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On the low-energy description for tunnel-coupled one-dimensional Bose gases
by Yuri D van Nieuwkerk, Fabian H L Essler
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|Authors (as registered SciPost users):||Fabian Essler · Yuri Daniel van Nieuwkerk|
|Preprint Link:||scipost_202005_00003v1 (pdf)|
|Date submitted:||2020-05-08 02:00|
|Submitted by:||van Nieuwkerk, Yuri Daniel|
|Submitted to:||SciPost Physics|
We consider a model of two tunnel-coupled one-dimensional Bose gases with hard-wall boundary conditions. Bosonizing the model and retaining only the most relevant interactions leads to a decoupled theory consisting of a quantum sine-Gordon model and a free boson, describing respectively the antisymmetric and symmetric combinations of the phase fields. We go beyond this description by retaining the perturbation with the next smallest scaling dimension. This perturbation carries conformal spin and couples the two sectors. We carry out a detailed investigation of the effects of this coupling on the non-equilibrium dynamics of the model. We focus in particular on the role played by spatial inhomogeneities in the initial state in a quantum quench setup.
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- Cite as: Anonymous, Report on arXiv:scipost_202005_00003v1, delivered 2020-06-06, doi: 10.21468/SciPost.Report.1742
1- It addresses a timely and relevant experimental question
2- Clearly written
3- It presents a clear and detailed introduction to the harmonic self-consistent method
1-The theoretical setup has been proved to be insufficient in describing the experimental observations
The authors provide an analytical study of an experimentally-relevant setup, namely two weakly coupled Bose-Einstein condensates through a strong barrier. This experiment is currently implemented and extensively studied in the Vienna’s group, greatly motivating any interesting result on this model.
At low energies, the system is known to be approximately described by the sine-Gordon field theory which the authors already studied in the self-consistent time–dependent harmonic approximation (SCTDHA) Ref. .
Here, the authors extend the previous setting including a more general dynamics in their self-consistent approximation, allowing for inhomogeneous field profiles and working in a hard-wall box potential. Compared with the previously studied periodic boundary conditions, boxes are expected to provide a better description of the experiment, which is realized in a harmonic trap. Most importantly, an additional correction to the Hamiltonian is considered, which couples the symmetric and antisymmetric sectors of the theory, allowing energy transfer between the two. In my understanding, this term has been included hoping it could capture the phase-locking observed in Ref. , however, as the authors write in the conclusions, this newly-introduced term seems to have mild effects on the dynamics and cannot provide a mechanism for the observed phase-locking.
In my opinion, the results discussed in this manuscript are correct, but from the technical point they only present an incremental advance compared with their previous publication Ref. . Including the new interaction and inhomogeneities in the self-consistent harmonic approximation surely presents additional technical difficulties and calculations, but I could not appreciate the theoretical novelty of the method.
I think that the most interesting finding is that the coupling between the symmetric and antisymmetric sectors is not enough to describe the phase-locking, which I heard to be pointed out as the most probable culprit in several instances.
Even though the energy scale at which the SCTDHA can be applied is too small compared with that of the present experiment, I believe they are still close enough to trust the qualitative results and rule out the symmetric-antisymmetric coupling as the major character in the phase-locking mechanism.
In general, I think this manuscript presents results worth to be published in SciPost Physics, however I have two questions:
- The SCTDHA is supposed to hold at short time-scales where non-gaussian corrections grow, but I could not find in the paper an estimation of the validity time scales. Is there any quantity that can be computed within the SCTDHA in order to check its validity? It would be interesting to compare such a time scale with the phase-locking time of the experiment.
- I wonder if more realistic inhomogeneities can be captured building on the curved CFT introduced in SciPost Phys. 2, 002 (2017), including of course a tunneling term among the two condensates and resulting in an inhomogeneous sine-Gordon model. Can the authors comment on this?
Moreover, I would suggest the following improvements:
- In the introduction, the phase-locking mechanism is discussed and it appears to me as the main motivation of this work, however the effect of the new terms is discussed only in the conclusions. I think it could be helpful to mention straight from the beginning (i.e. in the introduction) the fact that the proposed extensions to the SCTDHA cannot reproduce the phase-locking mechanism.
- I think that the list of references on the FCS is incomplete. I know that the list of papers studying the FCS is very long, but I think at least the three references below must be included
Rev. Lett. 122, 120401 (2019).
SciPost Phys. 7, 072 (2019)
EPL 129 60007 (2020)
I also found some typos
incompatable->incompatible pg 3
poisson->Poisson pg 13
Ref.  is the same as Ref. 
I would recommend the authors to go through the manuscript once again and fix possible additional typos.
1- Anticipate in the introduction that the new terms cannot provide a mechanism for the observed phase-locking
2- Update the list of references
3- Fix minor typos in the manuscript