Dear Editor,

we tend to agree with the referee's critique that we unnecessarily left on a
slightly negative note with the last revision, so we tried to focus more on
the core of the message in this work, namely the influence of the atomic
temperature on  the interaction with light focused to a near diffraction-limited spot size.

In the present work, we demonstrated conclusively the effect of the
temperature in experiment and theory. We chose to compare our results to a model which assumes an ideal lens rather
than a complicated model of a lens with aberrations, and agree with the referee that it is regrettable that our observed magnitude of
interaction does not match the expectation of this model. However, real lenses
are not ideal and we believe, as stated in the manuscript, that lens and wave
front errors are the main source for the reduced interaction.

In that sense, we would contest the assessment of the referee that we do not
provide a clear instruction on how to improve. To the contrary, our work
specifically quantifies one reason for the discrepancy between observed and
theoretically expected interaction, namely a motion of the atom around the
focus of the lens due to non-zero temperature, and sharpens the focus of future
work on such a system to lens aberrations.

Obviously, this came not as clearly across as we intended, so we made the
following changes to the manuscript to improve the readability, and to better
emphasize our main result, the temperature dependency. We also introduce the
possibility of a reduced interaction due to aberrations earlier in the text and refine the following paragraphs:

description of Eq 8, page 4

"For the probe field, we use the effective interaction strength Lambda_eff (r)
= (1 - alpha) Lambda(r) where we evaluate the spatial dependence of the mode
overlap Lambda(r) according to [13], which includes the changes of the local electric field
polarization of the probe light near the focus. In addition, we heuristically
introduce the parameter alpha which accounts for a reduced interaction strength
due to experimental imperfections."

caption of Figure 4b), page 4

"The temperature dependence is well reproduced by Eq. (8) with alpha = 0.54(1) as
a free fit parameter (red solid line, chi^2_red = 11.6). Dashed blue line is
the expected extinction for an ideal lens, Eq. (8) with alpha = 0."

second paragraph, page 5

"Figure 6(b) (solid red line) shows the theoretical extinction expected from
Eq. (8) with our focusing parameters using alpha = 0.54(1) as a free parameter.
The reduction of the extinction as a function of scattered photons is well
reproduced by the model. From Eq. (8) with alpha = 0.54(1), we extrapolate a
spatial overlap Lambda = 5.1% for a stationary atom which is approximately 10%
larger than the interaction observed for our lowest temperatures. This
estimation provides an upper bound for the temperature effect because our
model treats the atomic motion classically and therefore does not include the
finite spread of the motional ground state. The large value of alpha = 0.54(1)
means we observe less interaction compared to the tight focusing theory
outlined in [13]. This reduction is likely to be caused by imperfections of
the focusing lens and deviations of the incident field from a Gaussian beam."

Conclusion, page 5

"Further improvement of the interaction strength requires a more careful
analysis of the focusing lens, and the application of aberration corrections
to the incident probe field."

With this, we hope to have adequately addressed the resentment the referee
felt with the last manuscript revision, and hope for a favorable
consideration for publication in Physical Review A.

With Best Regards on behalf of all authors,

Christian Kurtsiefer