SciPost Submission Page
Phases and dynamics of quantum droplets in the crossover to two-dimensions
by Jose Carlos Pelayo, George Bougas, Thom\'{a}s Fogarty, Thomas Busch, Simeon I. Mistakidis
Submission summary
| Authors (as registered SciPost users): | Jose Carlos Pelayo |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202408_00003v1 (pdf) |
| Date submitted: | 2024-08-05 11:26 |
| Submitted by: | Pelayo, Jose Carlos |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We explore the ground states and dynamics of ultracold atomic droplets in the crossover region from three to two dimensions by solving the two-dimensional and the quasi two-dimensional extended Gross-Pitaevskii equations numerically and with a variational approach. By systematically comparing the droplet properties, we determine the validity regions of the pure two-dimensional description, and therefore the dominance of the logarithmic nonlinear coupling, as a function of the sign of the averaged mean-field interactions and the size of the transverse confinement. One of our main findings is that droplets can become substantially extended when their binding energies become small upon transitioning from negative-to-positive averaged mean-field interactions. To explore fundamental dynamical properties in the cross-over region, we study interaction quenches and show that the droplets perform a periodic breathing motion for modest quench strengths, while larger quench amplitudes lead to continuous expansion exhibiting density ring structures. We also showcase that it is possible to form complex bulk and surface density patterns in anisotropic geometries following the quench. Since we are working with realistic parameters, our results can directly facilitate future experimental realizations.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
1-Authors study both two-dimensional and quasi-two-dimensional geometries
2-ALternative approaches are used, such as doing numerics and using the variational procedure
3-The topic is relevant to the present experiments
Weaknesses
1-It might be not clear why this specific geometry (hard-walls) is used
Report
The Authors study both static and dynamic properties of self-bound droplets in two-dimensional and quasi-two-dimensional geometry. The Gross-Pitaevskii equation for the droplets is solved both numerically and by using the variational technique.
Overall the paper is well-written and the obtained results seem to be credible. The considered problem is relevant to experiments with ultracold atomic gases. The level of the research is appropriate for the Sci Post journal. Nevertheless, I do not find that in the present form, the presentation is clear enough to allow the publication in its present form.
Requested changes
1- It is said in the Abstract that "One of our main findings is that droplets can become substantially extended when their binding energies become small ...". Phrased this way this result seems trivial, as this is a rather general property of bound states, even not necessary droplets. Actually, one might rather check if the binding energy is inversely proportional to the square of the droplet's size.
2-The Authors opted for using a micrometer scale for the distances, instead of reporting the results in dimensionless quantities. This makes sense when specific experimental realization is kept in mind. Thus I would prefer to have a detailed explanation of which parameters are used and why.
3-I am a little bit puzzled by the geometry used by the Authors. It is said that hard-wall boundary conditions are used. There are two issues with that. In the 2D plane it is more common to use periodic boundary conditions for describing the gas-like unbound state. For the finite-size bound state, the boundary conditions are not important if the size of the bound state is small compared to the box size. This should be mentioned. Instead it is not obvious why the hard-wall condition is used in the transverse direction. Using a harmonic oscillator would sound to be more natural to me. So I would prefer to have a stronger argumentation of that particular choice.
4-Section 2 starts with an overview of 3D experiments. Immediately after an "experimentally verified condition" is given, which involves $na^2$, which seems to be more typical to 2D. Please clarify the dimensionality.
5- Section 2.1, I think that it would be beneficial for the clarity of the presentation to have two subsections, one on 2D, the other on the quasi-2D
6-Equation (7) should be introduced better, with detailed explanations of what are the main assumptions which are needed for obtaining this equation
7-I am puzzled by the statement that the relative error during the time evolution is $10^{-14}$. Firstly, the way it is written it is not clear if the whole time evolution is intended, or a single time step. Secondly, this number is pretty close to machine epsilon for a double and is smaller than that for a float.
8-Beginning of Section 3, I would prefer here and in other places to see also the physical terms added to $\delta a$, $L$, $\chi$, etc
9- "is small ... namely $\leq$0.2", it would be more natural to have $\lesssim0.2$
10-Figures 3a and 3b, the blue line is non-monotonous, why is that? Does that mean that at the maximum the flat-top regime disappears or that is a different effect?
To summarize, I believe that the mentioned commenters must be addressed before the article can be published.
Recommendation
Ask for minor revision