Dear Editor,

We first would like to thank both referees for their careful reading of the manuscript, and the constructive remarks to improve it. In the following, we address the points raised by the referees.

Reply to the first referee:

In response to the questions and comments, we have changed the manuscript as follows:

"One exception in the figures is in Figs. 5 and 6 where every single \mu for \mu K appears as a different symbol in my PDF version. It looks like a \propto symbol. That obviously must be corrected."

Our reply: We have changed the encoding for the \mu symbol to UTF-8 to ensure compatibility with a broader range of PDF readers.


"(1) Concerning Fig.3, the first two top panels show clearly the asymmetric fano profile but the asymmetry is not so easily observable in the two bottom panels. I think the results would benefit from a measure of the asymmetry, either empirically or somehow extracted from Eq.3, since it fits so well the data."

Our reply: We can use the Fano parameter to describe the skewness of a typical Fano profile. We would like to kindly direct the referee to the edits in the second paragraph in page 4 where we have included a discussion on the asymmetry of the profiles obtained.


"(2) Still in Fig.3, authors attribute the width of the resonance, much larger than the theoretical prediction to the superposition of “multiple Fano resonances resulting from other Zeeman sub levels”. I think the claim is reasonable but it lacks some more support. I suggest that authors use Eq.3 to simulate the several Fano resonances as independent \Lambda configurations to show explicitly this overlap and eventually their collective result as the measured profiles. To my opinion, it is not necessary to repeat such procedure for every panel in Fig.3, but if it is shown for a single panel or as a separate Figure (or a supplementary material?) it would support the claim of the authors for the width difference.."

Our reply: We have included an appendix to discuss the effect of multiple Fano resonances from different mF levels.


"(3) Still concerning the results of Fig.3, authors give a reasonable explanation for the shift of the dip of the spectrum from the expected 80MHz detuning. I wonder if performing the experiments at very large magnetic fields, increasing the Zeeman shift of the other levels, would not diminish such effect by decreasing the unwanted transition driven by the probe field."

Our reply: Indeed, performing the experiment at very large magnetic fields does increase the Zeeman shift of the other levels, and therefore decreases the light shift caused by the unwanted transition driven by the probe beam. However, since the Zeeman shift also applies to the lambda system of interest, the Fano feature that we want to observe will be affected.



"(4) Concerning the cooling by EIT: why do authors choose to go to the blue of the transition? The Fano resonance has been characterized on the red side so why not doing the cooling on the red side as well? I miss some explanation on that choice."

Our reply: The choice of having a blue detuning, as described in Section II, is to have the narrow Fano resonance overlap with the red motional sideband transition, leading to a transition toward a smaller phonon number and thus an effective cooling. Performing the same experiment on the red side will prefentially drive the blue motional sideband transition, which will result in heating. To improve clarity, we have added a sentence to highlight the need to have a blue detuning in the cooling section.


"(5) In Fig.5 the effective cooling range where the EIT works is very small. I think for the sake of completeness, authors should either state in the text and/or mark up the figure the range of detuning around 94.5MHz where they measure an effective cooling. Also, to my understanding this range should be taken for temperatures below 14 \muK, which is the temperature in which the single atom is prepared before the EIT"

Our reply: We have shaded the range of detunings where an effective cooling is measured in Fig.5 for better visualization.


"(6) Still on the temperature results of Fig.5, the 40\mu K “background" temperature seems like “universal" over the range of parameters investigated. Is this related to the pulse duration (20ms)? Intensities of the fields? I think some comment would be valuable."

Our reply: For frequencies far away from the Fano resonance feature, the single atom undergoes incoherent scatterings of the pump and probe beams. In this process, the atom experiences recoil heating which raises the atomic temperature to about 40\mu K. Indeed, this value does increase with the pulse duration, as well as the intensities of the fields. As both reviewers raised a similar question regarding this background behavior, we have included this discussion in the manuscript.


"(7) In the discussion and conclusion section authors discuss the discrepancies in mean phonon number and cooling time constant. The brief discussion ends with “We expect a steady state between these two processes settling at a final temperature approximately two orders of magnitude lower.” Indeed, this expectation is the result obtained, my I do understand where does this expectation comes from. Is there a more concrete physical reason for that claim?"

Our reply: The quoted statement is actually a hypothesis. We have revised this part to improve clarity.


Reply to the second referee:

"The main missing ingredient in the work is a comparison to existing approaches to cooling. In particular, lambda-enhanced gray molasses cooling has been implemented in several neutral atom array experiments, with similar experimental complexity and improvement over polarization gradient cooling."

Our reply: We have expanded our introduction to include the comparison between the EIT cooling technique and the gray molasses scheme.


"1. It would be useful to mention two-qubit gate error sources from finite atomic temperature as a motivation for lower temperatures in the introduction."

Our reply: We have included this point in the introduction.


"2. After cooling, in what mF levels is the atomic population? Does the population accumulate mostly in a specific mF level, or is it spread mostly equally between the F=2 levels?"

Our reply: At the end of the cooling sequence, the atom will fall into the dark state of the two-photon process, which is a superposition state between the mF=-2 and the mF=-1 Zeeman levels. The Zeeman level populations for this dark state are omega_c^2/(omega_p^2 + omega_c^2) in the mF=-2 level, and omega_p^2/(omega_p^2 + omega_c^2) in the mF=-1 level.


"3. I was surprised by the tweezer waist being as large as 1.1 micron, based on the high numerical-aperture. I wonder if the authors could comment on how this waist was characterized, and whether it is larger than the theoretical optimum because of optical aberrations or beam clipping on the objective lens."

Our reply: In our current configuration, the tweezer beam is only using an effective numerical-aperture of 0.27. The associated diffraction-limited beam waist is about 1.0 micron, which is slightly smaller than the measured value of 1.1 micron. This discrepancy is very likely due to optical aberrations. The experimental tweezer waist is deduced from the trap frequencies and trap depth experienced by the single atom. Particularly, for a Gaussian potential, the radial frequency of the tweezer is given by the square root of 4U/(mw^2), where U is the trap depth, m the mass of the Rb atom, and w the tweezer waist. We can obtain the trap frequencies from a parametric excitation measurement. The trap depth can be obtained from the AC Stark shift in a transmission measurement.


"4. The authors attribute the fact that the experimental Fano linewidths in Fig. 3 are larger than the theoretical expectation to the presence of multiple Fano resonances from different mF levels. Is the observed increase quantitatively consistent with this hypothesis?"

Our reply: The observed increase is slightly larger but comparable to the theoretical value predicted by this hypothesis. We have included an appendix to discuss the effect of multiple Fano resonances from different mF levels.


"5. In Fig. 5, why is the temperature so high away from the Fano resonance feature? Why is this
temperature not closer to the value from polarization gradient cooling?"

Our reply: For frequencies far away from the Fano resonance feature, the single atom undergoes incoherent scatterings of the pump and probe beams. In this process, the atom experiences recoil heating which raises the atomic temperature to about 40\mu K. As both reviewers raised a similar question regarding this background behavior, we have included this discussion in the manuscript.


"6. Have the authors considered implementing this cooling mechanism on the D1 line, where the heating effect from off-resonant scattering described in the manuscript can be mitigated?"

Our reply: We agree that implementing this cooling mechanism on the D1 line could suppress the heating effect from the off-resonant scatterings, which can potentially cool the atom to a lower temperature. This work is currently in progress.


"7. Atomic temperatures can be further reduced by adiabatically ramping down the trap depth after cooling. Is the tweezer trap depth kept constant throughout the cooling sequences employed in this work?"

Our reply: Yes, the tweezer trap depth is kept constant throughout the cooling sequence in our experiment to ensure a fair comparison between conditions with and without EIT cooling. Indeed, the atomic temperature can be further reduced by adiabatically ramping down the trap depth, but the mean phonon number will remain constant in this process. With the EIT cooling technique, we have demonstrated an improvement in both the mean phonon number and the atomic temperature.


"8. In the conclusion, the authors compare the observed temperature between this work and a previous demonstration of EIT cooling of an atom inside an optical cavity. It would be useful, if possible, to compare the observed mean phonon number, since this metric is arguably a more meaningful comparison."

Our reply: We have included in the conclusion the mean phonon number reported in the previous work for EIT cooling of an atom inside an optical cavity. The reported mean phonon number in that work is also comparable with the mean phonon number measured in our system.


With this, we hope to have addressed all points indicated by the referees. For convenience, we added a differential pdf version highlighting the changes of the revised manuscript compared to the original manuscript, and look forward to your reply.

With Best Regards on behalf of all authors,

Christian Kurtsiefer