Talk:Cold atom experiments in quantum chaos

Referee remarks

Referee A:

My overall opinion is that the review is of very good quality, at the same time pedagogical and scientifically sound and detailed. I would recommend some (minor) changes:

1) In the section `Introductioń´: ``This system must also be Hamiltonian in order for quantum effects to be manifested. This may be confusing for readers, quantum effects exist in dissipative systems

2) It might be useful to mention at the beginning of the `Phase space´ section that classical Hamiltonian systems are by definition constructed in phase space.

3) In the beginning of the section `Kicked rotor´, one has first the impression that the system is always localized. Then, towards the end of the section, the subsection `quantum resonance' explains that it is not the case. It will be clearer if some caveat or hyperlink is put in the introductory paragraphs of the section to mention the presence of the resonances.

4) In the section `Other experiments´, I would recommend to add a sentence about recent experiments using BEC, which allow a better momentum resolution (see e.g. Ryu et al Phys. Rev. Lett. 96, 160403 (2006) where high-order quantum resonances of the kicked rotor were observed, or A. Ullah and M. D. Hoogerland Phys. Rev. E 83, 046218 (2011) where an experiment of approximate time-reversal was realized with the kicked rotor)

Authors' Response to Referee A

We have incorporated all of the helpful comments and suggestions of Referee A.

1. We clarified in the "Introduction" that a Hamiltonian system is needed to observe quantum chaotic effects, to avoid confusion regarding other quantum effects that can be seen in dissipative systems.
2. We modified the section "Phase Space" to emphasize that phase space is constructed for Hamiltonian systems.
3. In the section on "Kicked Rotor" we added a caveat to the phenomenon of Dynamical Localization in special cases known as Quantum Resonances. The reader is directed to read the following section on this topic.
4. In the section on "Other Experiments" we added all the references suggested by Referee A.

Referee B

This is an excellent review.

I propose the authors consider the following clarifications:

1. It should be stated that for localization, the atoms should be kicked in the horizontal direction
2. the comment about the classical boundary is not clear.
3. In the context Quantum Resonances recent papers by Guarneri and coworkers should be cited
4. In the context of tunneling papers of Guarneri and coworkers as well as of Ketzmerick and coworkers should be cited.
5. Chaos assisted tunneling is a semiclassical concept. What is the effective Planck's constant for Fig. 11?
6. For rffects of noise, the work of Ott and coworkers and may be also of D. Cohen should be mentioned.
7. In "additonal reading" the book of Tabor should be mentioned
8. page 5, central paragraph "localizes" should be replaced by "localized"

Authors' Response to Referee B

We have incorporated almost all of Referee B's comments, which were very helpful, and we answered one inquiry:

1. We added a sentence to explain this in the "Other Experiments" section.
2. We have separated the discussion of the classical boundary into a separate paragraph and rewritten it for clarity.
3. We added the reference (Fishman et al., 2002) to the section on quantum resonance.
4. A literature search for Guarneri and tunneling turns up papers on tunneling between localized states and resonance-assisted tunneling. These are important topics, but not directly related to any experiments with cold atoms. Similarly, the tunneling work of Ketzmerick seems to be related to transport between chaotic and regular regions, and tunneling in billiard-type systems. Again, these are interesting topics, neither of which has been studied in cold-atom experiments. We are thus not sure what the Referee had in mind here; we are happy to incorporate more specific suggestions for citations.
5. Technically speaking, the phase space in Fig. 11 is only classical. The effective Planck constant for the data in Fig. 12 is around 2. This is not in the semiclassical regime but still represents chaos-assisted tunneling because the Floquet states still clearly associate with stable or chaotic regions in phase space, and a transition between two- and three-state behavior was clearly observed. This is discussed at length in the references (Luter & Reichl, 2002; Averbukh et al., 2002), and also the Ph.D. dissertation of Steck.
6. We added references: Ott et al. 1984 and Cohen 1991.
7. We added the Tabor book to the reading list.
8. We fixed this typo.