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Periodically and Quasi-periodically Driven Dynamics of Bose-Einstein Condensates

by Pengfei Zhang, Yingfei Gu

Submission summary

As Contributors: Pengfei Zhang
Arxiv Link: (pdf)
Date accepted: 2020-11-17
Date submitted: 2020-10-29 04:16
Submitted by: Zhang, Pengfei
Submitted to: SciPost Physics
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Theory
Approach: Theoretical


We study the quantum dynamics of Bose-Einstein condensates when the scattering length is modulated periodically or quasi-periodically in time within the Bogoliubov framework. For the periodically driven case, we consider two protocols where the modulation is a square-wave or a sine-wave. In both protocols for each fixed momentum, there are heating and non-heating phases, and a phase boundary between them. The two phases are distinguished by whether the number of excited particles grows exponentially or not. For the quasi-periodically driven case, we again consider two protocols: the square-wave quasi-periodicity, where the excitations are generated for almost all parameters as an analog of the Fibonacci-type quasi-crystal; and the sine-wave quasi-periodicity, where there is a finite measure parameter regime for the non-heating phase. We also plot the analogs of the Hofstadter butterfly for both protocols.

Published as SciPost Phys. 9, 079 (2020)

Author comments upon resubmission

Dear editor,

Thank you and all referees for carefully reviewing our manuscript. We are happy to see referees find our work interesting and novel. Now we have revised our manuscript according to your suggestions. Please see the "List of changes" for details.

Hope you find our revised manuscript satisfactory and would like to suggest its publication.

Pengfei Zhang and Yingfei Gu

List of changes

1. Add a physical justification for the criterion n_k\sim e^{\lambda_k t} corresponding to the system being in the heating phase.

Reply: We have now added “Consequently, the kinetic energy of atoms with the corresponding momentum, which is defined as k^2n_k/2, grows exponentially in time, implying the system is being heated. ” below equation (9).

2. Estimate the time scales for the breakdown of the Bogoliubov theory on the one hand and for reaching the asymptotic regime where the derived heating rates are valid on the other. Discuss the existence/duration of a time-window in which the derived results apply.

Reply: We have now added estimation of the time window in the last paragraph of the summary section. The result clearly shows such a time window exists when the interaction is weak.

3. More discussion of the relationship between the graphs of non-heating parameters they show and the usual Hofstadter butterfly (eigenvalues of 2DEG in a magnetic field or just Harper model).

Reply: To explain the relation, we have added: 1). The relation between our square-wave protocol and tight-binding models at the end of section 3.1; and 2). Explanations for the existence of the butterfly in sections 4.1.3 and 4.2.

4. Please fix the grammatical issues.

Reply: We have read through our manuscript carefully and tried our best to fix grammar errors.

5. Add reference after 'non-trivial dynamics'

Reply: We have fixed problems for the reference here.

6. There is a recent experiment in Hanns-Christoph Naegerl's group where the scattering length of ultracold atoms are modulated in time, which should be mentioned.

Reply: We have added the reference in footnote 3.

Reports on this Submission

Anonymous Report 3 on 2020-11-12 (Invited Report)


The authors have addressed the points raised in my previous report in a satisfactory way. Therefore ,I recommend publication of the manuscript in its present form.

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

Anonymous Report 2 on 2020-11-9 (Invited Report)


The changes detailed by the authors sound appropriate; I support publication.

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

Anonymous Report 1 on 2020-11-8 (Invited Report)


Following the updating of this manuscript, I believe it should be published in scipost physics.

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

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