Dear Editor,

first, we like to thank the referee for the constructive comments. We revised
our manuscript accordingly to address the issues where possible. Our responses
to the individual questions is as follows: 

Referee comment:
The manuscript reports on an experimental investigation of
light-matter interaction for a single atom trapped in strong optical
tweezers and irradiated by tightly focused light. On resonance, the
authors observe 17% reduction of the light transmitted through the
atom and 0.6% enhancement of the light reflected by the atom. These
are impressive (although state-of-the-art) results, and the overall
study is interesting for all single-atom experiments. Particularly
interesting are the time dependence of the light extinction and the
dynamical light shift in figure 6. The manuscript might therefore be
publishable in the Physical Review. However, a few important questions
remain:

1) The observed extinction is only half as large as the expected
extinction (~17% compared to ~36%). This huge discrepancy is not
explained, although the reported work aims to be a careful and
systematic study of light-matter interaction (as stated in the
introduction of the manuscript). Which big effect is missing? Without
such effect being properly identified, the presented work is not very
useful for other groups in the field.

Reply:  We agree that the discrepancy between the theoretical extinction
value and the observed one is a concern. The comparison of our results is made
to the model outlined in Ref.13, which makes several assumptions, including an
ideal Gaussian input field, an ideal lens, and a stationary two-level atom.
These assumptions are only an approximation to the conditions in a real
experiment. The present study addresses the effect of a finite atom
temperature in the trap on the atom-light interaction. 
We find that the residual motion of the atom reduces the interaction,
but that this effect is fairly small for sub-Doppler cooled atoms - hence, we
can exclude the thermal motion as the main cause for the missing
extinction. Unfortunately, we do not have a conclusive explanation for the
missing interaction at the moment. As mentioned in Sec. 5 and 6 of the
manuscript, we suspect that imperfections of the lens or phase errors of the
incident light to be the main cause, but we do not have sufficient experimental
evidence to support this hypothesis yet, and a detailed analysis of the
aberrations of the focusing system is beyond the scope of the presented study.


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Referee comment:
2) For tight focussing, the light polarization in the focus usually
differs from the polarization away from the focus.The authors do not
mention this at all. Is the effect irrelevant for circularly polarized
light as used in the experiment? Or could it explain the large
discrepancy between observed and expected transmission?

Reply:  The local polarization of the electric field in the focus and
in particular at the position of the atom is indeed very important for the
light- matter interaction. These effects are therefore included in the theory:
we compare our results to the predictions of the full vectorial model
described in Tey et al. (Ref.13), which derives the electric field
polarization in the focus for a circularly polarized Gaussian beam. To
emphasize this, we make it explicit in the revised manuscript that the
polarization effects are included with the following sentence in the main text
(just before equation 8):

'For the probe field, we evaluate the spatial dependence of the mode
overlap Λ(r) according to [13], which includes the changes of the
local electric field polarization of the probe light near the focus.'

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Referee comment:
3) The heating model used to explain the measurements in figure 6
assumes that _each_ scattered photon changes the kinetic energy of the
atom by two recoil energies, as clearly stated towards the bottom of
page 4 right column (where the directionality of the heating is also .
discussed). However, absorption-emission cycles in which the absorbed
photon is emitted (almost) into the direction of the laser beam would
leave the momentum of the atom and, hence, its energy (almost)
unchanged. The heating model therefore seems incorrect which makes the
good agreement between experiment and simulation in figure 6a somewhat
obscure. The authors must resolve this issue.

Reply: There seems to be a misunderstanding about how we estimate the heating
in the probe interval. In Eq.7 we define the number of scattered photons
contributing to recoil heating as the number of photons scattered out of the
laser beam path.  Therefore, absorption-emission cycles in which the absorbed
photon is emitted into the direction of the laser beam do NOT contribute to
the heating, as correctly pointed out by the referee. To explain more clearly
how we obtain the amount of the motional heating, we rewrote the corresponding
paragraph and Eq.7:

'Extracting the temperature dependency of the light-atom interaction directly
from the time-resolved transmission spectrum (Fig. 5) is difficult because the
scattering rate and therefore the motional heating varies during the probe
interval and depends on the probe frequency.
For a quantitative analysis, we sort the detection events for each probe
frequency according to the number of scattered photons instead of the probe
pulse duration t_p.
The number of scattered photons n_s(t), time-integrated from the
beginning of the probe interval to time t, is calculated from the
transmitted photons via

(Eq. 7)

where n_ref(t_i) and n_p(t_i)  are the numbers of detected photons at detector
D_f in time bin t_i during the reference and the probe interval, respectively,
eta_op=59(5)% is the optical loss from the atom to the detector, and eta_f is
the  detection efficiency....'


----------------------------------------------------
Referee comment:
4) Figure 4b claims to display results of a saturation experiment, and
serves to experimentally determine the saturation power. However, the
reflection continues to significantly increase even beyond power
levels as high as 4 times the saturation power. How can the saturation
power be determined from a measurement which shows no limit in the
amount of reflected light (although plotted on a logarithmic scale)?

Reply: For the saturation measurement (Fig.4b) we recorded the
reflection count rate for 15 different values of the incident probe
power spanning over two orders of magnitude (from 0.5pW to 123pW).
Compared to the prediction of the standard semi-classically driven two-
level atom (Eq.6), we find an good agreement when we fit to Eq.6
with two free parameters, the saturation power and the collection efficiency.
This agreement (reduced chi-square of 1.3) over a wide
range of incident powers gives us high confidence in the accuracy of
the extracted parameters.  In fact the relative uncertainty in the
collection efficiency obtained from the least-squares fit is only 1%,
as stated in the manuscript. As pointed out by the referee, the
extracted saturation power indicates that the highest incident probe
power corresponds to approximately four times the saturation power. We agree
that the detection count rate is expected to further increase for higher
powers. However, we had to limit the incident power to the range shown in the
figure to ensure a linear response of the photo detector, as the avalanche
photodetector we used (an actively quenched standard Excellitas device)
exhibits a nonlinear response for high count rates. The incident power range
we could therefore reliably measure covers what we 
believe is the most meaningful part of the saturation curve over two orders
of magnitude, at the expense of covering the last 20% of the reflected power
in a saturation behavior.

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Additional changes to the manuscript:

5) Changes in Fig 4b):  We relabeled the y axis to 'detection rate at D_b'
instead of 'reflection counts'. Furtermore, the range of the probe power axis
starts now from lower values; previously one data point was not visible.

6) We renamed the different "phases" of the experimental cycle to
"intervals" in order to avoid confusion with the phase used in the mode
matching explanation around equation 3.


With this, we hope to have addressed the questions raised, and look forward
for your reply.

With Best Regards on behalf of all authors,

Christian Kurtsiefer