# Interference dynamics of matter-waves of SU($N$) fermions

### Submission summary

 Authors (as Contributors): Wayne Jordan Chetcuti · Juan Polo
Submission information
Date submitted: 2023-01-23 12:03
Submitted by: Chetcuti, Wayne Jordan
Submitted to: SciPost Physics
Ontological classification
Specialties:
• Condensed Matter Physics - Theory
• Condensed Matter Physics - Computational
• Quantum Physics
Approaches: Theoretical, Computational

### Abstract

Interacting N-component fermions spatially confined in ring-shaped potentials display specific coherence properties. The angular momentum of such systems can be quantized to fractional values specifically depending on the particle-particle interaction. Here we demonstrate how to monitor the state of the system through homodyne (momentum distribution) and self-heterodyne system’s expansion. For homodyne protocols, the momentum distribution is affected by the particle statistics in two distinctive ways. The first effect is a purely statistical one: at zero interactions, the characteristic hole in the momentum distribution around the momentum k = 0 opens up once half of the SU(N) Fermi sphere is displaced. The second effect originates from the interaction: the fractionalization in the interacting system manifests itself by an additional ‘delay’ in the flux for the occurrence of the hole, that now becomes a characteristic minimum at k = 0. We demonstrate that the angular momentum fractional quantization is reflected in the self-heterodyne interference as specific dislocations in interferograms. Our analysis demonstrate how the study of the interference fringes grants us access to both number of particles and number of components of SU(N) fermions.

###### Current status:
Has been resubmitted

Reply to the Referee reports is included alongside the re-submitted manuscript, where the changes are highlighted in red.

### Submission & Refereeing History

Resubmission scipost_202207_00002v3 on 22 March 2023

Resubmission scipost_202207_00002v2 on 23 January 2023
Submission scipost_202207_00002v1 on 1 July 2022

## Reports on this Submission

### Strengths

Timely subject

Well complementing similar studies for bosons

Interesting results for momentum distribution and interferograms

Improved clarity

### Weaknesses

The study of attractive interactions is not complete

### Report

I read the revised version. I continue to think that the study of attractive interactions is not yet complete, as also the authors comment about, but at the same time I think the paper significantly improved both in clarity and in addressing the points I mentioned. The topic is interesting and timely, and the discussion of the fingerprints of the different regimes in the considered setup with N components rather readable. For these reasons I am in favour of the publication.

### Requested changes

No further requested changes.

• validity: high
• significance: high
• originality: good
• clarity: high
• formatting: excellent
• grammar: excellent

### Strengths

Comprehensive consideration of various interaction strengths

### Weaknesses

Insufficient attention to defining the relevant terms and physical quantities necessary for understanding the underlying physics.

Not clear to what extent the conclusions for small particle numbers in interacting systems are extendable to large particle numbers present in experiments.

### Report

I thank the authors for their corrections and clarifications. The manuscript has clearly been improved. At the same time, I still do not find it ready for being published.

The key issue for me is still “fractional angular momentum”. In Sec. 3.1, the authors define $\ell$ as “the total angular momentum”. In appendix A.2, they define the same $\ell$ as “the angular momentum per particle”. From the behavior outlined in Sec. 3.1, it appears to me that in both contexts $\ell$ is the angular momentum per particle.

Then the ability of $\ell$ to acquire fractional values is not surprising. Consider a non-interacting system with a single smallest particle-hole excitation: the total angular momentum is increased by 1, while the angular momentum per particle is increased by $1/N_p$. Therefore, in the presence of interactions, when the ground state does not correspond to a uniformly filled Fermi sphere, it is only natural to expect fractional values of the angular momentum per particle. The miracle would be if these fractional values were quantized instead of forming a smooth continuum. Based on the statement in the beginning of Sec. 3.2.1 and the energy-flux diagram in Fig. 12, for infinitely-repulsive interactions in the thermodynamic limit the “quantization step” of the angular momentum per particle tends to zero; i.e., the fractional values do form a smooth continuum.

Given this, I strongly oppose the phrasing “orbital angular momentum … quantized to fractional values” appearing in the abstract. Stating a reduced period of persistent current’s dependence on flux would be a much clearer way of describing the statement that makes the system interesting to the authors.

A technical remark on this issue: the newly-introduced relation between $\ell$, $n$, and $I_j$ in the beginning of Appendix A.2 does not help – and rather harms: an unsuspecting reader suddenly learns of existence of $I_j$ which have never been defined before. I would recommend removing this piece of text: the total angular momentum per particle is a much more understandable observable than Bethe-ansatz quantum numbers. Further, there is no need to introduce Bethe-ansatz quantum numbers when talking in terms of non-interacting particles (“Fermi sphere displaced by”).

Concerning the relevance of the paper to the broad audience. The paper is, as I wrote before, a comprehensive study of the signatures produced for various interaction strengths. However, the authors perform studies for interacting systems with the number of particles $\leq 10$. This is understandable from the point of view of the theory – interacting systems are hard to study. However, it is not clear to what extent the conclusions extend to larger numbers of particles. At the same time, the experiments of Refs. 4 and 5 from the author’s response letter (Refs. 41 and 42 in the manuscript) use $N_p$ of the order of 10 000.

Given this uncertainty of whether the predictions are relevant for the large numbers of particles in experiments, and given that the paper is rather hard to read to an advanced non-specialist (that is, myself), I would recommend publishing the paper in a more specialized journal. For specialists, it would be an important advance and a basis for further development, while the jargon concerning “fractionalization” and assumed understanding of the definitions would constitute less of a problem.

Given the acceptance criteria of SciPost Physics (https://scipost.org/SciPostPhys/about#criteria) and SciPost Physics Core (https://scipost.org/SciPostPhysCore/about#criteria), I would recommend publishing the paper in SciPostPhysics Core after the authors make the minor changes I request in the field "Requested changes".

A minor technical issue: reference to a figure (probably, Fig. 14) on page 22 is broken. (See the paragraph starting with “Attraction: For infinitely attractive interactions, the energy”).

### Requested changes

Explain the issue of "fractional angular momentum"/"reduced period of the persistent current dependence on the flux" in a correct, self-consistent manner. Possibly, exclude unnecessary aspects.

Clarify in the manuscript to what degree the formula stated for general $N_p$ and $N$ are valid. State what this validity is based on.

• validity: good
• significance: good
• originality: high
• clarity: ok
• formatting: perfect
• grammar: perfect