Dear Editor,

we first like to thank the referees for their careful reception of our
manuscript, and for their constructive and detailed remarks. We revised the
manuscript accordingly. Our replies and comments to the detailed comments:

Reply to the first referee:

"The selection of references in the manuscript is good, but has some flaws in the capitalization (e.g. Mollow should be uppercase, etc.). Furthermore, I miss some important references, such as from Herbert Walter, who spend quite some time with the Mollow triplet; also from Jurgen Hoeffges, who was HW's student. The references to the observations of the Mollow Triplet in quantum dots miss their first measurement (A. Mueller and coworkers)."

Our reply: Thank you for pointing out the capitalization issues in the references and it has been fixed.
We also added the additional references suggested by the first referee.


"In this context, I ask to compare Fig. 5 of [1] to the given presentation. I would state that the Mollow Triplet consists of four parts: The three described peaks and also the coherent scattering. Where is this part described in the present manuscript?"

Our reply: We also added the discussion about the coherent and incoherent scattering in first paragraph of part II.


"Also, I am not so happy about the unit "a.u. - I guess this should be "arb. units"?! But why is it arbitrary anyway? It would be good to get this on counts on the photodetector - at least as a second axis on Fig. 3."

Our reply: We removed the "a.u." altogether, as we use a dimensionless normalized intensity here to better illustrate the ratio between the central peak and sideband components and indicated this in the axes labels.
The typical count rate is 16500cts/s for the central peak.
However, the absolute counts on the detector vary between different measurement because one set of data (per spectrum) could take a few hours up to days depend on how many points we were taking.
The change in overall detection efficiency due to some external change make the absolute counts not very representative to put in the graph, so we prefer to leave it in the normalized representation.


"The author's discussion why the central peak goes to 3.7 might be caused exactly by the coherent scattering of the atom itself - it does not have to be the reflecting optics. This would clearly change with the effective Rabi frequency."

Our reply: The coherent scattering is a factor that we overlooked previously as we assume the contribution to be small at strong driving. 
After careful inspection, we found that the order of magnitude of the coherent contribution is the same as the laser reflection.
As such, we include now the coherent term in the equation and recharacterized the reflection at different driving intensities.
Interestingly, for the last three sets of data that we analyzed on this, the addition of coherent contribution and the laser reflection sum up to a similar number.
This is because as the laser reflection increases with Rabi frequency, the coherent component scale opposite as the reflection.


"Fig. 2 shows the Probe Power. It was measured with seemingly no error bar around 0.5 pW - this is hard to measure and I do not believe their given accuracy (their precision might be though okay). Where is this measured anyway? I assume that this is measured before the atomic cell. Since the Probe Power is linked to \Omega, I am not sure if and how Fig. 3 and Fig. 4 were measured simultaneously or subsequently. Presently, this looks that this was acquired subsequently. Then, unfortunately, the exact Rabi frequencies in Fig. 3 are missing, since they deviate from Fig. 4 b-e."

Our reply: The probe power is actually measured with the avalanche photodetector (APD1) after a ND filter.
We take into account fiber coupling, detector efficiency and OD of the filter to infer the power from the photon counts.
For the results in Fig.4 (old Fig.3) and Fig.5 (old Fig.4), they are measured subsequently.
We already added the Rabi frequencies into Fig.4, and most of the values are within 1MHz difference from their counterpart in Fig.5.


"The "convolution of two square pulses" is not very well described (triangle function?). I understand that the trapping and the read-out parts are pulsed - but Fig. 4 basically represents a CW measurement. Is this the slight decay in the graph? I.e. the deviation from unity around +/- 200ns?"

Our reply: We have added an explanation at the end of this section: "This is done to account for fluorescence from each detector being collected during a 2\,$\mu$s wide time window. The correlation between two such windows will result in a 4\,$\mu$s wide triangular envelope."
This also cause the slight decay mentioned by the referee.


"I wonder that the discussion about any detuning (which is, btw., nicely done in [1]) is limited to part V of the presented manuscript."

Our reply: We extended the discussion on detuning in section V of the paper
for slightly, but feel that including it to other parts of the paper would
make it very hard to digest.


"Section V discussed the cascaded emission from the side-bands. I miss the discussion on the height and the count-rates at this point. Is the peak height Fig. 5 limited by technical problems? Dark-counts? Does this correlated well to the collection and detection efficiency?"

Our reply: We added some discussion in Section V regarding the bunching height. The contribution of dark-counts to the coincidence rate is 5 orders of magnitude smaller compared to the signal that we collected in the open time windows.
The observed bunching peak is slightly lower than the theoretical prediction, which we attribute to the imperfection in spectral filtering which causes collection of photons outside the desired spectral window.


Reply to the second referee:

"In the introduction the authors state "This configuration minimised Doppler broadening due to atomic motion." Could they expand upon this? (i.e. was the atomic beam highly collimated? What was the residual Doppler? How did this compare to their results presented later?)"

Our reply: The residual Doppler contribution to the spectral width was around a few MHz even through the atomic beam was highly collimated. In contrast, in our system the temperature of the atom is 14uK which corresponds to Doppler broadening of 113kHz, which is significantly smaller than the natural line width.


"Figure 1 - I feel the authors should have an energy level diagram of the bare/dressed states, as it would make text relating to the levels used, and splitting of these levels, clearer."

Our reply: A figure of the bare and dressed state level diagram has been added.


"Figure 1 - I would suggest numbering the APDs so it is easier to discern which one is which (as opposed to "one APD" and "another APD")"

Our reply: We are happy to follow the suggestion and numbered the APDs in
Fig.2 (old Fig.1).


"I find the nomenclature confusing regarding $n$ and $N$: when they are first raised (p2 col1 para2) they both seem to refer to photon number. In the next paragraph $N$ now seems to refer to excitations?"

Our reply: In the original text "total number $N$ of photons plus atomic excitation is the same", we want to express the total number of excitations which include both photon and atomic excitation which caused some confusion.
We changed text to "In every manifold where the total number of excitations, $N$ is the same, ..." to explicitly state the correct definition of $N$.


"There are a number of areas where I would like to see more detail on the experimental set-up. For instance, I would like to better understand how the system is triggered/how the authors know when there is a single atom in the trap. Also, I would like more detail on the level of probe field suppression at the detection APDs, especially as this seems to affect the size of the peaks. The authors state a 7.6% contribution to the central peak - but won't this percentage be dependent on the level of probe power used? An extinction ratio measurement would be more apt."

Our reply: We have added more details on the atom trapping and triggering in appendix A.
The crosstalk of the probe field power ending up on APD2 without an atom is
around 4*10^-5. This crosstalk contributes to 4.5% of the total power in Fig.4(e).
As pointed out by the referee, we assumed the contribution of coherent
scattering will be small for strong driving, and did not take this into
account earlier. After a more careful inspection, however, we found that the
coherent contribution is of the same order of magnitude as the laser reflection.
We therefore now include the coherent term, and recharacterized the reflection
at different driving intensities. 
Interestingly, for the last three data sets, the addition of coherent
contribution and the laser reflection sum up to a similar number.
This is because as the laser reflection increases with the driving Rabi
frequency, while the coherent component decreases by a similar amount.
 

"Finally, I would like to see more details on the cavities used. What were the made of? How were they stabilized/scanned (the authors mention this briefly in the text for the (a) fabry-perot, but it would be much more helpful to include more detail in the text, as well as in the experimental figure). Also, as the FWHM of the (a) cavity is MHz, should the data in Fig. 3 have horizontal error bars? What exactly is the cavity transfer function (as it is used multiple times)? These comments also apply to the larger line-width cavities used for the off-resonance work."

Our reply: We have added more detail on the cavities in Appendix B.
The uncertainty of the cavity resonance is 257kHz, the error bars will be barely visible in Fig. 4 (old Fig. 3).
The transfer function for the smaller linewidth cavity is shown in Fig. 3(b) (old Fig. 2).
The cavities with a larger linewidth have the same structure, but contain
mirror coatings  with a lower reflectivity/higher transmission.
Consequently, their performance and stability will be similar.


"Is the difference between the measured central peak width of 7.3 MHz and the theoretical linewidth of 6 MHz due only to Doppler? What is the temperature of the atoms in the trap? Does this explain the additional width? What effect does this have on the other results presented in the paper?"

Our reply: The answer to the first question is likely no. The temperature of our single atom is 14uK which corresponds to Doppler broadening of around 113kHz.
We also estimated the differential light shift experienced by the atom in the
dipole trap, which should contribute around 200kHz of broadening in the
spectrum. Therefore, the broader width is still not fully understood.
The effect of this larger decay rate gamma can be seen in the second order
correlation measurement, where it determines the decay envelope of the g2
oscillation. If we set the gamma in Eqn.2 to be a free fit parameter,
we obtain a value of 7.5MHz.


"The authors need to clarify their statements relating to spectral intensity split (1:2:1) and why this is different to the height ratio (1:3:1) - is this simply to the narrowness of the central peak?"

Our reply: The answer is yes. Theoretically, the width of sidebands is 1.5 times the width of central peak.
We have added "owing to the fact that the sidebands have larger width compare
to central peak." to clarify this in the manuscript.


"When discussing the second-order correlations, where do the two square pulses that are added to the g2 fit originate?"

Our reply: The two square pulses originate from the collection window of 2μs and the effect of the convolution can be seen from the slight deviation from g2=1 around +-200ns of Fig.5(old Fig.4).
We have added text in the last paragraph before section V to clarify this.


"Figure 4 - it is good to have the Rabi frequencies listed here. Currently it looks like 4(a-e) correspond with 3(a-e). If that is the case, I'd suggest including the measured Rabi frequencies on Fig. 3 too - that would better allow the reader to confirm for themselves the comment by the authors in the text that the values "agree well with the values of \Omega obtained from the Mollow triplet spectra""

Our reply: We have included the Rabi frequencies for Fig.4(old Fig.3). Most of the values are within 1MHz difference from their counterpart for the second order correlation measurement.


"When off resonance, the power ratio between the peaks should start to change. This is not mentioned in the text when discussing the difference between on and off-resonance effects."

Our reply: We have added "The power ratio between the central peak and the sidebands deviates from the on-resonance case, with the central peak being suppressed as detuning increases."


"In the abstract, the authors mention "FUTHER indicates that there is a preferred time-ordering of the emitted photons from different sidebands". What does this "further" relate to? Is this a new/novel finding? If so, it is not clear from the text. Please relate to relevant literature."

Our reply: We have added citations that support this statement.


"In the conclusion, I find the new discussion on applications for heralded single photon sources would be better introduced in the introduction."

Our reply: We agree with this suggestion, and moved this part to introduction.


Reply to the third referee:

Our reply to general comment: 
The experimental works on particularly the fluorescence spectrum, second order intensity correlation, and filtered timing correlation function have been investigated in other systems. 
These individual features were studied oftentimes separately in different systems such as single solid state systems or atomic ensembles, limited by imperfections.
We are able to resolve all these features in this work. Particularly the output fluorescence light is free from phononic features and inherently narrowband, compartible for interfacing with quantum emitters.
Along with the use of high numerical lens for high single photon collection efficiency, we believe that an optically trapped single atom can be a clean novel platform for the implementation of quantum light sources with different timing signatures.

- p.2, second paragraph of section III: “This length is chosen to
maximize the duty cycle…” - bu length, I assume the authors mean
“duration” of pulse.

Our reply: We have changed it to "pulse length" to clarify the statement.

- fig. 3: It is important to report on the fitted Rabi frequencies for
each curve. Specially to justify the last phrase of section IV: “The
extracted values, shown in Fig. 4 for different driving powers, agree
well with the values for $\Omega$ obtained from the Mollow triplet
spectra.”

Our reply: We have included the Rabi frequencies for Fig.4(old Fig.3);  most values are within 1MHz from their counterpart for the second order correlation measurement.

- p.4, last paragraph: What’s the theoretical prediction for the
different timescales $\tau_{rise}$ and $\tau_{fall}$?

Our reply: The theoretical prediction following [Phys. Rev. A 45, 8045 (1992)]
for $\tau_{rise}$ and $\tau_{fall}$ are 7.96ns and 35.02ns,
respectively.



Furthermore, we did some minor language cleanup of the manuscript. We also
added a diff file indicating the changes from our earlier manuscript.

With this, we hope to have addressed the issues pointed out by the referees,
and look forward for a recosideration of our revised manuscript.

With Best Regards on behalf of all authors,

Christian Kurtsiefer