SciPost logo

SciPost Submission Page

Quantum engineering of a synthetic thermal bath for bosonic atoms in a one-dimensional optical lattice via Markovian feedback control

by Ling-Na Wu, André Eckardt

Submission summary

As Contributors: André Eckardt · Lingna Wu
Arxiv Link: (pdf)
Date accepted: 2022-06-07
Date submitted: 2022-05-13 06:56
Submitted by: Wu, Lingna
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


We propose and investigate a scheme for engineering a synthetic thermal bath for a bosonic quantum gas in a one-dimensional optical lattice based on Markovian feedback control. The performance of our scheme is quantified by the fidelity between the steady state of the system and the effective thermal state. For double-well and triple-well systems with non-interacting particles, the steady state is found to be an exact thermal state, which is attributed to the fact that the transfer rates between all pairs of coupled eigenstates satisfy detailed balance condition. The scenario changes when there are more lattice sites, where the detailed balance condition does not hold any more, but remains an accurate approximation. Remarkably, our scheme performs very well at low and high temperature regimes, with the fidelity close to one. The performance at the intermediate temperature regime (where a crossover into a Bose condensed regime occurs) is slightly worse, and the fidelity shows a gentle decrease with increasing system size. We also discuss the interacting cases. In contrast to the non-interacting cases, the scheme is found to perform better at a higher temperature. Another difference is that the minimal temperature that can be engineered is nonzero and increases with the interaction strength.

Current status:
Publication decision taken: accept

Editorial decision: For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)

Author comments upon resubmission

Dear Editor,

With this letter we resubmit our manuscript “Quantum engineering of a synthetic thermal bath for bosonic atoms in a one-dimensional optical lattice via Markovian feedback control” for publication in SciPost Physics.

We thank both referees for their professional criticism and useful comments, which allowed us to improve our manuscript considerably.

We hope the revised manuscript will live up to the standards of SciPost Physics and can be accepted for publication.

Thank you!

Sincerely yours,
Ling-Na Wu and André Eckardt

List of changes

1. The title has been changed from “Quantum engineering of a synthetic thermal bath via Markovian feedback control” to “Quantum engineering of a synthetic thermal bath for bosonic atoms in a one-dimensional optical lattice via Markovian feedback control”, as a response to Referee #2 (comment #1).

2. In the abstract, a sentence has been added: “(where a crossover into a Bose condensed regime occurs)”.

3. On page 3, a sentence “For cold atoms in cavity (which is a potential experimental setup to implement our scheme), the typical time scales (such as tunneling time) are on the order of milliseconds [69]. Hence, a control on the higher kHz scale is sufficient, which can be achieved easily using digital signal processors.” has been added to address comment #2 from Referee #1.

4. A figure (Fig. 1) has been added, as suggested by Referee #1 (see comment #1).

5. In Fig. 5, errorbars are added, as a response to Referee #1 (see comment #3).

6. On page 13, under Eq. (37), a sentence “which is an intensive quantity taking values between 0 and 1.” has been added to address comment # 4 from Referee #2.

7. On page 13, a new paragraph discussing the crossover to a finite-size Bose condensate has been added to address comment #5 from Referee #2. The last sentence is added as suggested by Referee #1 (comment #4).

8. The discussion of the interacting case (Section 5) has been extended, as suggested by Referee #2 (comment #3).

9. The interaction strength for Fig. 8 has been raised from 2J to 4J, to further stress the impact of interactions.

10. In Fig. 9 (b), a curve denoting the fidelity between the steady state and the ground state has been added.

11. The conclusion paragraph has been extended, including an outlook (as a response to comment #5 from Referee #1).

Reports on this Submission

Anonymous Report 2 on 2022-5-26 (Invited Report)


1 - The paper is well contextualized and acknowledges the work leading to it.
2- There is clarity in the derivation of the analytical results and good understanding of the numerical results.

3 - There is a good progression on their analysis working from small towards large system sizes, helping to build intuition for the reader.
4 - Experimental feasibility, even if briefly, is discussed.


1- The results are applicable in a restricted range of system sizes and no competing mechanisms working against the preparation scheme were considered.


I believe that the authors - by providing additional figures, explanations and outlook - have addressed all the proposed changes. As a result, I believe that the article deserves publication in its current form.

Requested changes

No further changes required.

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

Report 1 by Santiago Francisco Caballero Benitez on 2022-5-18 (Invited Report)


The authors have answered all my concerns and have improved the manuscript. The new additions to the interacting part improved the discussion. Therfore, I recommend the article to be published as it is in Scipost Physics.

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

Login to report or comment