The last two sentences of paragraph 2.2 don't convince me. ("This relation also implies that even though higher order radial modes appear to be “larger”, their beam waists are the same. This allows coupling between an atom and cavity modes with equal strength across all radial transverse modes.")  I strongly advise you to look closer at the physics involved. If you can clarify this, it would make the case of your paper much stronger.

Our response: We have provided a supplemental document which works out explicitly the atom-cavity coupling constant to clarify our argument. On another note, we change the phrase "their beam waist are the same" to "their intensity cross-section areas remain the same", as it may generate some confusion on which is our definition of a beam waist.