REFEREE REPORT(S):
Referee: 1

COMMENTS TO THE AUTHOR(S)
The manuscript presents a study of single-atom transmission spectra and the effect of optical trap depth and magnetic field.  The work is sound, but the manuscript does not have a clear objective or “main result.”  The authors present a collection of results without a unifying story, and without proper discussion of the field at large.  If the manuscript is rewritten with a clearer message and proper context, then it should be reconsidered for publication in NJP.

Some specific comments:

1. The present results should be put in context by including more discussion of the field, including other studies of light shifts and coherence in single atom traps.  References [R1]-[R4] are particularly relevant, and should be discussed in the manuscript.  

2.  Reference [R3] in particular merits detailed discussion, since there is significant overlap.  This reference has data and discussions about the effect of trap depth and optical polarization on single atom spectra.  It is surprising that the authors did not reference this work since they have done so in earlier publications.  The present manuscript presents different data (transmission vs. fluorescence) but it is not clear what this adds.  There should be discussion of why the authors focus on this figure of merit versus those used in previous works.  There are certainly interesting applications of strongly-coupled absorption beams but they are not clear in the current manuscript.

3. The effects of magnetic fields have also been previously considered, especially in [R1] and [R2], where a magnetic bias field is necessary for good coherence.  

4. [R1] and [R2] also discuss the well-known effect that a focused beam presents a “virtual” magnetic field, even with linearly polarized trapping light, due to the curved optical wave fronts.  Therefore the author’s claim that the vector light shift vanishes is not correct.  It is possible that the vector light shifts are negligible in this case, but that should be argued.

5.  References [R1]-[R2], and the manuscript reference [25], have considerably longer coherence time.  In particular, [R1] and [R2] are also using stretched (non-clock) states.  Ref. [25] uses the clock states, so perhaps the comparison is not fair, but the authors have not really justified why they prefer to use a state with an optical cycling transition.  The present work should be placed in the context of these other results.

6. The manuscript should have more technical details about the dipole trap, such as waist and axial width, as well as polarization purity and whether that is a limitation.

[R1] A. M. Kaufman, B. J. Lester, and C. A. Regal, Phys. Rev. X 2, 041014 (2012).
[R2] J. D. Thompson, T. G. Tiecke, A. S. Zibrov, V. Vuletic, and M. D. Lukin, Phys. Rev. Lett. 110, 133001 (2013).
[R3] C. Y. Shih and M. S. Chapman, Phys. Rev. A 87, 063408 (2013).
[R4] N. R. Hutzler, L. R. Liu, Y. Yu, and K.-K. Ni, New J. Phys. 19, 023007 (2017).