An Evaluation of the Zeeman Shift of the 87Sr Optical Lattice Clock at the National Time Service Center
Round 1
Reviewer 1 Report
The paper belongs to the area of metrology. Its intent is to improve the accuracy and the stability of atomic clocks. As such, it is important for applications to various technologies.
The authors performed accurate experimental measurements of the coefficient of the quadratic Zeeman effect. There experimental result is consistent with the corresponding measurements done by few other groups.
I recommend the paper for publication after the authors will implement the following. In addition to the Zeeman effect, there are other important factors affecting the accuracy and the stability of the 87Sr-based atomic clock: the Stark effect, collisions, and the gravitational field. From the paper it is unclear whether the influence of the Zeeman effect is much smaller, or of the same order, or much greater than the influence of the three other factors. Therefore the authors should provide a comparison of the influence of the Zeeman effect with the influence of the three other factors. Only thereafter the paper could be published.
Author Response
Comment: 1. I recommend the paper for publication after the authors will implement the following. In addition to the Zeeman effect, there are other important factors affecting the accuracy and the stability of the 87Sr-based atomic clock: the Stark effect, collisions, and the gravitational field. From the paper it is unclear whether the influence of the Zeeman effect is much smaller, or of the same order, or much greater than the influence of the three other factors. Therefore the authors should provide a comparison of the influence of the Zeeman effect with the influence of the three other factors. Only thereafter the paper could be published. Response: We are really appreciating your suggestion for improving this description more complete. In the revised manuscript, we have added a sentence to supplement how much the influence of the Zeeman shift compares to the three other factors in the one-dimensional 87Sr-based atomic clock. The added sentence is: “In terms of a one-dimensional optical lattice clock, generally, the Zeeman shift is much smaller than the Stark frequency shift and the gravitational frequency shift, and is at the same order of the collision frequency shift.” (Page 1, line 35) And we also carefully checked the spelling and expression over whole manuscript and have revised misspelled words and ambiguous expressions. All revisions have been highlighted by using the “Track Changes” function in the revised manuscript.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
In this manuscript, Lu et al. introduce a very accurate evaluation of the Zeeman shift in a 87Sr optical lattice clock operating at National Time Service Center of China. The research design is appropriate, the applied methodology is rigorous and correct, the experimental setup is very carefully described, and results are well-presented and properly discussed. English is quite satisfactory, even if the manuscript need some moderate changes here and there.
My biggest concern is about the prime novelty of the work. As authors correctly mention in the introductory section of their paper, measurements of the quadratic Zeeman shift coefficient in case of a 87Sr optical lattice clock, as well as studies on the effects of Zeeman shift on the performance of an optical lattice clock, are already present in the literature [Refs. 22-26], and published results are consistent with those introduced by the authors in the submitted manuscript. Therefore, authors should clearly highlight the novelty of their findings, or at least elaborate a little bit more on the differences between their work (in terms of methodologies and/or results) and the previous works published.
By the way, in my opinion, the paper deserves publication in Applied Sciences journal after minor revision.
Herewith a detailed list of minor comments:
I would add in the introductory section the reference “M. Takamoto et al, Nature 435, 321-324 (2005)”, aimed at providing the reader with a comprehensive and basic description of the operating principle of an optical lattice clock.
Line 14. I would rather say that the first-order Zeeman shift is “almost completely removed”, and not “removed” completely. Otherwise there wouldn’t be any “remaining” shift.
Line 16. I’d replace (here and at other lines in the text, e.g. line 188) “remaining first-order Zeeman shift” with “residual first-order Zeeman shift”.
Lines 17 and 19. Units of measurement of Zeeman shifts are missing.
Line 29. Replace “excellent performance in instability and uncertainty” with “excellent performance in terms of stability and accuracy”.
Line 33. “Stark” should be uppercase.
Line 39. “Landé” should be uppercase.
Line 74. Replace “repressing” with “suppressing”.
Line 165. Replace “Allen” with “Allan”.
Author Response
Comment: 1. My biggest concern is about the prime novelty of the work. As authors correctly mention in the introductory section of their paper, measurements of the quadratic Zeeman shift coefficient in case of a 87Sr optical lattice clock, as well as studies on the effects of Zeeman shift on the performance of an optical lattice clock, are already present in the literature [Refs. 22-26.], and published results are consistent with those introduced by the authors in the submitted manuscript. Therefore, authors should clearly highlight the novelty of their findings, or at least elaborate a little bit more on the differences between their work (in terms of methodologies and/or results) and the previous works published.
By the way, in my opinion, the paper deserves publication in Applied Sciences journal after minor revision.
Response: Thank you for your suggestion. In fact, in our experiment, the intensity of magnetic field is modulated in the range of 0-1.6 G, which is different from the PTB (with the range of 0-6 G according to reference [27]). The greater magnetic field can obtained more accuracy result at the same measurement time because of the larger lever arm (according to reference [18]) and the second-order Zeeman shift coefficient measured by PTB is -23.0(3) MHz/T2. The first measurement of the second-order Zeeman shift coefficient of JIL, with a similar magnetic field range to this work, is 23.7(33) MHz/T2 according to reference [23]. The second-order Zeeman shift coefficient of this work is -23.0(4) MHz/T2, which not only redetermines the second-order Zeeman shift coefficient (with a similar precise to the PTB and much more accuracy than the first measurement of JIL) but also indicates that our system has a good stability.
Comment: 2. I would add in the introductory section the reference “M. Takamoto et al, Nature 435, 321-324 (2005)”, aimed at providing the reader with a comprehensive and basic description of the operating principle of an optical lattice clock.
Response: Thanks for your thoughtful proposal. This reference is a milestone article in the area of the optical lattice clock and we have added this reference in line 27 in the revised manuscript.
Comment: 3. Line 14. I would rather say that the first-order Zeeman shift is “almost completely removed”, and not “removed” completely. Otherwise there wouldn’t be any “remaining” shift.
Response: Thank you for your correction which is more proper for our paper and we have revised“removed” to“almost completely removed” in line 13 in the revised manuscript.
Comment: 4. Line 16. I’d replace (here and at other lines in the text, e.g. line 188) “remaining first-order Zeeman shift” with “residual first-order Zeeman shift”.
Response: We have replaced“remaining first-order Zeeman shift” with “residual first-order Zeeman shift” in the whole manuscript.
Comment: 5. Lines 17 and 19. Units of measurement of Zeeman shifts are missing.
Response: In fact, we should account for it here. In generally, a kind of frequency shift should have a unit, e.g. Hz. However, this expression of Zeeman shift is, actually, a ratio which equals vZeeman/vSr, vZeeman representing the measured value of Zeeman shifts (with a unit of Hz), vSr representing the clock transition frequency (about 4.29228×1014 Hz). This expression is common in terms of describing the frequency correction of a clock (such as in reference [23-27]), because it is convenient for readers to compare the performance of our clock with other clocks.
Comment: 6. Line 29. Replace “excellent performance in instability and uncertainty” with “excellent performance in terms of stability and accuracy”.
Response: We have replaced“excellent performance in instability and uncertainty” with “excellent performance in terms of stability and accuracy” in line 28 in the revised manuscript.
Comment: 7. Line 33. “Stark” should be uppercase.
Response: We have modified it in line 32 in the revised manuscript.
Comment: 8. Line 39. “Landé” should be uppercase.
Response: We have modified it in line 40 in the revised manuscript.
Comment: 9. Line 74. Replace “repressing” with “suppressing”.
Response: We have modified it in line 89 in the revised manuscript.
Comment: 10. Line 165. Replace “Allen” with “Allan”.
Response: We have replaced “Allen” with “Allan” in line 198 in the revised manuscript.
All revisions have been highlighted by using the “Track Changes” function in the revised manuscript.
Author Response File: Author Response.pdf
