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When does a Fermi puddle become a Fermi sea? Emergence of Pairing in Two-Dimensional Trapped Mesoscopic Fermi Gases
by Emma Laird, Brendan Mulkerin, Jia Wang, and Matthew Davis
Submission summary
| Authors (as registered SciPost users): | Emma Laird |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202408_00033v1 (pdf) |
| Date submitted: | 2024-08-30 04:34 |
| Submitted by: | Laird, Emma |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Pairing lies at the heart of superfluidity in fermionic systems. Motivated by recent experiments in mesoscopic Fermi gases, we study up to six fermionic atoms with equal masses and equal populations in two different spin states, confined in a quasi-two-dimensional harmonic trap. We couple a stochastic variational approach with the use of an explicitly correlated Gaussian basis set, which enables us to obtain highly accurate energies and structural properties. Utilising two-dimensional two-body scattering theory with a finite-range Gaussian interaction potential, we tune the effective range to model realistic quasi-two-dimensional scattering. We calculate the excitation spectrum, pair correlation function, and paired fraction as a function of increasing attractive interaction strength. For up to six fermions in the ground state, we find that opposite spin and momentum pairing is maximised well below the Fermi surface in momentum space. By contrast, corresponding experiments on twelve fermions have found that pairing is maximal at the Fermi surface and strongly suppressed beneath [M. Holten et al., Nature 606, 287-291 (2022)]. This suggests that the Fermi sea — which acts to suppress pairing at low momenta through Pauli blocking — emerges in the transition from six to twelve particles.
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
Report 1 by Zheyu Shi on 2024-9-15 (Invited Report)
Report
The manuscript investigates the BCS pairing properties in mesoscopic 2D Fermi gases. The authors employ a stochastic variational approach with an explicitly correlated Gaussian basis to compute eigenenergies and corresponding wave functions for up to six fermions in a harmonic trap. The calculated monopole excitation energy behavior indicates a potential few-body precursor of the many-body normal to superfluid quantum phase transition, as well as the Higgs mode. The resulting pair correlation function reveals that the pairing reaches its maximum below the Fermi surface, which contrasts with experimental measurements for twelve fermions in the trap, suggesting that the Fermi sea emerges in the transition from six to twelve particles.
The emergence of the Fermi sea as particle numbers increase presents a compelling question, closely aligned with recent experiments conducted by S. Jochim's group. The manuscript by Laird et al. offers a valuable contribution to this inquiry from a few-body perspective. The authors present a well-structured paper with a rigorous numerical analysis of the few-body problem, effectively addressing this intriguing phenomenon. I would recommend the manuscript to be published in Scipost Physics, if the authors could address the following comments.
1. On page 6, line 189, the authors wrote “In practical computations, we tune the effective range to large negative values through a shape resonance…”. Could the authors clarify the term "large" in this context? The subsequent calculations utilize a model potential with an effective range of $-0.1 l_r^2$, which may not be considered large by conventional standards.
2. The critical binding energy ($0.953\hbar\omega$ for $r_{2d}=-0.1 l_r^2$) is presented towards the end of the manuscript. It would be beneficial to introduce this value earlier in the paper to enhance readers' comprehension of the pair correlation function trends.
3. As a suggestion for further analysis, I think it would be beneficial to examine the behavior of the largest eigenvalue of the two-body density matrix. This metric potentially serves as a better indicator of superfluidity compared to the pairing number defined in the manuscript and Ref.[24]. According to the original work on off-diagonal long-range order (RMP 34, 694 (1962)), this eigenvalue approaches O(N) when superfluidity occurs, with the corresponding eigenfunctions revealing the pairing wavefunction. Given that the authors have already computed the two-body density matrix, it is recommended that they investigate this quantity to enhance the depth of their analysis.
Recommendation
Ask for minor revision