Reviewer #1 (Remarks to the Author):

"Time-resolved scattering of a single photon by a single atom" by V.
Leung, et. al.

This article presents the results of measuring the absorption of a
single photon, whose temporal envelope is tailored to resemble an ideal
decaying or rising exponential profile, by a single, trapped atom. This
work is very painstaking and careful, requiring a long duration (months)
to acquire sufficient signals for their quantitative analysis. The main
result presented is that the excitation dynamics of a single atom by a
single photon depends on the photon's temporal pulse envelope and not
just on its power spectrum. Namely, that the maximum excitation
probability is markedly different for photons with an exponentially
rising temporal envelope compared to photons with an exponentially
decaying envelope. This result is in fair agreement with the model of a
photon absorption by a two level atom presented in this work.
The authors have demonstrated how to prepare and manipulate photons with
exponentially rising and exponentially falling envelopes (many of the
details of the different elements of the experimental apparatus are
contained in the references cited in this article). One of the
remarkable results of this work is the agreement between the simplified
2 level atomic model and the experimental results presented. The
manuscript is well written: there is a clear motivation given, a concise
description of the model explored, and a good presentation of the
results and analysis. In my review of the work, there are only a few
recommendations I have which may help improve the article:
a)	In figure 3, the raw data are shown (The coincidence probability as a
function of the time from the heralding event) for the exponentially
rising and for the exponentially falling photon envelopes, with and
without an atom trapped in the experimental chamber. It could be helpful
to demonstrate how well the time-reversal of the envelope is
accomplished experimentally by taking the two traces without an atom
present, time-reversing one of them, and plotting the residuals of their
difference.  Alternatively, the predicted coincidence shape for the
exponential rising and falling envelopes could be plotted with the
observations to quantify the deviation from the model behavior.
b)	The discrepancies between the model predictions and the data in
Figures 4 and 5 merits a more in-depth discussion.
In Figure 4, the authors plot the differences between the coincidence
probabilities with and without and atom present for each tailored photon
envelope. These data are fit using the model presented (Note: In the
caption to Figure 4, the authors state the fit is to Eq. (2)-(5),
although I believe these data are fit using Eq.(1) and to the
expressions found in the text just prior to Eq. (5)). There is a notable
discrepancy for the decaying envelope data and the model near the
maximum (t \approx 15 ns). This discrepancy lies outside the error bars
for this plot. By contrast, the model shows no such discrepancy for the
rising envelope data set. In Figure 5, the plots of the predicted and
observed excitation probabilities as a function of time from the
heralding event, once more (not surprisingly) demonstrate the same
asymmetry between the model and the results. Again, this is outside the
quoted error bars for the decaying envelope measurements compared to the
model predictions.
              The source of this discrepancy could lie in the non-ideal
transfer function of the Fabry-Perot cavity used to control the photon
temporal envelopes, the behavior of the AOM switching on/off, motion of
the atom in the trap as opposed to being stationary, and/or due to the
light interacting with the atom having non-ideal polarization, for
example. That the discrepancy depends on the shape of the photon
envelope is remarkable. I would appreciate like some small discussion of
the potential sources of this effect. [Also see d) below].
c)	The authors also say that "corrections for accidental coincidences
were applied in the analyzed data shown in Fig. 4 and Fig. 5".  I would
appreciate a short explanation of these corrections here. The authors
are taking the difference between two, almost equal traces to extract
small, precise readings. The form of the correction and the method for
correcting the data are relevant here.
 d)	In the text at the top of p.4, the authors state the percent
differences between the excited state populations produced by the
different shaped envelopes. The measured value shows a 56% larger peak
excited state fraction as compared to the model prediction of 78%
increase. This discrepancy should be commented upon in context with
point b).
e)	Finally, the authors state: "The advantage of using exponentially
rising photons is, therefore, to excite atoms at well defined instants
in time."  I suggest changing this to a more specific statement such as:
"The advantage of using exponentially rising photons to excite a single
atom is that this provides a larger peak excitation rate which is more
temporally localized."
Overall, I enjoyed reading this manuscript: The authors present the
results of carefully executed and thorough work. With some of the minor
adjustments I suggested above, I recommend publication of this work: The
findings are of great interest to researchers in this field as well as
to a general audience.



Reviewer #2 (Remarks to the Author):

The authors examine the excitation process of a single atom by a single
photon. In particular, they investigate the influence of the shape of
the wavepacket of the incoming photon, whether it is exponentially
decaying or rising. The experimental results are valuable because some
theoretical predictions had stated that efficient coupling of photons to
atoms requires exponentially growing light fields to mimic the inverse
of the spontaneous emission process.
The experiment is a continuation of a series of efforts in the lab of
Prof. Kurtsiefer, where extinction of a focused laser beam by a single
atom was studied. In 2013 they investigated the effect of the laser
pulse shape on the excitation process. In 2014 they reported the
production of single photons with exponentially rising profile. The
current manuscript puts those two experiments together in a real tour de
force effort, involving 1500 hours of data acquisition. The work would
be a very nice addition to the literature in quantum optics. Therefore,
I recommend this work for publication in Nature Communications once the
following issues have been addressed:

1- The authors show convincingly the difference between the peak
excitation probability for the cases of exponential rising and decaying
pulses. They also state the important conclusion that when integrated
over a long time interval both photon shapes are equally likely to be
scattered. The latter statement should be included in the bold abstract
(first paragraph) to avoid misleading/confusing the general reader about
the necessity of pulse shaping when performing spectroscopy.

2- In the second paragraph, the authors write "More recently, signicant
light-matter interaction has also been observed between single quantum
systems and weak coherent fields in free space [18-21]." The authors
seem to have selected references to vacuum experiments. Since the
physics does not change in any way when the excitation is done in a
dielectric, they should also includes references to G. Wrigge, et al,
Nature Physics 4, 60 (2008) and Vamivakas, et al. Nano Lett. 7, 2892
(2007) where this type of work was first demonstrated on molecules and
quantum dots.
3- In the last paragraph, the authors state "Our experimental results
also contribute to a long-standing discussion about differences between
heralded and "true" single photons." They should cite the literature on
this long-standing discussion.






Reviewer #3 (Remarks to the Author):

1. Summary
The authors present their experiment on scattering a single photon off a
single atom. The temporal shape of the input photon is set to be either
exponentially rising or falling, depending on the detuning of a cavity.
They demonstrate that the excited state probability as a function of
time is different for the two cases, and that a higher probability is
reached for the rising mode. The integrated probability is however the
same, as predicted by the theory.
2. General comments
In general, I found the manuscript interesting and nicely written. The
topic of the manuscript should be of interest to the general physics
community. The authors show a nice agreement between experiment and the
theory. The results are trustworthy and the statistical analysis
(errorbars are shown and numbers are displayed with uncertainties) is
ok. In conclusion, I find the manuscript appropriate for Nature
Communications and I recommend publication.

Detailed comments:

3. Spatial overlap Lambda
Can you discuss how you can improve the value for Lambda? For a Gaussian
spatial mode, what is the best overlap with the atomic dipole pattern?
Are there any ways to experimentally produce an input photon with Lambda=1?

4. Forward and backwards detectors:
Why do you have a better signal to noise ratio using the forward
detector compared to the backwards detector? The atomic dipole emission
should be the same in the forward and backwards directions, and I would
therefore think that the number of detected photons (and thereby the
signal to noise ratio) would be the same in the two directions.
5. y-label on Fig 3.
I am a bit confused about the y-label of figure 3. It says "Coincidence
probability x 10^-5" and the y-axis goes from 10^-5 to 10^-3. Does this
mean that the actual probability goes from 10^-10 to 10^-8? To avoid
confusion, I would suggest that you delete the "x 10^-5", and just write
out whatever the correct numbers are on the y-axis. Also, is is not
clear to me how G_f and G_f,0 normalized? What is the relation between
the value of G_f and the time-bin duration of 2 ns?

6. Equation (7)
I am a bit puzzled about Eq. (7). The function Lambda*(1-Lambda) is
maximal for Lambda=0.5. Why is this Lambda optimal? I would expect that
Lambda=1 would give the biggest epsilon. However, I see that epsilon= 0
for both Lambda=0 and Lambda=1. Please explain. Also, how can one make
epsilon=1? I see that epsilon=1 for tau_p>>tau_0. Is there a simple
physical explanation why this is optimal? I would expect that
tau_p=tau_0 would be optimal according to your argument about
time-reversal.
7. 1500 hours
On the one hand, it is impressive that you can run your experiment for
such a long time. On the other hand, it is not so nice that you need so
long time to get good statistics. I think that it would be nice if you
added some text in the methods section describing the main reasons for
needing so long measurement time and give some suggestions for how you
can improve your setup in order to do faster measurements.
8. Formatting of figure 2
Figure 2 has many details but is quite small. The figure would be more
readable if it was larger and covered the full page width.

9. Formatting of Fig. 3, 4 and 5.
There is a problem with the formatting of Fig. 3, 4 and 5. The figure
and the figure caption are partially on top of each other, making it
hard to read the first two lines of each figure captions.