# Beyond Lee-Huang-Yang description of self-bound Bose mixtures

### Submission summary

 As Contributors: Miki Ota Arxiv Link: https://arxiv.org/abs/2005.10047v2 (pdf) Date accepted: 2020-08-04 Date submitted: 2020-07-30 12:26 Submitted by: Ota, Miki Submitted to: SciPost Physics Discipline: Physics Subject area: Atomic, Molecular and Optical Physics - Theory Approach: Theoretical

### Abstract

We investigate the properties of self-bound ultradilute Bose-Bose mixtures, beyond the Lee-Huang-Yang description. Our approach is based on the determination of the beyond mean-field corrections to the phonon modes of the mixture in a self-consistent way and calculation of the associated equation of state. The newly obtained ground state energies show excellent agreement with recent quantum Monte Carlo calculations, providing a simple and accurate description of the self-bound mixtures with contact type interaction. We further show numerical results for the equilibrium properties of the finite size droplet, by adjusting the Gross-Pitaevskii equation. Our analysis is extended to the one-dimensional mixtures where an excellent agreement with quantum Monte Carlo predictions is found for the equilibrium densities. Finally, we discuss the effects of temperature on the stability of the liquid phase.

###### Current status:
Publication decision taken: accept

Editorial decision: For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)

Dear Editor,

we want to thank you for handling the manuscript. We are also grateful to the Referees for their positive feedbacks about our work, as well as for their valuable comments.

We would like to submit a new version of our paper, taking into account the suggestions made by the Referees. Below we give the details about the modifications brought in this new version.
We hope that our manuscript will be accepted soon for publication in SciPost Physics.

Sincerely Yours,

Miki Ota,
Grigori E. Astrakharchik

### List of changes

# General changes
- We have added a new section (Sec. 6) discussing the stability of the droplet at finite-temperature.
- We have changed the notation for the speed of sound, as well as the compressibilities, for more clarity. We now denote by $c_d$ the density sound, and $c_s$ the spin sound, and avoid the notation $\pm$ in the whole paper.

# Regarding the requests from Referee 1

- Sec. 2 p3 We have added the definition of the coupling constant in terms of the *s*-wave scattering length, after Eq. (1).
- Sec. 2 p4 We have added a discussion about the relationship between our macroscopic approach and the Beliaev diagrammatic theory, before Eq. (5).
- Sec. 3 p5 We have added the expression for the Bogoliubov sound in the symmetric case Eq. (7).
- Sec. 3 p7 We have added the missing curve (black dotted one) in Fig. 2.
- Sec. 3 p7 We have added a formal discussion about the contribution of each theory on the energy functional, Eq. (14).
- Sec. 4 p10 We have added the missing $\Phi$ on the right-hand side of Eq. (16).
- Sec. 4 p12 We have added the values of $\tilde{N}$ for the Petrov approach in the caption of Fig. 6.

# Regarding the requests from Referee 2
- Sec. 2 p5 We have added a sentence clarifying the origin of complex value in the compressibility, before Eq. (11).
- Sec. 2 p6 We have added a discussion about the experimental possibility to observe the theoretical findings made in of our work.
- Sec. 3 p7 We have added the missing curve (black dotted one) in Fig. 2.
- Sec. 3 p7 We have added a formal discussion about the contribution of each theory on the energy functional, Eq. (14).
- Sec. 4 p10 We have added a sentence about the limitation of the single-mode approximation $\Phi_1 = \Phi_2$, after Eq. (15).
- Sec. 7 p16 We have added a sentence about coherent coupled BECs as an open-question.

# Other minor changes
- We have added a sentence in the abstract, as well as in the introduction, referring to the newly added finite-temperature study.
- We have fixed an error found in the calculation of the black dotted line in Fig. 7(b).
- We have added a note at the end of the manuscript to refer to recent works on the same topic appeared recently as preprints.
- We have fixed some typography misses.