## SciPost Submission Page

# Collective oscillations of a two-component Fermi gas on the repulsive branch

### by Tomasz Karpiuk, Piotr T. Grochowski, Mirosław Brewczyk, Kazimierz Rzążewski

#### This is not the current version.

### Submission summary

As Contributors: | Piotr Grochowski |

Arxiv Link: | https://arxiv.org/abs/1908.07771v2 |

Date submitted: | 2019-11-21 |

Submitted by: | Grochowski, Piotr |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Atomic, Molecular and Optical Physics - Theory |

Approach: | Theoretical |

### Abstract

We calculate frequencies of collective oscillations of two-component Fermi gas that is kept on the repulsive branch of its energy spectrum. Not only is a paramagnetic phase explored, but also a ferromagnetically separated one. Both in-, and out-of-phase perturbations are investigated, showing contributions from various gas excitations. Additionally, we compare results coming from both time-dependent Hartree-Fock and density-functional approaches.

###### Current status:

### Submission & Refereeing History

## Reports on this Submission

### Anonymous Report 2 on 2020-2-24 Invited Report

### Strengths

1-clear and well written article

2- TImely work

3- comparison with hydrodynamics and sum rule approaches

### Weaknesses

1- choice of the trap geometry leading to misleading conclusion about comparison between hydrodynamics and TDHF

### Report

In this article, the authors study the dynamics of a repulsive mixtures of fermionic gases confined in an isotropic trap within Hartree-Fock’s approximation. They focus on the lowest quadrupolar modes and consider identical and opposite excitations on the two species. The results are then compared to hydrodynamic approaches.

This article is interesting, clear and well written and the reported results are timely since the experimental study of repulsive Fermi gases is currently under way and is still largely open.

One shortcoming of the work though is the choice of a highly degenerate trap geometry that may lead to misleading conclusions if one wants to transpose the results of this work to more relevant trapping geometries (usually traps are anisotropic and more often than not strongly elongated). Indeed, one of the conclusions of the authors is that TDHF agrees with hydrodynamics (except for the quadrupole). This agreement is in my opinion coincidental and purely a consequence of the choice of trap. Indeed, if one considers an elongated trap, the prediction for the quadrupole modes of a weakly interacting gas is essentially twice the trapping frequencies. By contrast, hydrodynamics for instance predicts for the axial breathing mode a frequency equal to (12/5)^(1/2) times the axial trapping frequency. Conversely, is there a deep reason why hydrodynamics should be applicable to a weakly interacting gas in an isotropic trap?

Moreover, it would be interesting to compare the oscillation frequencies of the different modes, since it seems to me that the upper branches of all graphs are essentially all the same (this is pointed out when discussing symmetric vs antisymmetric excitation of the monopole compression mode, but I didn’t see it stated for the other modes). I have the impression that there are only three independent frequencies. Can the authors confirm? And if so, is there a simple explanation?

Finally, the numerical resolution of 3D nonlinear PDE being notoriously challenging, can the authors provide more details about the implementation of their numerical scheme (grid size, solver…)?

### Requested changes

1-clarify the role of the trap geometry

2- Explicitely compare the oscillation frequencies

3- Provide more details on numerical implementation.

### Anonymous Report 1 on 2019-12-11 Invited Report

### Strengths

1) The manuscript contains new physics: the authors investigate the frequencies of collective oscillations of two-component Fermi gas, for repulsive interactions.

### Weaknesses

1) Some points are unclear.

2) The quality of Figs. 3-8 is poor.

### Report

In this paper the authors presents a theoretical study of the frequencies of collective oscillations of two-component Fermi gas, on the repulsive branch of its energy spectrum. The analysis is carried out by means of some approximation, and for a limited number of particles (2 x 56), well below the typical numbers available in the experiments. Notwithstanding, the results may be interesting for the community working on this subject.

Before I can make a final recommendation, the author should consider the following points.

1) In equation (1) the authors employ a notation where the coordinates x_i refer to "both spatial and spin variables", but soon after they change to a different notation, with explicit indices for spin variables, and with an explicit dependence on time. I would suggest to unify the notation, for the sake of clarity.

2) The Fourier transform, which enters the discussion from pag. 7 on, it is never defined. Please include an explicit definition (in terms of formulas, I mean).

3) Figs. 3-8 have two problems, at least. They use much space, and this result in a dispersion of information. I would suggest to collect them in a _single_ figure, with different panels, restricting the horizontal axis up to k_F*a=1 (nothing is plotted beyond that limit). Then, what are those blueish in Figs. 3,6,8? maybe the FT? It is totally unclear and aesthetically poorly plotted. Please revise the figure carefully.

4) The sentence "Recapitulating, we have filled the gap in the literature" (in the conclusions) is excessively presumptuous, I would suggest to remove it.

5) The English needs some revision. In particular, please check carefully the use of articles.

### Requested changes

1) Unify the notation of equations (1)-(3).

2) Define qualitatively the Fourier transform.

3) Revise Figs. 3-8 (see report).

4) Avoid presumptuous claims.

5) Revise the English.