Nonequilibrium Steady State in a Large Magneto-Optical Trap

Round 1

Reviewer 1 Report

In the present manuscript, Gaudesius et al have investigated the dynamics of large magneto-optical traps. In particular, they have observed the transition between the non-equilibrium steady-state (NESS) and the unstable MOT regime They have made use of a Vlasov-Fokker-Planck model to describe the phase-space dynamics of the atoms, where the cooling and trapping forces are included in the model, together with the re-scattering forces.

The paper is very well written and deserves publication in this journal. I would just be happy if the authors clarify the following points:

1. What is the exact format of F_rs in Eq. (1) that they are using? And how to they express it in terms of the experimental parameters (\delta, \gradB, I)?

2. The same question holds for the shape of the diffusion coefficient. Moreover, what are the difdusion processes the authors have in mind that leads to a dependence on the velocity, D=D(v)?

 

The remainder of the manuscript is very easy to follow. 

Author Response

Dear Reviewer,   Thank you for taking your time to provide feedback. Please see below the answers to your questions:   1. The form of F_{rs} is seen in Eq. (7) of PhysRevA.74.023409 (their F_{mf} is our F_{rs}). The rescattering force in the integral is the one seen in Eq. (15) of PhysRevA.105.013112 (Eqs. (16) to (25) show its dependencies on the experimental parameters \delta, \gradB, I). Note that we do not solve the kinetic equation (Eq. (1) of the manuscript) directly but rather employ a numerical approach based on the superparticle method, described in Sec. II.B of PhysRevA.105.013112. This allows us to straightforwardly implement the equations seen in Sec. II.A of PhysRevA.105.013112.   2. The diffusion coefficient is given by Eq. (7) of PhysRevA.105.013112 (Eqs. (8) to (12) show its dependencies on the experimental parameters \delta, \gradB, I). It depends on the velocity due to the Doppler effect (see the term +-k_L v_\alpha in Eq. (12) of this reference).   Additionally, please note that due to the concerns of other referees, we have updated Figs. 3, 5, 7 as well as done modifications in figure texts (Figs. 3, 5, 7, 8) and the main text (lines 90-94, 108-111, 144-145, 150-152, 185-187, 197, 228-229); the text modifications are in bold.   Regards, Marius

Reviewer 2 Report

In this work, the authors presented results of numerical simulations on the behavior of a large ensemble of cold atoms held in a magneto-optical trap (MOT).  Specifically, they looked into the momentum/velocity distributions and spatio-temporal dynamics of the MOT with respect to experimental parameters.  The authors argue that there is a region of nonequilibrium steady state (NESS) in a MOT outside the stable and unstable regime.

 

The manuscript is well-written and relatively straightforward to read.  The arguments were easy to follow, and the discussion of the MOT behavior with the different experimental parameters was systematically presented.  The figures used are adequate for presenting their results.

 

I have only one question/comment: 

 

In Figure 6, the authors showed the resulting momentum anisotropy of the NESS near the threshold of the unstable region with respect to laser intensity.  They noted its similar behavior with the instability threshold, but also pointed out the difference at higher intensities.  They attributed the difference to the instability threshold reaching a plateau.  

I wish that the authors can provide additional comments on this decrease in anisotropy at higher intensities.  Does this mean the NESS region is getting smaller?  Will there be a point that the NESS region won’t exist at all or will it reach a plateau?  If there is a point that the NESS region vanishes, does it simply mean that the parameters will not result in a MOT?  Also, can the authors provide a discussion of the possible physical mechanisms that can cause this decrease in anisotropy?

 

In addition to that comment, I enjoyed reading this manuscript and would recommend acceptance for publication after some minor revisions.

 

Minor superficial errors:

1.     The superscripts of the authors’ affiliations are incorrect.

2.     The keywords are “keyword”.

Author Response

Dear Reviewer,   Thank you for taking your time to provide feedback. We have added text in lines 185-187 (in bold) to address parts of your concern. Regarding the possible mechanism behind the decrease in the velocity anisotropy, we do not know what causes it rather than it depends on the complex interplay/antagonism between the shadow force and the rescattering force, and there is no straightforward relation between the anisotropy size and the proximity of the unstable regime to the atomic resonance.   Additionally, please note that due to the concerns of another reviewer, we have updated Figs. 3, 5, 7 as well as done modifications in figure texts (Figs. 3, 5, 7, 8) and the main text (lines 90-94, 108-111, 144-145, 150-152, 197, 228-229); the text modifications are in bold.   Regards, Marius

Reviewer 3 Report

Dear authors, please see the referee report in the attached PDF file.

Comments for author File: Comments.pdf

Author Response

Dear Reviewer,   Thank you for taking your time to provide feedback resulting in significant improvements of the manuscript. Please see below the answers to your questions (note that the modifications in the manuscript text are in bold):   1. Text in lines 90-94 has been added, explaining the appearance of the MOT parameters in the model's effects. Moreover, text in lines 108-111 has been added, providing a rationale behind the MOT parameters chosen in the simulations.   2. a. To clarify the issue on the NESS threshold extraction, Fig. 3 has been updated (threshold lines have been removed, as we believe these can cause confusion), text in several lines has been added/reformulated (144-145, 150-152, 197) and Fig. 8 text has been updated.    b. We'd like to omit elaborating this in the manuscript. We may speculate that the discrepancy may be related to the vortex behavior. On a technical note, though, this may have been caused due to insufficient data (the amount of images processed already had to be increased to 1000, from 200, used in producing other figures).   c. Fig. 5 and its text have been updated as a result. Also, lines 228-229 were added in the conclusion, to make it clear that the NESS belongs to a stable MOT.   d. Fig. 7 and its text have been updated as a result.   e. We believe the updated Fig. 7 and its text provide sufficient visualization why 2 branches should appear [the 4 lobes are of similar size, with lobes 1 and 3 together being at a similar level as well as lobes 2 and 4 (the first pair is lower in z than the latter one)}.   Additionally, please note that due to the concerns of another reviewer, we have added text in lines 185-187.   Regards, Marius

Round 2

Reviewer 3 Report

The authors have properly responded to the comments left by the referee and made corresponding adjustments to the manuscript. With all the detailed information the authors provided, I think the results presented in the paper are sound and the quality of the research meets the standard of Atoms, therefore, I would recommend the acceptance for publication.