SciPost Submission Page
Energetic and Structural Properties of Two-Dimensional Trapped Mesoscopic Fermi Gases
by Emma K. Laird, Brendan C. Mulkerin, Jia Wang, and Matthew J. Davis
Submission summary
| Authors (as registered SciPost users): | Matthew J. Davis · Emma Laird |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202506_00049v2 (pdf) |
| Date submitted: | Dec. 25, 2025, 5:47 a.m. |
| Submitted by: | Emma Laird |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We theoretically investigate equal-mass spin-balanced two-component Fermi gases in which pairs of atoms with opposite spins interact via a short-range isotropic model potential. We probe the distinction between two-dimensional and quasi-two-dimensional harmonic confinement by tuning the effective range parameter within two-dimensional scattering theory. Our approach, which yields numerically exact energetic and structural properties, combines a correlated Gaussian basis-set expansion with the stochastic variational method. For systems containing up to six particles, we: 1) Present the ground- and excited-state energy spectra; 2) Study non-local correlations by analysing the one- and two-body density matrices, extracting from these the occupation numbers of natural orbitals, the momentum distributions of atoms and pairs, and the molecular 'condensate fraction'; 3) Study local correlations by computing the radial and pair distribution functions. This paper extends current theoretical knowledge on the properties of trapped few-fermion systems as realised in state-of-the-art cold-atom experiments.
Author comments upon resubmission
Please find our revised manuscript attached. Responses to the referees are provided below each report, with all corresponding revisions highlighted in orange in the manuscript. Below, we list the line numbers where changes have been made; expanded explanations are given in our replies to the referees.
Thank you for your consideration.
Kind regards,
Emma
List of changes
- motivated the choice of interaction potential, lines 148–159
- clarified the logarithmic asymptotic behaviour of the wave function, lines 105–107
- resolved ambiguity in figure captions 1 and 6 on pages 6 and 19 (relative energy)
- specified the optimisation criterion in the stochastic variational method, lines 235–239
- expanded the contextual discussion of the natural-orbital decomposition, lines 247–255 and 259–261
- clarified the reference to finite occupation numbers, lines 289–291
- substantially revised the discussion of the molecular condensate fraction, lines 332–398
- clarified the definition of local observables, lines 442–450
- expanded the explanation of the Gaussian one-body radial density profiles, lines 461–469
- expanded the physical interpretation of the finite effective-range effects, lines 499–564
- substantially revised the conclusion, lines 565–610
Current status:
Reports on this Submission
Strengths
I already commented on the strengths of the Manuscript. So here I only comment on the differences as compared to the original version.
- I find that the majority of my comments were properly taken into account
- Some parts of the Manuscript were completely rewritten and the presentation was improved
- A number of possibly ambiguous points were improved
Weaknesses
I already commented on the weaknesses of the Manuscript. So here I only comment on the differences as compared to the original version.
- Still I am not convinced that there are methodological problems in defining the BEC limit, although I agree that reaching the BEC limit might be challenging
Report
Requested changes
1) "two-Gaussian form ... provides a minimal finite-range model that reproduces a target 2D scattering length a2D ..."
Althougth I find that newly added justification of the used potential is quite complete still I am not absolutely convinced by the first point which says that the two Guassian form is the minimal finite-range model that reproduces a target 2D scattering length, as a single Gaussian already has two degrees of freedom and is enough to fix a single parameter (a2D), while two-Gaussian form has 4 parameters.
2) in Eq. (21) I would separate parenthesis [] by a comma from the main equation, or even would put (n,m)\neq (0,0) under \max
3) I am not entirely convinced that there is a methodological problem in defining the BEC limit for a small number of particles. Numerically, this might be quite demanding as this requires a separation of energy scales, so that the molecular binding energy is much larger as compared to any other scale in the problem. Furthermore, in such a situation, any correction to this energy (due to finite range, due to compression of the molecule by the trapping potential, etc) can be as well comparable to other energy scales in the problem, and should be properly taken into account. On the other hand, by solving 1+1 problem under the same conditions (interaction potential, trap) can be used for extracting correctly molecule-molecule effective interactions. I guess, if the separation of scales is present, the BEC regime should be seen, if not, it is reasonable that it is not reached.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Author: Emma Laird on 2026-01-04 [id 6193]
(in reply to Report 1 on 2025-12-28)We thank the referee for the encouraging assessment in their second report and for their very prompt follow-up. All revisions made in response to this referee report are highlighted in orange in the manuscript (version three) attached to this comment.
1) In the first sentence of the relevant paragraph we refer to “the two-Gaussian form of the interaction potential in Eq. (3)”, which is not a general four-parameter two-Gaussian potential but a minimal two-parameter model depending only on r_0 and V_0. In the next sentence the term “minimal” was intended to apply to the statement as a whole — i.e., to the combined capability of reproducing a target scattering length and simultaneously allowing the effective range to be tuned — rather than to the first clause concerning the scattering length alone. We now realise that our original wording could possibly be interpreted differently, so we have edited these two sentences to make our intended meaning fully clear. [lines 148–151]
2) We have removed the square brackets around “(n, m) \neq (0, 0)” and instead separated it from the main expression with a comma, following the presentation used in Eq. (16) of Ref. 25. We chose not to place this restriction directly under the “max” operator, as this makes the numerator look quite cramped and harder to read. [Eq. (21) between lines 343 and 344]
3) We thank the referee for sharing their perspective; this is a valuable suggestion and something we may pursue in future work. We agree that in few-body systems identifying the BEC limit hinges on the emergence of a clear separation of energy scales and that this can be numerically demanding. Accordingly, we have re-written the third paragraph of the Conclusions to discuss how the BEC limit should be defined for small particle numbers and to re-emphasise why this regime is challenging to reach in practice. [lines 585–600]
Thanks again, and please let us know if these latest edits are satisfactory.
Attachment:
2D_Few-Fermion_Systems_v3.pdf