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Stabilizing the Laughlin state of light: dynamics of hole fractionalization
by Pavel D. Kurilovich, Vladislav D. Kurilovich, José Lebreuilly, S. M. Girvin
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Pavel Kurilovich |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2111.01157v3 (pdf) |
| Date accepted: | 2022-07-12 |
| Date submitted: | 2022-06-13 01:34 |
| Submitted by: | Kurilovich, Pavel |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Particle loss is the ultimate challenge for preparation of strongly correlated many-body states of photons. An established way to overcome the loss is to employ a stabilization setup that autonomously injects new photons in place of the lost ones. However, as we show, the effectiveness of such a stabilization setup is compromised for fractional quantum Hall states. There, a hole formed by a lost photon can separate into several remote quasiholes none of which can be refilled by injecting a photon locally. By deriving an exact expression for the steady-state density matrix, we demonstrate that isolated quasiholes proliferate in the steady state which damages the quality of the state preparation. The motion of quasiholes leading to their separation is allowed by a repeated process in which a photon is first lost and then quickly refilled in the vicinity of the quasihole. We develop the theory of this dissipative quasihole dynamics and show that it has diffusive character. Our results demonstrate that fractionalization might present an obstacle for both creation and stabilization of strongly-correlated states with photons.
Author comments upon resubmission
List of changes
- Promoted the section of the conclusion devoted to the off-resonant injection of photons to be the first one in Section 5 (now it is Section 5.1 instead of 5.3).
- Added a paragraph about the experimental feasibility of the stabilized Laughlin state (second to last paragraph in Section 3 in the new version of the manuscript).
- Removed the emphasis on the relaxation dynamics being “slow” and instead emphasized that this dynamics is governed by the loss rate as opposed to the naively expected refilling rate.
- Added a note saying that the possible effect of hole fractionalization was mentioned in [47] (end of the paragraph starting on page 3 and ending on page 4 in the new version).
- Added a reference to Ref. [49] after equation (17).
- Added a reference to Ref. [49] in Sec. 5.1.
- Added explicit expression for the quasihole wavefunction with a given angular momentum projection (see Eq. (22) in the new version of the manuscript).
- Subdivided Section 4.1 into subsections 4.1.1 and 4.1.2.
- Rewrote a part of section 4.1 following the comments of the second Referee.
- Added a new section of the appendix, Appendix A in the new version. This appendix provides the derivation of the relaxation eigenmodes.
- Modified the appendix devoted to the derivation of relaxation rates for modes with different angular momenta (now appendix B) to make it more comprehensible.
- Added a footnote about the dependence of the hopping rates on the angular momentum at page 17.
- Added two sentences to paragraph 1 page 19 to emphasize the importance of approximate dark states with exponentially suppressed refilling.
- We added a paragraph about the comparison between Eq. (13) and (37) at the end of Section 4.2.
- We corrected the typos mentioned by the second referee.
- Following the comments of both referees, we reformulated one paragraph in the introduction to make the tone less pessimistic (second to last paragraph in Section 1). We emphasized that our results present a hurdle which can potentially be overcome with further engineering efforts.
- We added a paragraph to the end of Section 3 which emphasizes that the scaling of the quasihole number is only a power law despite the fractionalization. From this we conclude that the stabilization of the Laughlin state should in principle be feasible, in line with previous works on the dissipative stabilization.
Published as SciPost Phys. 13, 107 (2022)
Reports on this Submission
Strengths
1. Timely theoretical investigation of one among the hottest challenges of contemporary quantum optics
2. Work of great interest for a broad spectrum of physicists from cond-mat and open quantum systems
3. Generally clear and exciting presentation
Weaknesses
1. None
Report
The authors have satisfactorily addressed all my remarks. I recommend the manuscript for publication.
Requested changes
1. None