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_00049v1 (pdf) |
| Date submitted: | June 25, 2025, 9:22 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 the 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.
Current status:
Reports on this Submission
Strengths
2 Energetic and structural properties are found and reported in detail. Energy spectrum and occupation numbers are reported.
Weaknesses
1 It is not cleear why BEC regime is not fully reached. 2 Discussion of the effective-range effects can be improved
Report
While overall, the Manuscript is of good quality, still a number of points should be improved before it can be accepted.
Requested changes
Line 89, a very specific shape for the interaction potential is used, additional motivation or justification for this shape should be mentioned here
Line 112, 115, it might be appropriate to mention that the used definition of the scattering length implies logarithmic dependence of the wave function as ln(a_{2D} / r)
Fig 1, 6, “relative energy” E / (hbar omega) might sound ambiguous, I would suggest using the "energy of relative motion" instead to make it clear.
Line 220, “parameters … are optimized stochastically”, it is appropriate to specify which criteria for optimization are actually used
Line 230 Natural orbital analysis reminds me of this article Phys. Rev. A 68, 033602, 2003 which is not cited, as all references are limited to Ref. [25]. I think the Authors could add more references for the decomposition of the OBDM
Line 259 “these finite occupation numbers decrease”, it would be better to say explicitly what is meant by “these”
Fig 3, it is not clear if Ncond is expected to increase or decrease as the binding energy is increased
Line 381 “any local property …”, at this point I can imagine a potential energy or density profile, as an example of a local observable. Line 386, {\bf r}, is used but not defined in Eq. (33). I think the presentation can be improved. It is clear that a local observable can be written as an integral over the square of the wave function, but the knowledge of the observable should be introduced to Eq. (33)
Fig 5a, it is not clear why for zero Eb the density profile is different from a Gaussian.
Section 3.5 contains only 15 lines, while referring to four pages of figures. It feels like more discussion is needed, especially as Eq (5) is explicitly introduced to provide the value of the effective range. Is it possible to describe the seen effects in terms of r2D?
As a general observation, it is not clear why a deep BEC regime is not seen in this article.
Recommendation
Ask for minor revision
Strengths
1- the scope of the paper is broad for an exact few body calculation. Covering both energetic properties and a range of correlation measures. 2-The paper has a clear relevance to ongoing experimental work. 3-Novel insights into the finite effective range effects.
Weaknesses
1- The condenstate fraction is adapted from the 3D few -fermion definition to the 2D few-body case. In your results the behaviour is non-monotonic and shows only a small variation with binding energy, unlike the monotonic growth seen in 3D. It was unclear to me why this is the case.
Report
Requested changes
1-Could the authors explain more clearly why the 3D definition does not work as well in 2D few-body systems. As this was unclear to me.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)