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Report of Referee A -- LF16076/Nguyen
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The paper "Single atom coupled to a near-concentric cavity" present
the coupling of single atom randomly loaded from a MOT into a dipole
trap to the mode of near-concentric cavity. Near concentric cavities
have the advantage to have a very small waist at the center of the
mode, allowing the authors to get a coupling g0 on the order of 1.7
times the natural decay rate of the atom. Although this is impressive,
the cavity itself is very lossy (with a linewidth on the order of 100
MHz), and the final cooperativity is C~0.08, which has already been
achieved in the context of near concentric cavity. As a result, I do
not believe the paper in this present form should be published in PRL.

I have a few questions:

- Formulae (3): it is not clear how the value of \Delta n is measured.
Is it a guess to fit l_cav? It seems to me that 1044 or 1042 would
work as well. How did you determine \nu_780 and \nu_810? With which
precision do you know their values?

- Figure 3: How is determined the threshold? To what correspond the
event at 1 s?

- Finally, even after the averaging over the CB coefficients, the
expected value of g0 is still larger than what is measured. Can you
comment on that?

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Report of Referee B -- LF16076/Nguyen
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Experiments in which single atoms are coupled to optical cavities have
achieved strong atom-photon coupling, that is, a coupling rate faster
than the decay rates of the atom and the cavity field, using highly
reflective mirrors and short cavities. In contrast, in this
manuscript, the authors achieve a high coupling rate (though not yet
in the strong coupling regime) by using a near-concentric cavity, less
than 2 microns from instability, coupled to single Rb atoms. This
approach is promising because it obviates the need for expensive,
customized mirror coatings, and because it may be easier to trap,
image, and manipulate atoms in longer cavities.

I find the experimental results presented in the manuscript
interesting, but it's also clear from the manuscript that there are
serious costs to this implementation. The authors found that the
cavity mirrors needed to be re-aligned in situ every 15 minutes, a
substantial experimental constraint. Furthermore, the mirror losses in
their current system are quite high, rendering the system not suitable
for many cavity-QED experiments, but with a higher finesse (as
suggested at the end of the manuscript), wouldn't the system be even
more sensitive to misalignment? The authors also suggest the a factor
of 10 improvement in the distance from the concentric threshold might
be possible, but they don't elaborate on how this could be achieved.

In short, given the limitations of this approach, it's not clear to me
that it represents a significant advance in the field.

Other points:

- I have a concern about the measurement of the cavity length, as it
is claimed in both the abstract and in the manuscript that this is
determined with error bars of 10 nm (!). However, the radius of
curvature of the mirrors is stated as 5.5 mm, with no error bars
given. Certainly there are error bars inherent in the mirror
polishing, which should then play a role in the determination of l_cav
and its uncertainty?

- 1st page, 1st paragraph: "by coupling atoms (or other quantum
emitter)" - emitter should be plural

- 1st page, 2nd paragraph: The mode volume is introduced but not
defined. It is particularly important to define the mode volume
clearly in this paper because in the case of near-concentric cavities
(or any cavity where the length is not much shorter than the mirror
radii of curvature), the relevant parameter in the coupling strength
is not the actual mode volume but, as the authors mention in the same
paragraph, the effective mode volume.

- 1st page, 2nd paragraph: "A cavity is concentric when the separation
of the two mirrors l_cav..." Strictly speaking, the relevant length is
not just the mirror separation but also takes into account penetration
of the cavity field into the mirror coatings; see, e.g., the
discussion in Ref. 20.

- 1st page, 4th paragraph: A concentric cavity is described as being
"marginally stable." It might be also worth mentioning that the spot
size on the mirrors would have to be infinite.

- 2nd page, 2nd paragraph: I'm confused about why the reflection
measurement is disregarded in determining the cavity linewidth. I
understand that using the transmission value is a worst case, but
shouldn't the error bar at least reflect the two measurements?

- 3rd page, 1st paragraph: "From the low frequency of loading events
we infer that the probability of simultaneously loading two atoms in
the center region of the trap to be negligible." This statement ought
to be made more quantitative. What is the loading frequency? What is
the estimated two-atom rate? Also, why is the inferred survival
probability in Fig. 3b 75% at time t=0? What role is the motion
(temperature) of the atoms understood to play in these measurements?
What about the registration of the FORT with respect to the cavity?

- 4th page, 2nd paragraph: "for a clean two-level atom" - perhaps the
authors could be more precise about what they mean by "clean"

- There seems to be some mix-up among citations 27-29. Presumably 27
and 28 belong to the Rydberg atom example and 27 to ions.