Two-Atom Superradiance Including Magnetic State Degeneracy

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Please take a look at the attached file.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript contains a theoretical analysis of the radiation from a pair of atoms - the simplest atomic system which can display superradiance. Specifically, the manuscript extends the original study of Lehmberg to include magnetic state degeneracy.

The manuscript contains a brief introduction to the problem with some historical context, a description of the model used to describe the system and calculate the radiated intensity. The analysis considers different spatial configurations (atoms aligned the x-axis and along the z-axis) and shows that although the results of Lehmberg are recovered for alignment along the z-axis (time0integrated radiation pattern equals that of independently radiating atoms), the situation differs for atom alignment along the x-axis, with additional terms in the expression for the time-dependent radiation pattern which arise from interference and are dependent on the separation of the atoms. Specific results for the time-integrated radiation pattern are presented for the case where ground state angular momentum G=0 and excited state angular momentum, H=1.

The manuscript is well written. To my knowledge, the results presented are novel and the analysis is correct. The manuscript will be of interest due to shining new light on a fundamental aspect of light-atom interactions.

In my opinion, the manuscript is suitable for publication in Atoms, but I recommend amendments to the manuscript before publication :

• Although the system being analyzed is fairly simple, I think most readers would find one or two simple schematic diagrams, useful, particularly since spatial orientation is such an important aspect of the study.

• In line 43, the author states that a hybrid approach is used where the rotating wave approximation (RWA) and Weisskopf- Wigner approximation (WWA) are used when calculating expectation values of operators but not for the source-field expressions. Some additional words explaining why this hybrid approach is required would be useful. What would be the consequences if it was not applied?

• The main result of the manuscript is the effect of the relative position of the atoms on the time-integrated radiation pattern. It would be useful if the author could explain more about the physical reasons for the result, in addition to the mathematical details.

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

In this article, the author describes in which cases the starting point of superradiance of two close-by atoms differs from independent decay. In particular, he finds that atoms along the quantization (z-) axis look like independent atoms, while atoms perpendicular to that (along the x-axis) do show interference. This result is derived in a complete and appropriate mathematical model, and explains in detail some results that might have seemed puzzling before. 

Altogether, I think this is a very good paper to publish in "Atoms." I have a few comments that would potentially improve the manuscript. 

1. It would be nice to also provide a somewhat more intuitive explanation in addition to the math on why these results appear. (Even putting the analytical results in better context with work describing these results without the full math would be helpful.)
2. This might go hand-in-hand with point 1: If at all possible, it would be good to provide some numerics and curves, including angles between 0 and pi/2, just for completeness. 
3. Fig. 3 is a bit hard to puzzle out. Could the definition of \theta and \phi be given here again (such that one doesn't have to go back in the text if one is just looking at figures)? That said, also both (red and blue) results are given with the same \theta = \pi/2. Is that a typo?

Other than that, this is ready to go!

 

Author Response

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Author Response File: Author Response.docx

Reviewer 4 Report

Comments and Suggestions for Authors

The author discusses the radiation pattern from two atoms, which interact with each other via the vacuum radiation field. The results are obtained for the magnetic state degeneracy and initial inversion. The author shows that the time integrated radiation pattern from the atoms lying on the z−axis is the same as for non-interacting atoms, but differs from the atoms lying on the x−axis. I think that the obtained results provide readers with new information about the superradiance. I recommend publication.

Author Response

I thank the referee for their comments.