Dear Editor, first, we would like to thank the reviewers for their careful reading of our manuscript, and their constructive comments to improve on it. As the main critique addressed context and referencing, we rewrote large parts of the introduction, and added specific information in other parts of the paper. We attach a PDF document to better highlight the changes in the manuscript, and provide a point-to-point reply below to the issues brought up by the referees: Referee 1: Comment: 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. Reply: We agree with the assessment that we did not provide sufficient context, and that we were clearly missing important references. In this manuscript, we present an analysis of the influence of the trapping light on the light-atom coupling efficiency and demonstrate the realization of a hyperfine qubit with strong, qubit-state selective coupling to a propagating free space mode. We believe that such a system will be useful for the generation of entangled photons. Therefore, we extended the introduction to clarify our motivation and put our work in context with published research; we added nine references (Ref: 6-7, 10-16) to that extent, including those suggested by the referee. -------------------------------------------------------------- 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. Reply: Reference [R3] is certainly relevant and we included the article in our references. We are interested in combining good light-atom coupling with good hyperfine coherence. Thus we use the transmission to investigate the system because it allows us to precisely quantify the light-atom interaction strength. We believe that the extended/updated introduction of the revised manuscript clarifies this. -------------------------------------------------------------- 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. Reply: We agree with this assessment, and now give appropriate reference to these works. In our work, we show that the effect of the magnetic field has also significant influence on the optical coupling, complementing the finding in these references. -------------------------------------------------------------- 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. Reply: Compared to the experiments described [R1] and [R2] (our new references 13 and 14], our trapping beam is actually not strongly focused; the trap beam waist is about 2~lambda, for which the “virtual” magnetic fields are negligible. To clarify the situation, we added the beam waist to the description of the experiment in the first paragraph of section III. -------------------------------------------------------------- 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. Reply: We aim to realize a hyperfine qubit with strong, qubit-state selective coupling to a propagating free space mode. We believe that such a system will be useful for the generation of entangled photons. We extended the introduction to clarify state what our motivation is and put our work in context with published research. On top of the suggested references [R1-R4, 13,14,15,11 in the revised manuscript], we found that references [6,7,9,1,12] were relevant as well. Regarding the comparison of the observed coherence times, references [R1]-[R2] show damping times of Rabi oscillations on the order of few hundreds microseconds. We observe similar damping values (Fig 5b). However References [R1]-[R2] don't report any coherence decay rates for Ramsey or spin echo sequences. -------------------------------------------------------------- 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. Reply: Our setup has been described in detail in previous work, in particular in references [21, 27 and 28], so in this manuscript, we tried only to give a concise summary of the setup. In order to make the manuscript still a bit more self-contained, we added the waist of the dipole trap beam and the polarization purity to the main text, which should clarify many questions without the need to refer to these references. The polarization purity is not the main limitation for the hyperfine coherence time: the polarization extinction ratio for the dipole trap beam is about 34dB, from which we expect the vector light-shift induced dephasing rate to be more than an order of magnitude lower than what we observe. Our coherence time is most likely limited by magnetic field noise. We added this information to the first paragraph of section III as well. -------------------------------------------------------------- Referee 2: general comment: Since the results of the present manuscript are directly and specifically tied to the authors system potential publication would require an effort to identify the additional physical insight which is gained form the author’s efforts with respect to the already published material. reply: We believe our results are relevant to many researchers working with neutral atoms in optical tweezers. In this field the effective coupling of light to the atoms is a big challenge. We demonstrated some subtle effects of the tensor light shift on the optical coupling and our approach to achieve good coherence with good optical coupling will be of interest to the community. We tried to address this motivation in the expanded introduction section, and expanded significantly the reference to published material. Specific comments: 1- The dipole trap has linear polarization perpendicular to the quantization axis (so balanced sigma+/-), to avoid the vectorial light shifts. Would there be an advantage to have it parallel to the B field, i.e. Pi- polarized? Reply: To be able to drive the closed sigma^- transition F=2 m=-2 to F'=3 m=-3, we apply the magnetic field along the optical axis of the high-NA lens. Thus a dipole trap that is parallel polarized to the B-field would require another high-NA lens with an optical axis perpendicular to the quantization axis. While this is possible for low-NA lenses, we don't see an obvious way to implement this with high-NA lenses which (by definition) cover a large part of the solid angle. 2- There must be an error of an order of magnitude in the B-field axis of Fig. 3 since the maximum is around 14 Gauss = 1.4 mT, and in the text the maximum reported value is 144 uT. Reply: Thanks for pointing this out; we corrected the error, and changed also the horizontal axes in Figure 3 consistently to SI units. 3- In part IV to test the discrimination of bright and dark states during state detection, it is not clear if they drive the atom with the probe beam along the quantization axis, or from the side with the "state redout beam" (Fig. 2). If they drive it from the side, which polarization is used? In that case the sigma- polarization is not defined, and the coupling should be lower and differ from their previous characterization (Fig. 3). Reply: Our state readout method is based on state-selective fluorescence detection and we use a dedicated state readout beam for the discrimination of bright and dark states during state detection. This beam the drives the F=2 to F'=3 transistion but not specifically the closed transition as it consists of two counterpropagating waves with opposite circularly polarization. It is correct that the state readout beam is not strongly coupled to the atom, i.e., strongly focused through the high-NA lenses. The strongly coupled mode is the strongly focused, propagating mode through the high-NA lenses. We extended our description of the readout method in Section IV to clarify this. With this, we hope to have addressed the issues raised by the referees. Additionally, we fixed a number of issues with mathematical formatting and language. All changes should be visible from the difference manuscript. With this, we look forward for your consideration of our revised manuscript.