Prospective Optical Lattice Clocks in Neutral Atoms with Hyperfine Structure

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper is well written with many details and equations, and with a good introduction underlying current problems in the field of optical clocks.

I have several small suggestions that might improve the paper. The authors are free to dismiss them as they are not significant.

1) The last paragraph of 2.1 (lines 136-146).
The angle θp is defined by magnetic field and can be actively stabilized in some cases. It requires some extra work and takes up some percentage of "useful" measurement cycles but it is still doable. I do not think it is fair to dismiss a lot of atomic species so easily. J=0 is simpler of course.

2) Equations 8-9
It should be mentioned at least once that {...} is a notation for Wigner 6-j symbol.

3) Section 2.4, line 182
I believe the suppression of the tensor shift follows from both eq. 8-9 and from some properties of Wigner 6-j symbols. It is not that obvious (simply by looking at eq. 8) so I think it should be mentioned explicitly as it was in Ref. [30].

4) Section 2.5.1, line 202
One could also actively stabilize or average out the quadratic Zeeman shift even at large magnetic fields with the use of clock transition between other hyperfine states (if possible) in the same atom.

5) Equations 10-11
It should be explained in 2.5.1 and 2.5.2 the origin of equations 10-11. A small note or a reference as it is not derived from the previous text.

6) Section 4.6, line 387
At this magnetic field, magnetic sublevel splitting may become so small that quantization axis is not defined by the external magnetic field. Please, add some discussion of this problem. Maybe it is not a problem at all, however, it is not obvious. Perhaps again, the suppression of quadratic Zeeman shift using different clock transitions between other hyperfine levels would allow one to work at "usual" magnetic field?

7) The paper has a lot of discussion of shifts for clock transitions in Mn and Cu. Perhaps a table that combines all the mentioned shifts with the necessary conditions and possible caveats would help readers to see the advantages and disadvantages of the two atomic species?

Author Response

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Reviewer 2 Report

Comments and Suggestions for Authors

The paper by Bothwell outlines interesting so far not  considered elements for optical lattice clocks. They are identified by a systematic analysis of the atomic properties that are required to be successfully employed in an accurate clock. Bothwell gives estimates and some relevant properties the support his conclusions. I think that these ideas and their description justify publication.

While the second part of the manuscript containing the detailed examples is very clear I believe that the first part would benefit from revisions. While the author tries to give a general introduction, he fails to provide the equally general context such that the statements are confusing me at several points. This starts in the abstract with lines 11 and 12 where the suppression of vector and tensor lattice light shifts is asked for (and further on in 32/33). A moderately informed reader will notice thar several publications discuss the existence and magnitude of these shifts in strontium lattice clocks, which do not seem to cause large problems. It should be made clearer way earlier in the manuscript that these effects already benefit from some suppression and how the suppression is motivated physically. Absolute statements like in lines 37 – 40 are not helpful because they are contradicted by the mentioned publications. I understand the author’s point of view but believe that these sections can be phrased in a way that triggers less objections.

On Fig. 1 and the related text, I would have benefited from a more explicit statement about the required quantum numbers. Since there is no distinction between quantum numbers of both states (F, F’), it is at this stage somewhat unclear if both states require an m_F = m_F’ = 0 level. I believe that this requirement leads to the necessity of an half-integer nuclear spin.

In lines 114 – 117, I think that the reference to J and Eq. 4 does not give a convincing argument as it is phrased now because J does not appear in Eq. 4.

I believe there is incorrect statement in lines 153 and 154: The reduced matrix element does not refer to the one between the clock states, does it?

Lines 182, 183: Again, the argument could be made clearer. The vanishing vector shift for m_F = 0 can be seen very clearly from Eq. 4. Reading the statement ‘deeply suppressed’ confuses me, if I come after some thinking to the conclusion that some multiplicative 6J symbols are zero due to a not fulfilled triangle relation.

The origin of the increase of hyperpolarizability in Sec. 2.5.2 is not well motivated. A reference or more explicit description would be helpful.

In the discussion of the possible magic wavelengths, I would expect a short comparison of the polarizabilities to those of e.g. Yb and Sr. An estimation of photon scattering rates at typical trap depth would also be valuable.

Minor comments:

All labels of angular momentum quantum numbers should be set in italic, values in math mode. Similar for R in line 259.

The label for the Zeeman levels should be written with the label for the main total angular momentum as subscript (m_F).

Spelling of sub-Doppler should be unified.

Spaces should be introduced in lists of quantum numbers, e.g. lines 178, caption Fig. 2.

The references show many typos in capitalization of journal names or other places (12, 18, 19, 24, 31, 35, 47, 55) and incorrect superscripts (3, 7, 20, 21, 35, 55).

Line 158 {^3\mathrm{P}_0}

Table 2 J’ = 1/2, missing spaces

Line 208 missing space

Line 232 1000 °C?

Line 241: The first line is not a sentence.

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

The article is well written and structured, although there are some typos. For example, I didn’t understand why in table 1 the symbol "a" is written differently for ground and excited states.  I also recommend to check the caption for the figure 2. Units along the x-axis at the figure 3 are not very convenient for a reader. I would change it to more usual 400, 600, 800 nm. The slope of the differential polarizability curve in the blue region is very large. It would be interesting to estimate how well should be the magic wavelength defined if using a blue one. The red one seems to be much less sensitive. 

 

Author Response

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Reviewer 4 Report

Comments and Suggestions for Authors

The paper describes alterative realization possibilities of optical lattice clocks. The work seems to be careful done.

I only suggest some minor changes:

1- Change font type in Fig. 1, e.g. to TimesNewRoman. Wit the present font,

J=I can be read easily as J=1

2- in the description of the transitions, you schould insert J=I before F=0 :

... with J=I, F=0 and J=1/2, F=1,2 and ...

in header of Fig.1, page 6, line 181, and header of Table 2

3- mention somewhere, that this condition can be fulfilled only for isotopes having half-integer nuclear spin quantum number

4- page 3, lines 69,70: change to

... light shift control - as demonstrated ... atoms - can be realized ...

5- page 7, line 230: change to

... a single stable isotope (55Mn) ...

6- page 8, line 248: change to:

The Kurucz dadabase [40] provides ...

7- page 9, line 270: in the text, the transition wavelength is 381 nm, while in Fig.2 380 nm

8- page 11, lines 342,343: what you mean by "two-photon transitions between states of different parity"? Usually for 2-photon transitions the intermediate virtual state has opposite parity, thus ground and final state must have the same parity.

Author Response

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Reviewer 5 Report

Comments and Suggestions for Authors

The manuscript by Botwell reports a theoretical proposal for new species of optical lattice clocks (OLCs). It proposes exploring two new types of clock transitions in bosonic atomic species with hyperfine structure, for instance by considering the manganese (Mn) and copper (Cu), two unexplored species within both the cold atoms and optical clock communities.
The paper is organized in six sections, which consist in an extensive theoretical description of the lattice light shift in OLCs and its application to the new hyperfine OCLs, a section dedicated to the application to the Mn atom with details on the cold atomic reference preparation by laser cooling, then two sections dedicated to the prospected clock operation with Mn and Cu atoms, and finally some concluding remarks.

The manuscript is well organized and interesting to read, offering a neat contribution to the discussion about the future of OLCs and possible candidates to the redefinition of the SI second with prospect for searches of new physics. Apart for few questions (see the list of minor comments at the end of this report), I think the manuscript is suitable for publication.

Minor comments and questions

- Eq.4-5: I assume the derivation of this formula is not an original work. Please add a reference for the non-expert reader.

- p. 9: "Direct laser cooling to 25 uK in a MOT operated on a metastable state may provide a novel continuous atomic source."
This statement is either not clear or misleading. I suggest to change into:
> Direct laser cooling to 25 uK on a metastable state may provide a novel continuous atomic source if operated in a 2D-MOT [some 2D-MOT atomic source reference]

- Sec. 6: I suggest to the author if possible to add a table summarizing the different sensitivities in current state-of-the-art clocks (Cs, Sr, Yb, Hg) compared to Mn and Cu, rather then simply pointing to the literature. This would emphasize the importance of this work.


- Ref. [1]: probably this is not the most appropriate reference to cite about magic-wavelength lattice. I suggest to change it with

Katori, H., Ido, T., & Kuwata-Gonokami, M. (1999). Optimal design of dipole potentials for efficient loading of Sr atoms. Journal of the Physical Society of Japan, 68(8), 2479-2482.

- Ref. [30] The European Physical Journal D 2013, 67, 1–16 > The European Physical Journal D 2013, 67, 92

 

Author Response

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