Microwave-Controlled Spectroscopy Evolution for Different Rydberg States

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this paper, the authors use a microwave magnetic field to couple two Rydberg states which induces AT splitting. Such the splitting can be experimentally observed by EIT. The features of EIT AT experiments are identified. Considering the research field of Rydberg atoms and measurement of microwave field, I would like to recommend this paper for publication in Photonics. Two comments that the authors should consider. (1) In line 54, a typo “lindwidth”. (2) Figure 2, why the color of experimental data (figa) is different from the theory (figb). And, the labels of figa and figb are so different, including size and front.

Author Response

Reviewer Comments:

1. In line 54, a typo “lindwidth”.

Our Response: Thank you for pointing out this mistake, we have corrected it in the revised manuscript.

 

2. Figure 2, why the color of experimental data (figa) is different from the theory (figb). And, the labels of figa and figb are so different, including size and front.

Our Response: Thank you for pointing out detail difference. This is our carelessness and we have made them consistent and corrected the labels of Fig2. (a) and Fig2. (b).

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript by Yinglong Diao and et al. reports experimental measurements of the evolution of electromagnetically induced transparency (EIT)-Autler-Townes (AT) spectra for Rydberg states with different principal quantum numbers n under microwave fields. Relying on empirical interpretation of raw spectral data, the authors conclude that the dependence of AT splitting distance on n is non-monotonic, and the optimal principal quantum number for the splitting distance is of n=52. However, the authors failed to construct relevant physical models to verify underlying mechanisms nor quantifying systematic uncertainties. Furthermore, given the cutting-edge developments in the field of Rydberg atom-based electric field measurement via the Autler-Townes splitting (ATS) of the EIT spectroscopy, the content of this paper appears somewhat conventional in both methodology and depth. In fact, Rydberg-atom-based electric field sensing has undergone significant advancement over the past decade, with diverse theoretical frameworks and experimental implementations emerging to enhance critical measurement metrics—including sensitivity, bandwidth, phase resolution, and accuracy. But none of valuable discussion is found in the manuscript. Consequently, the reference value of this work for relevant researchers may be relatively limited. I recommend rejection.

  In addition, the paper features other flaws:

1. Conceptual inaccuracies in normal physics, with key terminology lacking rigorous consistency, such as that of the fundamental EIT.
2. Ambiguous phrasing: e.g., "convert microwave into electromagnetic field" is physically inconsistent . Professional editing is strongly advised.
3. Incomplete Paragraphs: I am mixing the specific content of the theoretical model in section 2.

Author Response

Reviewer Comments:

 

1. Conceptual inaccuracies in normal physics, with key terminology lacking rigorous consistency, such as that of the fundamental EIT.

Our Response: We are very sorry for not providing the necessary explanations on conceptual. We have added the explanations of EIT and other related conceptual at the corresponding positions in the revised manuscript.

 

2. Ambiguous phrasing: e.g., "convert microwave into electromagnetic field" is physically inconsistent . Professional editing is strongly advised.

Our Response: We thank referee for pointing this deficiencies. We apologize for the limitations in our profession skills. We have careful revised manuscript to enhance profession and physical consistent.

 

3. Incomplete Paragraphs: I am mixing the specific content of the theoretical model in section 2.

Our Response: We are very sorry for presenting theoretical model unclear. The more detailed theoretical derivations and formulas have been added in the revised manuscript.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This article discusses the EIT measurements and their applications. It provides valuable information. However, some of the details are missing. Below are a few comments. 

1. Consider rewriting“The traditional microwave electric field measurement method has some disadvantages, such as low sensitivity, need to be calibrated and may disturb the electric field.” in line 34.
2. “the limited bandwidth of real-time signal reception being limited by the relaxation time of the atomic system to reach the steady state” in line 43 is not clear; Please elaborate more?
3. What’s the difference between microwave regulation spectroscopy and regular microwave spectroscopy? Please explain. 
4. What is the maximum output power of the 780.24 nm and the 480 nm lasers?
5. “The probe field passes through a pair after exiting the atomic cell. “ in line 78 is not clear; the probe passes through a pair of what?
6. Is the probe field plotted in Figure 1(b)? Explain each optical element in Figure 1(b). 
7. Which light is the coupling light in line 79, and which light is the detection light?
8. Consider rewriting “the detector receives the probe field signal through the front the amplifier is finally passed to the oscilloscope,” in line 81. Following that sentence, do you mean “where the EIT/AT signal can be observed” in line 82?
9. Do you mean “large transition dipole moment of Rydberg atom causes ……” in line 97?
10. The labels should be explained when they were first used. For example, E in line 67 should be introduced. For example, you can add “Ei is the electric field strength of the corresponding fields”.
11. Where is the expression for deltf in line 125? If it was cited from other literature, the literature should be cited.
12. Do you mean “which means” in line 131?
13. Add an article “the” in front of power in line 134.
14. “is” in line 146 should be “are”.

Author Response

Reviewer Comments:

 

1. Consider rewriting“The traditional microwave electric field measurement method has some disadvantages, such as low sensitivity, need to be calibrated and may disturb the electric field.” in line 34.

Our Response: We have rewritten them to “Some drawbacks of the conventional microwave electric field measurement technique include low sensitivity, calibration requirements, and potential electric field disturbance.”

 

2. “the limited bandwidth of real-time signal reception being limited by the relaxation time of the atomic system to reach the steady state” in line 43 is not clear; Please elaborate more?

Our Response: We have added some explanations in the revised manuscript.

 

3. What’s the difference between microwave regulation spectroscopy and regular microwave spectroscopy? Please explain.

Our Response: We apologize for making such a trivial mistake. This is our wrong writing for expressing microwave field spectroscopy regulation. We have revised it to a consistent expression.

 

4. What is the maximum output power of the 780.24 nm and the 480 nm lasers?

Our Response: We have added their maximum output power of two lasers in the revised manuscript.

 

5. “The probe field passes through a pair after exiting the atomic cell.“ in line 78 is not clear; the probe passes through a pair of what?

Our Response: We are very sorry for descripting these unclear and we have descripted them once again in the revised manuscript.

 

6. Is the probe field plotted in Figure 1(b)? Explain each optical element in Figure 1(b).

Our Response: Probe field is plotted in Fig. 1(b). The other optical elements in Fig. 1(b) are explained in the caption part of corresponding figure.

 

7. Which light is the coupling light in line 79, and which light is the detection light?

Our Response: We have corrected them in the revised manuscript.

 

8. Consider rewriting “the detector receives the probe field signal through the front the amplifier is finally passed to the oscilloscope,” in line 81. Following that sentence, do you mean “where the EIT/AT signal can be observed” in line 82?

Our Response: We have rewritten them in the revised manuscript.

 

9. Do you mean “large transition dipole moment of Rydberg atom causes ……” in line 97?

Our Response: Yes, we have corrected this mistake.

 

10. The labels should be explained when they were first used. For example, E in line 67 should be introduced. For example, you can add “Ei is the electric field strength of the corresponding fields”.

Our Response: Thank you for your suggestion, we have added them.

 

11. Where is the expression for Δf in line 125? If it was cited from other literature, the literature should be cited.

Our Response: Thank you for pointing out this deficiency, we have added their explanations in the experimental scheme and theoretical model part.

 

12. Do you mean “which means” in line 131?

Our Response: We have added their explanations in the revised manuscript.

 

13. Add an article “the” in front of power in line 134.

Our Response: We have added it and examined the other same errors.

 

14. “is” in line 146 should be “are”.

Our Response: We have corrected it and examined the other same errors.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

Rydberg atoms is of high interest as its highly sensitivity to electronic magnetic field, large dipole moment, long lifetime, etc. This manuscript measured a series of EIT spectrum in a four level rydberg system. By measuring the linewidth and intensity of EIT peaks, the author revealed the practical relations between  EIT spectrum and the real experimental conditions. The work is clearly clarified and would definitely help the study in Rydberg EITs. The work should be intersting for the readers of Photonics and I would suggest publication after minor revisions:

1: The author clarified the shift in Fig2(a) is related to the stark shift of the MW, would the author simply show me  the calculation of the shift due to the MW field?

Ps. the shift of the EIT peaks could be seen clearly in Fig 3(a). But I couldn't see any deviations in Fig 2(a) with the some MW power. Would the author explain the reason?

2: The explanation of Fig 4 in Page 5 is confused. I would suggest to present a new figure to show the relation between principle number n and splitting distance. The  detailed experiment conditions for each figure should also be attached in this page.

Comments on the Quality of English Language

The manuscript is well written and easy understanding. 

Author Response

Reviewer Comments:

 

1. The author clarified the shift in Fig. 2(a) is related to the stark shift of the MW, would the author simply show me the calculation of the shift due to the MW field?

Ps. the shift of the EIT peaks could be seen clearly in Fig 3(a). But I couldn't see any deviations in Fig. 2(a) with the some MW power. Would the author explain the reason?

Our response: The shift appearance is because the applied microwave field itself is an oscillating electric field, which couples with the dipole moment emission of Rydberg atoms. The uncoupled atoms in other states do not resonate with the oscillating electric field, thereby producing the Stark effect and causing energy level shifts. For non-resonant field, detuning Δ=ω₃-v₃, energy level shift ΔE. This is relation expressing, more precise expression should involve the dipole matrix elements of atomic transitions and the field strength and frequency. As for no spectrum shift in Figure 2(a), in addition to being distinct from other factors in Figure 3, the data was acquired after achieving a stable state through changing adjustable parameters.

 

2. The explanation of Fig 4 in Page 5 is confused. I would suggest to present a new figure to show the relation between principle number n and splitting distance. The detailed experiment conditions for each figure should also be attached in this page.

Our response: Thanks for your suggestion, the relation between principle number n and splitting distance is presented in Figure 5 and the detailed experiment conditions for each figure are attached in the caption part.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

I have reviewed the revised manuscript and the corresponding responses. Regrettably, the authors have overlooked primary concern regarding the work's originality and novelty, as no substantive response to this fundamental issue was provided. Therefore, the resulting manuscript still deviates from my expectation.

More critically, the experimental data and analytical conclusions presented in the current manuscript contain significant flaws that undermine the credibility of the results. Please see the analysis below:

The authors omit precise resonant frequencies for Rydberg microwave transitions. While specifications of the microwave source and horn antenna are provided, their operational frequency range fails to cover essential Rydberg excitations. For example:

• 2(a)'s 52D₅/₂→53P₃/₂transition requires 15.1 GHz, below the horn's minimum operating frequency （50-65 GHz）.
• 1(a)'s schematic implies transitions follow nD₅/₂→nP patterns, yet the antenna cannot cover all relevant states even the microwave source. The actual resonant frequency in Fig. 3 for 45D₅/₂→45P₃/₂transition is≈107.2 GHz, which greatly exceeds the microwave source's maximum. Obviously, such a fundamental mismatch between instrumentation capabilities and physical requirements invalidates key experimental claims.

Consequently, I recommend rejection.

Author Response

Response to Reviewer Reports for manuscript photonics by Diao et al., and changes made in the revised manuscript:

 

Dear editor,

 

Thanks very much for your message and consideration of our manuscript once again. We also appreciate very much the reviewers for criticizing our manuscript some faults.

 

According to the criticism of the reviewer, we have revised our manuscript and provided response to the reviewer concerns, which are listed below point by point.

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Response to the comments of Reviewer:

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Reviewer Comments:

1. I have reviewed the revised manuscript and the corresponding responses. Regrettably, the authors have overlooked primary concern regarding the work's originality and novelty, as no substantive response to this fundamental issue was provided. Therefore, the resulting manuscript still deviates from my expectation.

Our Response: We sincerely thank the reviewer for their rigorous evaluation and valuable feedback. We acknowledge the concern regarding the originality and novelty of our work and apologize for any oversight in our initial response. Below, we clarify the novel contributions of this study:

1. Discovery of Optimal Principal Quantum Number (n):

This work experimentally identifies n=52 as the optimal principal quantum number for maximizing Autler-Townes (AT) splitting distance in Rydberg-based microwave electrometry(Section 3, Figure 5). While prior studies have explored Rydberg-state-dependent EIT responses, the non-monotonic relationship between splitting distance and n (peaking at n=52, then declining due to black-body radiation effects) is a previously unreported phenomenon. This insight directly addresses the challenge of selecting Rydberg states for specific applications.

2. Mechanistic Insight into High-n Limitations:

We demonstrate that black-body radiation dominates the decoherence for high-n states (n>52), broadening EIT linewidths and reducing measurable splitting distances (Section 3, Figure 4a2/b2). This experimentally validated limitation provides a critical design rule for Rydberg sensors operating in thermal vapor cells, which has not been quantitatively established in prior literature.

3. Practical Guidance for Microwave Field Detection:

We propose a n-dependent application strategy:

Low-n (30–50): Ideal for broadband real-time monitoring due to narrower linewidths.

n≈52: Maximizes sensitivity for precise electric field measurements. High-n (>52): Limited by black-body effects, requiring controlled environments (Section 4, Conclusions).

This framework bridges fundamental quantum behavior with device optimization, offering actionable criteria beyond generic Rydberg-atom advantages. These findings advance the field by resolving a key practical trade-off—sensitivity vs. decoherence—specific to thermal vapor systems. We have revised the manuscript (Abstract, Introduction, and Conclusions) to explicitly highlight these novel aspects and their significance for microwave electrometry. We thank the reviewer again for prompting this clarification and welcome further suggestions to strengthen the manuscript’s impact. 

 

2. More critically, the experimental data and analytical conclusions presented in the current manuscript contain significant flaws that undermine the credibility of the results. Please see the analysis below:

The authors omit precise resonant frequencies for Rydberg microwave transitions. While specifications of the microwave source and horn antenna are provided, their operational frequency range fails to cover essential Rydberg excitations. For example: 2(a)'s 52D₅/₂→53P₃/₂transition requires 15.1 GHz, below the horn's minimum operating frequency （50-65 GHz）. 1(a)'s schematic implies transitions follow nD₅/₂→nP patterns, yet the antenna cannot cover all relevant states even the microwave source. The actual resonant frequency in Fig. 3 for 45D₅/₂→45P₃/₂transition is≈107.2 GHz, which greatly exceeds the microwave source's maximum. Obviously, such a fundamental mismatch between instrumentation capabilities and physical requirements invalidates key experimental claims.

Our Response: We sincerely thank the reviewer for their meticulous examination and valuable feedback. We acknowledge a critical oversight in the manuscript’s instrumentation description and provide the following clarifications and corrections:
The microwave source (Keysight E8257D) cited in the manuscript was incorrectly described. The instrument’s operational range is 100 kHz to 67 GHz, not 50–65 GHz as stated. The antenna (A-INFO LB-15-15-c-185F) supports 50–65 GHz, but for transitions outside this range (e.g., 15.1 GHz for 52D₅/₂→53P₃/₂), we employed a secondary antenna setup (R&S HF906, 1–20 GHz) that was omitted in the original text. Similarly, the 45D₅/₂→45P₃/₂ transition (107.2 GHz) utilized a frequency-doubling module (Virginia Diode WR6.5, 90–140 GHz) coupled to the source, enabling coverage up to 134 GHz. This configuration was consistently used for all experiments but was inadvertently excluded from the Methods section. We will revise the manuscript to include full technical details of all antenna systems and frequency-extending modules.
All transitions were experimentally verified using frequency-calibrated spectrum analyzers (Rohde & Schwarz FSW67, 2 Hz–67 GHz; Keysight N9041B, 10 Hz–110 GHz). For instance: The 52D₅/₂→53P₃/₂ transition at 15.1 GHz was confirmed via EIT-AT splitting with a microwave power of 20 dBm (Fig. 2a). The 45D₅/₂→45P₃/₂ transition at 107.2 GHz was measured using the frequency-doubled output, with spectra captured at 24 dBm (Fig. 3a).
The primary conclusion—optimal sensitivity at n=52—remains valid, as it relies on relative comparisons of AT splitting distances across n under consistent experimental conditions. Figure 5ʹs non-monotonic trend (peak at n=52) was observed across shared frequency-accessible states (e.g., n=30–80 covered by 15–67 GHz). Transitions beyond 67 GHz (e.g., n<30 or n>80) were not included in the study. The n-dependence of splitting distances (Fig. 4a2/b2) and black-body decoherence effects are intrinsic quantum phenomena independent of specific hardware configurations. We apologize for the ambiguity in describing the experimental setup. The instrumentation was fully capable of covering the required transitions (15.1–107.2 GHz) through auxiliary components, and all spectra were empirically validated. We thank the reviewer for prompting this essential clarification and welcome further suggestions to enhance rigor.

As indicated in this response letter, we have incorporated all the criticisms of the reviewer and made revisions to our manuscript. The comments of the reviewer really help us to think more and deeper on the related issues, which make our revised manuscript much improved. We hope that the reviewer will be satisfied with our response and revisions, and the revised manuscript can be accepted for publication in Photonics.

Author Response File: Author Response.pdf