Dear Editor, we would like to thank the reviewer for the careful reading of the manuscript, and the constructive comments. We would like to submit a revised manuscript, addressing the issues brought up in the review (see detailed responses below). We hope to have addressed all issues, and look forward for your reply. With Best Regards on behalf of all authors, Christian Kurtsiefer ------------------------------------------- General changes: - we merged figures 1 and 2; this changes the figure numbering in the manuscript. ------------------------------------------- Editorial comments: - corrected units in Fig.1 (previously Fig.2) to "units of" - updated Ref. 41 from arxiv to published version ------------------------------------------- Point-to-Point response to referee comments: 1)The introduction should also mention Raman sideband cooling, that was also employed in several of the references. Reply: We included Raman Sideband Cooling in the Introduction: Page 1, first paragraph: "Efficient PGC enables further cooling to the vibrational ground state by Raman sideband cooling [13–15]." ------------------------------------------- 2)The x, y, z orientation of the beams could also be indicated in Fig.2. In several places the "orientation of the PGC field" (the E field?) is mentioned, where actually the direction of beam propagation is relevant. Reply: We merge Fig.1 and 2 to clarify the beam orientation. We also replace "orientation of the PGC field" with "direction of the PGC beams". ------------------------------------------- 3) The residual magnetic fields and the corresponding shifts should be given. Reply: We added a comment about the residual magnetic fields. Page 3, first paragraph: "Residual magnetic fields are compensated to approximately 4uT at the position of the atom." ------------------------------------------- 4) The physical reason for the missing tensorial shift in the case of the employed atomic states should be mentioned. From the observed significant sensitivity to the purity of the linear trap polarization, I wonder, if the strongly suppressed residual HFS induced vectorial shift might still be relevant. Giving an estimate of its magnitude could be helpful. Reply: The residual tensorial shift due to the finite detuning of the FORT compared to excited state HFS, is negligibly small (less than 1 Hz) and smaller than the precision of our magnetic field compensation (residual Zeeman shifts of about 30kHz). We thus conclude that the cooling limit is not affected by the residual tensorial ac stark shift. We added a similar statement in the manuscript and one reference [27]. Page 1, paragraph 3: "In a pi-polarized trap, all spin states within the ground state 5S 1/2 , F =2 manifold are shifted equally as the tensorial shift is negligible for far off- resonant trapping fields [25-27]." ------------------------------------------- 5) Ref. 12 mentions a vectorial shift even with linear polarization due to the non-paraxial focus in the large-NA trap. In the present experiment the conditions seem to be similar. What would be the corresponding influence on the level structure and the temperature? Reply: In our experiment the FORT is focused to beam waist of approximately 1.4um, therefore variations of the polarization due to tight focusing are relatively small. We added the size of our beam waist, a corresponding statement, and one reference [36]. Page 2, second paragraph: "The large beam waist ensures that the variation of the polarization near the focal spot is insignificant [13, 14, 36]." ------------------------------------------- 6) Fig. 4: The error bars indicate statistical uncertainties. Is there any estimate of systematic uncertainties in the temperature measurement? Reply: The systematic uncertainties of the temperatures estimate caused by the error of the trap frequencies and the beam waist are a factor of 3 smaller than the statistical uncertainties. We added a corresponding statement in caption of Fig. 3: "Error bars represent statistical uncertainty (one standard deviation). Systematic uncertainties, caused by errors in the determination of trap frequencies and the beam waist, are smaller than the statistical uncertainties."