Nonlinear Dynamics in Isotropic and Anisotropic Magneto-Optical Traps

Round 1

Reviewer 1 Report

In their manuscript, the authors present a three-dimensional hydrodynamical model for a magneto-optical trap (MOT). A Lagrangian density is set up in the case where multiple-scattering effects are relevant. Given the Lagrangian, with a Gaussian ansatz adopted, equations of motion for the cloud center-of-mass and the cloud widths (x, y, z) are derived. Numerical solutions are obtained for the widths in the anistropic and isotropic MOT cases, and a comparison is made. This model shows some potentialities in studying nonlinear dynamics in a MOT, making it of interest to the community.

However, there are some questions as well as suggestions that I have:

1. The authors state to review recent advances in the field of nonlinear dynamics of atomic clouds in MOTs. In this context, the following reference can be considered relevant: PRA 105, 013112 (2022). Comparison with the model in this reference is recommended (a nonlocal kinetic model, which includes multiple-scattering and thermal effects, without using spherical assumptions). In this context, can your model, in some form, make the predictions seen in this reference?

2. How come Gaussian density is assumed (see Eq. (6)), although in the multiple-scattering regime the density is uniform? Gaussian density assumption is appropriate in the case of a regime governed by single-atom physics (where multiple-scattering effects are negligible). 

3. Would the authors consider commenting Figures 1 and 2? It is, for instance, very strange Figure 1 is not being commented on in Section 3.1; the result seems to be just put there with the reader trying to make sense of it. Also, more commentary for Figure 3 would be appreciated. 

4. Conclusion could discuss potentialities of your model in terms of studying nonlinear dynamics.

5. Additional things:

(a) The title has a typo. Optical is spelled with a zero, "0".

(b) Line 17. Unclear statement about the cooling. What about sub-Doppler cooling mechanisms?

(c) Line 24-25. "Also can be formally...". Unclear way of starting a sentence.

(d) Line 26-27. "These MOT’s forces originate, respectively, from the Zeeman and Doppler shifts.". Unclear which respective parts you are referring to. Harmonic and dissipative; or harmonic, dissipative and collective? (I am certain you meant the former two; write it like that.)

(e) Line 31. "for closure". This seems to imply there aren't more effects in a MOT. 

(f) Line 43. Typo. "Due" -> "Due to".

(g) Line 70. The authors probably meant \sigma_L instead of \sigma_{\perp}. Also, isn't \sigma_L supposed to be absorption cross section and \sigma_R the reabsorption one?

(h) Line 115. Missing dot at the end of the sentence.

(i) Line 149. What do the authors mean by "is valid"? Is that a question?

(j) Line 154. Typo. "Eq." -> "Eq. (23).

(k) Line 174. Can the authors be more specific what they mean by "truly real MOTs"?

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

In this manuscript, authors reviewed the nonlinear dynamics of trapped atomic clouds in anisotropic and spherical MOTs. When the thermal and multiple scattering effects are considered, the axial symmetry conditions and the three axial motion equations under the conditions of the axis were derived. And a fitting analysis of the damping coupling oscillation of different models was performed. The review summarized the authors' previous works [Physica Scripta., 94, 125214 (2019), Acta Phys. Pol. A, 139, 6. (2021) (Ref. 14 and 15 in manuscript)], and the presentation of manuscript is clear and logical. In summary, I recommended to publish it in Atoms after considering my personal comments as follow.

1. The manuscript give a conclusion that “the frequently adopted spherically symmetric approximation is not faithful in truly real MOTs.”. Is the conclusion aimed at all kinds of MOTs or specifically at MOTs using a pair of anti-Helmholtz coils? Can the employment of multiple pairs of coils make the results closer to the spherically symmetric model?

2. The figures in the article lack legends, and authors should mark each line with their physical meanings. Meanwhile, the orange dotted line in Figure 1 is not clear enough, a more visible color is a better choice.

3. The experimental articles for comparison [Eur. Phys. J. D, 67, 270. (2013), AIP Conf. Proc. 862, 211 (2006), Eur. Phys. J. D 46, 507 (2006) (Ref. 33-35 in manuscript)] are classic as references, but is there any recent experimental results as a reference?

4. There are some format errors, such as:

in the title of Page 1, “Magneto 0ptical Traps”;

in the line 24 of Page1, “for pulsating stars”;

in the line 154 of Page 6, “the simulations result for Eq. for” loses the specific equation numbers.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf