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Self-stabilized Bose polarons

by Richard Schmidt, Tilman Enss

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Submission summary

Authors (as registered SciPost users): Tilman Enss · Richard Schmidt
Submission information
Preprint Link:  (pdf)
Date submitted: 2021-03-08 17:32
Submitted by: Enss, Tilman
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Theory
Approach: Theoretical


The mobile impurity in a Bose-Einstein condensate (BEC) is a paradigmatic many-body problem. For weak interaction between the impurity and the BEC, the impurity deforms the BEC only slightly and it is well described within the Fr\"ohlich model and the Bogoliubov approximation. For strong local attraction this standard approach, however, fails to balance the local attraction with the weak repulsion between the BEC particles and predicts an instability where an infinite number of bosons is attracted toward the impurity. Here we present a solution of the Bose polaron problem beyond the Bogoliubov approximation which includes the local repulsion between bosons and thereby stabilizes the Bose polaron even near and beyond the scattering resonance. We show that the Bose polaron energy remains bounded from below across the resonance and the size of the polaron dressing cloud stays finite. Our results demonstrate how the dressing cloud replaces the attractive impurity potential with an effective many-body potential that excludes binding. We find that at resonance, including the effects of boson repulsion, the polaron energy depends universally on the effective range. Moreover, while the impurity contact is strongly peaked at positive scattering length, it remains always finite. Our solution highlights how Bose polarons are self-stabilized by repulsion, providing a mechanism to understand quench dynamics and nonequilibrium time evolution at strong coupling.

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Reports on this Submission

Anonymous Report 3 on 2021-5-4 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2102.13616v1, delivered 2021-05-04, doi: 10.21468/SciPost.Report.2874


See attached file.


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Anonymous Report 2 on 2021-4-21 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2102.13616v1, delivered 2021-04-21, doi: 10.21468/SciPost.Report.2811


- A relatively simple solution to the Bose polaron problem that removes the divergence in the energy.


- The GP theory is unlikely to be valid for short-range impurity-boson potentials. This should be more clearly discussed.


This paper certainly meets the requirements for publication. It investigates the behavior of an impurity in a BEC, a topic of intense interest in quantum gases, and it provides a way to remove the divergence in the ground-state energy that has plagued many previous approaches, such as Ref [30]. It also presents a simple classical picture of how bosons effectively screen the impurity and thus reduce the strength of the attractive impurity potential.

The main points that require more discussion are the validity of the classical-field approach and how the current work fits with other theoretical approaches. Specifically, I would like the authors to address the following questions/comments:

1. What is the precise condition for the classical field (GP) approach to be valid? I would expect that the range $R$ has to be sufficiently large but does it need to be larger that the healing length or just $a_{BB}$?

2. How does that the current approach differ from that in Ref. [38]? The authors of Ref [38] appear to use the same GP equation, yet claim a larger regime of validity, i.e., $R \sim a_{BB}$.

3. Does the approach in the paper capture the perturbative results in the limit of weak boson-impurity coupling? For instance, it is known that the GP approach in Ref [43] does not recover it properly, while the coherent-state approach in Ref. [30] does.

4. I was confused about why it was claimed that higher order extensions of the Chevy ansatz lead to a spurious divergence. In Ref. [41] the dependence on a high-momentum cutoff is due to Efimov physics, which is a physical effect that is also present in QMC calculations.

5. Can the approach be extended to non-zero temperature?

Requested changes

1. A clear discussion of the validity of the GP theory in the paper.

2. More comparison with previous work. In particular, how does the theory compare with the QMC calculations for an ionic impurity in Ref. [44]?

3. Can the authors comment on the limit of a zero-range potential? Since this has been used in other works including QMC calculations.

4. The authors should also comment more on Ref [55], which shows that an infinitely heavy impurity can trap an infinite number of bosons but still have a lower bound on the ground-state energy. An infinite number of bosons trapped by a short-range potential was also shown in Chen et al., PRA 98, 041602(R) (2018).

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

Anonymous Report 1 on 2021-3-31 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2102.13616v1, delivered 2021-03-31, doi: 10.21468/SciPost.Report.2744


1. Provides a simple picture of stabilization of the Bose polaron with a simple theory, whereas previous theories fail to account for this stabilization.


2. The range of validity of the theory is not sufficiently discussed.


This is an interesting work investigating the stabilization of the Bose polaron by the repulsion between bosons, in the framework of the Gross-Pitaevskii theory. It constitutes an important contribution since this stabilization was absent in most theories. The paper is very clearly written and the results are physically sound. All of the journal's acceptance criteria are met, and I think it duly deserves publication once the authors have clarified a few points and considered the following suggestions.

Requested changes

Here are some points I would like to clarify:

1) The authors should specify more clearly the range of validity of their theory. In Section III.5, they state "our local Gross-Pitaevskii theory is reliable as long as the potential range $R$ is not so short that the assumption of a slowly varying potential is violated". With respect to which length scale should the range R not be too short? Later they hint that the theory could be extended to $r_{eff} \ll a_{BB}$, so I suppose the relevant length is $a_{BB}$. If so, why is it the relevant length scale? This should be discussed more explicitly.

2) The authors investigate the universality of their results by considering two different potentials: a Gaussian and an exponential potential. These two potentials are relatively similar. To get a more convincing evidence of universality, it would be interesting to consider a markedly different potential. For instance, if it is not too much work for the authors, it would be interesting (and more physically motivated) to use a van der Waals potential, such as a Lennard-Jones potential. This is just a suggestion.

3) In Fig. 5, it would be instructive to plot the impurity-boson dimer energy for comparison. If possible, it would also be interesting to plot results for vanishing n0. Intuitively, that limit should brige the mean-field regime and the dimer energy.

4) In Fig. 5, it is stated that the polaron energy at negative scattering length is universal for $r_{eff} \gtrsim \xi$. Is it a numerical observation for that particular calculation or a more general statement? The authors should clarify the generality of this statement.

5) It is pointed out that a deep Gaussian potential can have several bound states, which makes the polaron energy non-unique. At first, it is not clear why an emphasis is put on the Gaussian potential. It would seem that the exponential potential would equally have several bound states if sufficiently deep. I presume that in the range of effective ranges considered, the required depth of the potentials is such that a second bound state appears for the Gaussian potential, but not for the exponential potential. Is that right? Somehow this discussion could be clarified. It might help to specify either in the text or on the curves of Fig 5(d) the number of bound states supported by each potential.

I have a few additional comments:

6) The authors explain that the stabilization of the Bose polaron comes from the repulsion between the bosons. However, it has been shown in Ref. [55] that even for non-interacting bosons, the interaction between the impurity and bosons can have a stabilizing effect. The authors may want to comment on this additional effect and whether it is present in their theory (presumably not) and what it would take to include this effect.

7) In section II.A, the authors state that their ansatz "is based on a coherent ansatz". I think the product form they consider is actually a Fock state, and not a coherent state.

8) In Section VI, the authors state "However, when the coherent state ansatz or higher-order excitation extensions of the Chevy ansatz [41, 55] are applied to the truncated Hamiltonian (4) they lead to the aforementioned, spurious divergence of the ground-state energy". I do not think that there is any spurious divergence of the ground-state energy in Refs. [41][55]. Perhaps the authors meant to refer to Ref. [30]?

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

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