Dear Editor,

we acknowledge that both referees do not find the manuscript suitable for
publication in Physical Review Letters because they consider the reported
experiment not sufficiently relevant for it, or suspect usage of inadequate
or perhaps even sensationalistic wording.  We disagree with this view, and
believe that our experiment illuminates some peculiarities of heralded single
photons that are perhaps less 'straight forward' as the assessment of the
referees suggest.

With both reports being rather critical, however, we doubt that we can
convince the referees about these aspects.  At the same time, the referees
acknowledge the scientific correctness of our work.

We have addressed points raised by the referees as indicated below, and
believe that the modified text better expresses the relevance of our
work. As further consideration for publication in PRL at this point seems not
very likey to us, we would be glad if you could consider the manuscript,
together with the referee history, for transfer to Physical Review A.

If this reqires some specific action from our side besides this letter,
please do let us know.

With Best Regards on behalf of the authors,

Christian Kurtsiefer

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Reply to the Referee A


1) In the manuscript we explicitly acknowledged that the exponential shape of
   the waveform, per se, it is not surprising:
   "This can be easily understood by the timing sequence of a cascade decay,
   where the signal photon heralds the population of the intermediate level,
   which subsequently decays exponentially, leading to the characteristic
   decaying envelope of the idler photon according to the Weisskopf-Wigner
   solution [23, 24]" 

On the other hand, we do like to stress the rising nature of the exponential
envelope of the signal photon when heralded by the detection of the idler
photon. This type of temporal envelope to our knowledge has not been observed
very often in the past decades, but has instead been sought for its predicted
properties of enhanced interaction with a two level system (see e.g. Ref. [5]).


2) We agree with the Referee that cross correlation experiment lead to
asymmetric shapes. 
This is why we extended our experimental investigation beyond the measurement
of the cross correlation to the measurement of the field envelope using
optical homodyning technique: not looking for surprises but to confirm what
the cross correlation measurement suggested. However, a postselection
process of one way or the other heralding the presence of a single photon is
employed by a vast majority of the cases where experiments with single photons
are reported. We therefore believe that the heralded photons from the pair
generation process in our experiment is a reasonable implementation of a
'single photon', supported by the g(2) measurements we presented. What we
wanted to demonstrate is that we can find a somewhat 'surprising' rising field
envelope in such a heralding process.

3) We thank the Referee to rise this point, but like to point out that in our
previous work [16] we have already addressed in a quantitative way the effect
of the atomic density on the bandwidth of the generated photon pairs. 
We modified the manuscript in order to make it explicit that for a
quantitative analysis of the correlation between the photon bandwidth and the
optical density of the atom cloud the interested reader can refer to our
previous work.

The paragraph that in the original manuscript read:
"The time constants for the exponential rise or fall times are compatible with
the distribution of detection time differences we observe in the cascade decay
[16], enhanced by the dense atomic ensemble [26]"

now reads:
"The time constants for the exponential rise and decay profiles are shorter
than the lifetime of the intermediate state. This is due to collective decay
effects observed in dense atomic ensembles [25]. The measured value is
compatible with our previous measurements of the distribution of detection
time differences for this optical density [15]."

4) We agree with the Referee that the observed photons present a larger
bandwidth than the natural linewidth of the atomic transition of
interest. Since we do not directly interact the generated photons with an
atomic system in the presented work, we do not consider the bandwidth a
fundamental limit. As indicated in reply to point 3), the bandwidth of the
generated photons depends on the optical density of the atomic cloud, a
parameter we can control, as demonstrated in our previous work, and -- at the
expense of event rate -- can be lowered close to the natural bandwidth of an
atom.

5) We agree with the Referee that in order to easily observe an interaction
between the generated photons and an atomic system the photon need to be
resonant to a ground state transition of the atom.
We modified the text of the manuscript to state explicitly that the photon
with exponentially rising waveform is not directly suitable for interacting
with an atom in free space.
We also indicate how the temporal correlation of the generated photons
combined with a recently published time shaping technique (and named 'time
reversal' by its authors) [Bader, et al., New Journal of Physics 15, 123008
(2013)] can be used to generated photons with the desired time shape and
resonant with a ground state transition.

The first paragraph of the manuscript was changed from:
"Strong atom-light interaction at the single quantum level is a prerequisite
for many quantum communication pump and computation protocols [1-4]. In free
space the optimal coupling of photons to atoms requires the temporal profile
of the incoming photons to match the time reversal of photons generated by
spontaneous decay from the transition of interest. [5-7]."

to:
"Strong interaction in free space between a single photon and a two-level
quantum system is a prequisite for many quantum communication and computation
protocols [1–4]. This interaction has been demonstrated to be optimal when the
incident photon has an exponential rising temporal envelope [5-8]."

The conclusion of the manuscript has also been modified to address this, from:
"If heralded single photons are practically not distinguishable from "true"
single photons, the latter should -- at least in principle -- efficiently be
absorbed by a single atom in free-space in a time-reversed Weisskopf-Wigner
situation. Such an experiment would therefore not only demonstrate strong
atom-photon interactions, but also provide a better understanding to what
extent heralded photons are equivalent to single photons emerging from a setup
with a well-defined initial condition." 

to:
"If heralded single photons are practically not distinguishable from "true"
single photons, the latter should at least in principle be efficiently
absorbed by a two-level system in free-space in a time-reversed
Weisskopf-Wigner situation. Such an experiment also would provide a better
understanding to what extent heralded photons are equivalent to single photons
emerging from a setup with a well-defined initial condition. This test would
require a photon driving a ground state transition of a two level system. The
heralded photons with the exponentially rising waveform generated by our
scheme are resonant with an excited transition and there- fore cannot be used
directly. However, waveform reshaping techniques demonstrated in [8] can be
employed to address this problem."


----------------------------------
Reply to Referee B


1) We agree with the Referee that the homodyne method is indeed not new and,
as such, it is also well known the difference between measuring the
correlation between two fields, as presented in Ref.6, and the envelope of a
field, as presented in the manuscript.

2) After reading carefully the comment of the Referee, we removed the world
'counterintuitive' from the title of the manuscript.
We still believe that the experimental measurement of a rising exponential is
relevant in the context of modern quantum optics. The correlation measurement
presented in our previous work [ref. 6] clearly hinted at the presence of two
symmetrical temporal waveform, presence that we decided to confirm by
experimentally measuring the temporal shape of the individual photons.

3) We are aware of the works of Harris group (cited in the original
manuscript). We are also aware of Du's group efforts, based on the original
works of Harris. We claim that our approach as an inherently distinguishing
prerogative: the temporal shape of the photons is governed only by the
dynamics of the cascade process. This rises also interesting questions
regarding the reality of the heralding process as state preparation, described
in the conclusion of the manuscript.
We added the following text to the introduction of the manuscript to clarify
the difference between the approach used in previous works cited by the Referee:

In the introduction, the text was modified from:
"Single 87Rb photons with an exponentially rising temporal envelope have been
prepared from such a heralded single photon source by direct modulation of one
of the photons of the pair [14]."

to:
"Heralding has already been used to generate single photons with rising
exponential temporal envelopes: the intensity of one photon of the pair is
modulated in time using fast modulators [12, 13].
 This modulation technique resulted in unavoidable losses due to the small
overlap between the temporal shape of the generated photons (exponential
decay) and the desired one (exponential rise)."

4) We thank the Referee for noticing an error in the transcription of the
normalization formula. The correct formula, that now appears in the revised
manuscript, was the one used to obtain the plots in Fig. 2.
Regarding the reference to Aspect's work: in their work the authors did not
take into account the use of coincidence time windows of different
duration. In our work we sample the arrival of the detection events with a
resolution of 125ps. This allow us to observe the correlation as function of
the difference in arrival time for the Hanbury Brown Twiss detection scheme. 
In order to properly normalize the correlation here, we had to devise a more
complete normalization function to take into account both the sampling of the
delay between the two arms of the interferometer and the time window opened by
the heralding event.
We have verified that our normalization reduces to the one of Aspect et
al. when we take a fixed coincidence window for the threefold coincidence
events.

We would also like to stress how all the values used in the normalization and
in the derivation of the g(2) are measured. 
Therefore, in equations (2) and (3) the factor 1/Ns has been added and in the
text just before the equation the following sentence has been added: 
"[...] normalized to the total number of triggers Ns."