscript.\nReturning to Figure 4, for this demonstration we chose a field strength of 1 V/m to\nguarantee a response from each state at each of the different frequencies that we were\nprobing. As a result, in some cases this field is very large and therefore leads to weak\nobserved signals (which would appear more prominent at lower fields). We note that that\nfigure was intended to demonstrate the frequency orthogonality of this new method rather\nthan quantify the sensitivity.\nThe motivations driving Rydberg RF sensors are accuracy and sensitivity. For accuracy,\nbefitting the core mission of NIST, I don't care about the sensitivity. But this paper is all about\nthe \"potential to serve as agile and wideband electromagnetic receivers\". Receivers are all about\nsensitivity. A key point to any advance in the technology is that it has to preserve the\nsensitivity; it really doesn't matter what new methodologies are presented if they sacrifice the\nsensitivity.\nWhile we agree that sensitivity and accuracy are important metrics for Rydberg RF\nsensors, bandwidth is another critical element. For secure communications protocols, such\nas frequency hopping shared spectrum (FHSS) or orthogonal frequency division\nmultiplexing (OFDM), the goal is to make sure no other receiver can decode the\ninformation. These protocols are normally limited to narrow bands of a single antenna. To\ncover our demonstrated range of bands, roughly five separate antennas would be necessary.\nThus, we note that our approach is not centered on producing a more sensitive sensor but\nrather unlocking fundamentally new capabilities that have not previously been possible\nwith Rydberg sensors. To clarify this point in the manuscript we have added an additional\ndiscussion to the introduction.\nIn my view, the authors failure to demonstrate their advertised 300 microV/cm/sqrt(Hz)\nsensitivity labels this work as incremental. They've got to show that the multiplexing preserves\nthe sensitivity, otherwise I'm just not interested. I'm guessing that the reason they didn't do this is\nthat it is complicated, both experimentally and in analysis, to add the 7 local oscillators. But that's what a real system would have to do. This is an ongoing challenge for sensor arrays,\nwhich this essentially is. If a new capability adds too much complexity, it will remain a curiousity\nand not really advance the field.\nWe note that given that this is an initial demonstration of this method, we did not employ\nlock-in detection. Lock-in detection has been shown to increase the sensitivity of Rydberg\nsensors by more than two orders of magnitude through a reduction in low frequency noise\n(see the figure below) [From Simons, M. T. et al. J. Appl. Phys 123, 203105 (2018)].\nThe minimum detected field (shown above at 69 mV/m) and this expected scaling based\nupon the use of lock-in detection yields a sensitivity which is consistent with the value\npreviously given in the paper. In light of the comments from the reviewer we have rewritten\nthat section of the paper and believe the sensitivity is better supported. However, we believe\nthe merit of the present paper is given by the dramatically expanded capabilities of the\nmethod and that there is substantial room for future engineering and optimization to\nfurther improve the sensitivity."}]

Decision letter