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Entangled states of dipolar bosons generated in a triple-well potential

by Arlei P. Tonel, Leandro H. Ymai, Karin Wittmann W., Angela Foerster, Jon Links

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Submission summary

Authors (as registered SciPost users): Jon Links
Submission information
Preprint Link:  (pdf)
Date submitted: 2019-09-12 02:00
Submitted by: Links, Jon
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Mathematical Physics
  • Quantum Physics
Approach: Theoretical


We study the generation of entangled states using a device constructed from dipolar bosons confined to a triple-well potential. Dipolar bosons possess controllable, long-range interactions. This property permits specific choices to be made for the coupling parameters, such that the system is integrable. Integrability assists in the analysis of the system via an effective Hamiltonian constructed through a conserved operator. Through computations of fidelity we establish that this approach, to study the time-evolution of the entanglement for a class of non-entangled initial states, yields accurate approximations given by analytic formulae.

Current status:
Has been resubmitted

Submission & Refereeing History

Resubmission 1909.04815v2 on 20 February 2020

Reports on this Submission

Anonymous Report 2 on 2019-12-23 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:1909.04815v1, delivered 2019-12-23, doi: 10.21468/SciPost.Report.1413


The paper studies the behaviour of the system with respect to a variety of initial conditions for the integrable Hamiltonian and it provides a clear analysis of the entanglement generated under time evolution.


1) No particular effort is done to motivate the study: it is written
that "the main goal is to expand on the analysis conducted in [18]", and
explore a variety of initial conditions plus a study of dynamics. Despite
it is understandable why this analysis may be desirable, the Authors do not elaborate enough on it in my opinion: what they expect from this study? why it is interesting? Since this analysis is restricted to states (4) where the number is defined, it is also clear that the analysis on these initial states is partial.

2) The Authors refer to their system as a "device": no effort is done to motivate the possible use in atomtronics, where, e.g., one would like to explore deviations from the integrable point. If from one side to call it "system" or "device" may be (to a certain extent) a matter of taste, at the same time it would be desirable to better motivate the use of the terminology "device", and may be to write "(e.g. see [20])" is not enough.

3) It would be important in my opinion to write the Hamiltonian of dipolar
bosons in a trimer configuration, and then discuss under what specific fine
tuning one gets the integrable Hamiltonian (1). If the Authors like to
emphasize that "Physical realisation of the system is feasible using dipolar atoms such as 52 Cr or 164 Dy" they should describe how and if this tuning is realistically possible.

4) It would be important to see (or at least to mention or discuss) the possible effect of periodic boundary conditions a^\dag_1 a_3.


I consider the paper interesting and without flows, on a deserving subject,
but I see that several points may be improved according the previous list.
I then suggest the Authors consider the previous points.

Requested changes

According the previous list of improvable points:

1) I suggest to improve the motivational point of the paper, and discuss what other initial conditions could have been interesting to explore and why they
have been not considered (or perhaps left for future consideration?)

2) clarify the connection with atomtronics motivation - in that case please explain why the deviations from the integrable point may not spoil the analysis and the conclusions presented

3) present a derivation of (1) from the Hamiltonian of dipolar bosons in a three-well potential and discuss the fine tuning of parameters needed to obtain it

4) comment on the role of periodic boundary conditions

  • validity: high
  • significance: good
  • originality: ok
  • clarity: high
  • formatting: excellent
  • grammar: excellent

Anonymous Report 1 on 2019-11-18 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:1909.04815v1, delivered 2019-11-18, doi: 10.21468/SciPost.Report.1324


In this paper the authors study the population and the entanglement dynamics for an integrable Hamiltonian describing a three-well Bose–Hubbard model obtained for a particular set of parameters. The time evolution sets in starting from non-entangled Fock states. What they predict is a coherent oscillation in the imbalance population between the first and the third well.
This result is verified comparing it with an analytic calculation obtained in the large interaction regime, the so-called resonant tunneling regime.
The paper is sound and well written, therefore I can recommend it for publication. However I would like the authors to clarify only few issues:

- In Fig. 8 the maximum value of the entropy is 1. Is it the plot of S/S_max instead of S? (is the entanglement entropy normalized by its maximum value?)
- Is there any reason why the time evolution of the entanglement entropy is lower for initial states with k=0, namely when the third well is empty at the initial time?
- I would expect that the fidelity, defined as the overlap between the exact state and the one obtained by the coherent state approximation, approaches value 1 upon increasing U, namely going deeply in the coherent tunneling regime, while Fig. 9 does not show such expected behavior. Fig. 9 shows, instead, that the fidelity seems sensitive to the initial polulation of the second well. Could the authors comment on that?

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

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