Experimental Observation of the Suppression of the Dephasing in a Floquet Engineering Optical Lattice Clock

Round 1

Reviewer 1 Report

The authors present some interesting results about the modification of the dephasing of the Rabi oscillation caused by periodic perturbations in time. I can not judge the quality and the reliability of the experimental work but the results seem to be reasonable and would certainly initiate further research. However the quality of the paper should be improved before the publication.

1. The motivation of the work and the theoretical background are too sketchy and render the paper readable only for specialist. The sensitivity of the dephasing on periodic perturbation is an interesting phenomenon which should be accessible for a wider audience. Therefore some improvement should be made in the presentation.

2. Few features of the experimental results should be explained or commented in a more complete manner.

2a. Can one understand qualitatively the ratio of the height of the peaks in Fig. 3(b)? Why do the three central peaks have approximately equal height?

2b. What makes the peaks in Fig. 4? Can one estimate the order of magnitude of the pulse duration at the peak? Why is the suppression of the dephasing by FE is the strongest in Fig. (d)?

Author Response

1. The motivation of the work and the theoretical background are too sketchy and render the paper readable only for specialist. The sensitivity of the dephasing on periodic perturbation is an interesting phenomenon which should be accessible for a wider audience. Therefore, some improvement should be made in the presentation.

Response: We thank the referee for this helpful suggestion. For attracting a wider audience, in the introduction, we have added this sentence “In addition, dephasing is also one of the major challenges in many quantum sciences, such as quantum communication [20], and quantum information processing [21].” to underline the dephasing effect is the one of the major challenges in many quantum sciences.

2. Few features of the experimental results should be explained or commented in a more complete manner

Response: We thank the referee for thoughtful suggestion. In the revised manuscript we added the following sentences to explain the experimental results:

On the caption of Figure 3, we added “The reason why the 0th and 1th Floquet sidebands have approximately equal height is that the 0th and 1th sidebands have similar effective Rabi frequencies at this modulation amplitude.” to explain why the three central peaks have approximately equal height.

On the Page 6, we added “This shows that the FE can simultaneously suppress the dephasing caused by the thermal distribution of atoms and the atomic interaction.”

2a. Can one understand qualitatively the ratio of the height of the peaks in Fig. 3(b)? Why do the three central peaks have approximately equal height?

Response: The ratio of the height of the peaks in Fig. 3(b) is determined by the modulation amplitude A. In this work, A=0.72, and thus, J1[2A]~J0[2A], which  indicates that the 0th and 1 th Floquet sidebands have the similar effective Rabi frequency and so, have approximately equal height. However, the ratio of the height of the peaks is irrelevant to the research focus of this paper, as we only used the peak excitation fraction of the 0th sideband.

2b. What makes the peaks in Fig. 4? Can one estimate the order of magnitude of the pulse duration at the peak? Why is the suppression of the dephasing by FE is the strongest in Fig. (d)?

Response: The peaks in Fig. 4 are determined by the effective Rabi frequency (Ωeff) of carrier. One can approximately estimate the pulse duration (tp) at the peak by the relationship of Ωeff×tp=π. In terms of the last question, we think the FE can simultaneously suppress the dephasing caused by the temperature of cold ensemble and the atomic interaction, and thus in Fig. 4(d), the suppression of the dephasing is the strongest as there are both high temperature and atomic density. In the future, combining with theorical calculations and more experimental measurements, the possible mechanism behind the experimental results may be revealed.

Author Response File: Author Response.pdf

Reviewer 2 Report

Authors investigate the suppression of the dephasing in the optical lattice clock by Floquet engineering effect on the excitation of clock transitions. Experiments show utility of low-intensity, low-modulation frequency (RF) Floquet driving to engineer Rabi flopping process of an ultracold atomic gas in an optical lattice. Figure 4 suggests that additional dephasing introduced from atomic motion and inter-atomic interactions is suppressed due to new dynamics in the Floquet manifold induced by sinusoidally modulating the incident lattice laser frequency and resulted in a split of 1S₀ and 3P₀ levels in a series of Floquet quasi-levels with a frequency gap determined by modulation frequency.

It would be interesting to do a theoretical investigation into phase transport in the decoupled Floquet sideband spaces and observe a possible mechanism. Considering the choice of parameters, some further context is needed on the choice of the driving amplitude, A. Increasing A would increase the number of sidebands and distribute the pulse intensity among them. How would this affect the range of values for the Rabi frequency to suppress dephasing? The paper stated that Rabi=4.1 Hz to avoid additional dephasing, and it's interesting to see the changes with increasing spectral density in other modes. The choice of low frequency, low intensity clock field makes interactions between Floquet sidebands negligible which is theoretically and experimentally useful (in particular there isn't currently as much theoretical investigation in the low-frequency weak field regime for Floquet driving, compared to high frequency strong driving).

Overall, this is an outstanding result that shows the great potential in Floquet engineering (especially in the low-frequency region) to compensate for dephasing phenomena in optical clock lattice and other quantum many-body systems. The manuscript scientifically sound and I recommend it for publication in Applied Science. However, it needs language revision prior to publication.

Author Response

Authors investigate the suppression of the dephasing in the optical lattice clock by Floquet engineering effect on the excitation of clock transitions. Experiments show utility of low-intensity, low-modulation frequency (RF) Floquet driving to engineer Rabi flopping process of an ultracold atomic gas in an optical lattice. Figure 4 suggests that additional dephasing introduced from atomic motion and inter-atomic interactions is suppressed due to new dynamics in the Floquet manifold induced by sinusoidally modulating the incident lattice laser frequency and resulted in a split of ¹S₀ and ³P₀ levels in a series of Floquet quasi-levels with a frequency gap determined by modulation frequency.

It would be interesting to do a theoretical investigation into phase transport in the decoupled Floquet sideband spaces and observe a possible mechanism. Considering the choice of parameters, some further context is needed on the choice of the driving amplitude, A. Increasing A would increase the number of sidebands and distribute the pulse intensity among them. How would this affect the range of values for the Rabi frequency to suppress dephasing? The paper stated that Rabi=4.1 Hz to avoid additional dephasing, and it's interesting to see the changes with increasing spectral density in other modes. The choice of low frequency, low intensity clock field makes interactions between Floquet sidebands negligible which is theoretically and experimentally useful (in particular there isn't currently as much theoretical investigation in the low-frequency weak field regime for Floquet driving, compared to high frequency strong driving).

Response: We thank the referee for raising this concern. In the revised manuscript, we added “Herein, the driving amplitude of A=0.72 is optionally chosen as we found that changing the driving amplitude from 0.4 to 1.5 will not lead observable variation to the Rabi flopping process.” to clarify the reason of the choice of the driving amplitude (A=0.72) and the effect of the range of values for the Rabi frequency to suppress dephasing. To search a theoretical model to reveal the corresponding experimental results and observe a possible mechanism is attractive, but this needs many original works, which exceeds the scope of this paper.

Increasing the driving amplitude from zero (within small range) may observe obvious variation of the Rabi flopping process, but this needs to control carefully the driving amplitude. Considering lack of theorical guidance, at this stage, we reported our preliminary experimental results for attract other researchers to study this phenomenon. We will also try to study theoretically this phenomenon in the future and reveal the possible mechanism combined more experimental measurements.

 

Overall, this is an outstanding result that shows the great potential in Floquet engineering (especially in the low-frequency region) to compensate for dephasing phenomena in optical clock lattice and other quantum many-body systems. The manuscript scientifically sound and I recommend it for publication in Applied Science. However, it needs language revision prior to publication.

Response: We would like to thank the referee for positive reviews of this paper. We have carefully revised this manuscript and optimized the language as shown in revised manuscript.

Reviewer 3 Report

The paper "Experimental Observation of the Suppression of the Dephasing in A Floquet Engineering Optical Lattice Clock" was submitted for publication in Applied Sciences. The topic is relevant to the journal. Overall, the manuscript presents valuable results on daphasing suppresion by Floquet engineering. The authors determine specific values of the temperature and the number of atoms that lead to the opticam reduction of the dephasing effect. The topic selected by the authors is described in a neat manner. However, a revision is necessary before making a final decision.

Major comment

1. Dephasing is a serious problem in varous aspects of quantum science. Therefore, I belive the paper will benefit if the authors elaborate on the introduction to include references to other areas where such effect has to be taken into account (e.g., quantum communication, quantum information processing).

Minor comments

1. Figure 1 is not legible.

2. Editing problems:
- some equations are misaligned (they are above the line where they belong),

- the first paragraph in Sec. 3.1. is written in italics,

- the font size in Figs. 2 and 3 (axes lables) is unproportionally large,

- acronyms should be defined the first time they appear in each of three sections: the abstract; the main text; the first figure or table. The acronym FL that stands for Floquet engineering  is not defined in the abstract.

 

Conclusions. I believe the manuscript has the potential for publication in Applied Sciences. If the authors respond to the issues indicated in the report, I will eagerly read the manuscript again to evaluate the improvement.

Author Response

The paper "Experimental Observation of the Suppression of the Dephasing in A Floquet Engineering Optical Lattice Clock" was submitted for publication in Applied Sciences. The topic is relevant to the journal. Overall, the manuscript presents valuable results on daphasing suppresion by Floquet engineering. The authors determine specific values of the temperature and the number of atoms that lead to the opticam reduction of the dephasing effect. The topic selected by the authors is described in a neat manner. However, a revision is necessary before making a final decision.

Major comment

1. Dephasing is a serious problem in varous aspects of quantum science. Therefore, I belive the paper will benefit if the authors elaborate on the introduction to include references to other areas where such effect has to be taken into account (e.g., quantum communication, quantum information processing).

Response: We thank the referee for this helpful suggestion. In the introduction, we have added this sentence “In addition, dephasing is also one of the major challenges in many quantum sciences, such as quantum communication [20], and quantum information processing [21].” to underline the dephasing effect is the one of the major challenges in many quantum sciences.

 

Minor comments

1. Figure 1 is not legible.
2. Editing problems:

- some equations are misaligned (they are above the line where they belong),

- the first paragraph in Sec. 3.1. is written in italics,

- the font size in Figs. 2 and 3 (axes lables) is unproportionally large,

- acronyms should be defined the first time they appear in each of three sections: the abstract; the main text; the first figure or table. The acronym FL that stands for Floquet engineering is not defined in the abstract.

Conclusions. I believe the manuscript has the potential for publication in Applied Sciences. If the authors respond to the issues indicated in the report, I will eagerly read the manuscript again to evaluate the improvement.

Response: Thank the referee for helpful comments. In the revised manuscript, we have corrected above problems and carefully checked the whole manuscript for avoiding similar errors. Corresponding changes can be found in the revised manuscript in detail.