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A unified theory of strong coupling Bose polarons: From repulsive polarons to nonGaussian manybody bound states
by Nader Mostaan, Nathan Goldman, Fabian Grusdt
Submission summary
Authors (as registered SciPost users):  Nader Mostaan 
Submission information  

Preprint Link:  https://arxiv.org/abs/2305.00835v3 (pdf) 
Date submitted:  20230623 14:03 
Submitted by:  Mostaan, Nader 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We address the Bose polaron problem of a mobile impurity interacting strongly with a host BoseEinstein condensate (BEC) through a Feshbach resonance. On the repulsive side at strong couplings, theoretical approaches predict two distinct polaron branches corresponding to attractive and repulsive polarons, but it remains unclear how the two are related. This is partly due to the challenges resulting from a competition of strongly attractive (destabilizing) impurityboson interactions with weakly repulsive (stabilizing) bosonboson interactions, whose interplay is difficult to describe with contemporary theoretical methods. Here we develop a powerful variational framework that combines Gaussian correlations among impurityboson scattering states, including up to an infinite number of bosonic excitations, with exact nonGaussian correlations among bosons occupying an impurityboson bound state. This variational scheme enables a full treatment of strong nonlinearities arising in the Feshbach molecule on the repulsive side of the resonance. Within this framework, we demonstrate that the interplay of impurityinduced instability and stabilization by repulsive bosonboson interactions results in a discrete set of metastable manybody bound states at intermediate energies between the attractive and repulsive polaron branches. These states exhibit strong quantum statistical characteristics in the form of nonGaussian quantum correlations, requiring nonperturbative beyond meanfield treatments for their characterization. Furthermore, these manybody bound states have sizable molecular spectral weights, accessible via molecular spectroscopy techniques. This work provides a unified theory of attractive and repulsive Bose polarons on the repulsive side of the Feshbach resonance.
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Strengths
1. The work is timely  there is currently a strong interest in Bose gases with impurities
2. The work suggests a novel (to the best of my knowledge) variational approach to the problem
Weaknesses
1. It seems that the work does not provide a rigorous validation of the proposed variational approach.
Report
The manuscript suggests a novel variational ansatz to tackle the Bose polaron problem in ultracold gases with positive scattering lengths. Using this ansatz, the paper studies attractive and repulsive quasiparticle branches. The focus is in particular on what happens to the Bose polaron spectrum across an impurityboson Feshbach resonance, see Fig. 1 for an illustration.
I read the work with great interest. The manuscript is somewhat technical and sometimes hard to follow but overall it is written well, and will definitely be useful for researchers working on Bose polarons.
The main weakness of the paper is that it does not provide a mathematical or numerical proof of the proposed variational ansatz. This ansatz seems definitely reasonable for a
bound state with (approximately) one boson bound to an impurity, but I am not sure that I understand why it should work for Nbosonplusimpurity bound states, here N is (approximately) the number of bound bosons.
Looking at the acceptance criteria of SciPost Physics, the manuscript might "Open a new pathway in an existing or a new research direction, with clear potential for multipronged followup work". However, in my opinion, to meet this criteria, some further work is needed to validate the ansatz.
Requested changes
Major:
1. The manuscript should provide a stronger justification for the use of the variational ansatz. Is it possible to estimate the effect of the neglected piece of the Hilbert space in the spirit of the mentioned in the manuscript BornOppenheimer approximation? Alternatively, are there any numerical results in the literature for few or manybody systems that can be used for benchmarking?
Minor:
A. Annals of Physics 19, 234 (1962) and J. Phys. B: At. Mol. Opt. Phys. 53 205302 (2020) are relevant references that might be considered together with the mentioned meanfield studies of the Bose polaron, e.g., [6163].
B. The manuscript states that "the repuslive [typo!] polaron cannot exist without its attractive counterpart." This statement should probably be clarified, as the repulsive polaron is expected to be a stable ground state for purely repulsive interactions, see for example Fig. 7 of Atoms 10, 55 (2022).
C. What is meant by "the third solution" on page 5 (at the very top of the right column)?
D. The manuscript uses a delta function to model bosonboson interactions. It is unclear if this is justified for the present beyondmeanfield study, i.e., when H_3 and H_4 are included. The manuscript should clarify this issue.
E. The manuscript states that "it is essential to include the effects of
quantum fluctuations through Γ" for low spatial dimensions. It is worth clarifying this point. Naively, one would assume that quantum fluctuations become important only when one considers longrange physics, but it might be that I am missing something.
F. Related to E. Note that a low dimensional geometry might provide a testbed for the employed variational approach  there are a number of various numerical techniques that can provide accurate results. Therefore, it might make sense to motivate further studies of lowdimensional Bose polarons using the proposed variational ansatz.
G. The manuscript introduces r_0 to model the range of the bosonimpurity interaction. Unfortunately, the reader is left wondering what is the role of r_0 on the reported results. What will happen if r_0 is changed?
H. The manuscript states "it takes into account the quantum correlations of bound Bogoliubov excitations exactly, without restricting the number of excitations." It is worth clarifying what is meant by `exactly' here.