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Emergent nonHermitian skin effect in the synthetic space of (anti)$\cal PT$symmetric dimers
by Ievgen I. Arkhipov, Fabrizio Minganti
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Submission summary
As Contributors:  Ievgen Arkhipov 
Arxiv Link:  https://arxiv.org/abs/2110.15286v3 (pdf) 
Date submitted:  20220128 11:52 
Submitted by:  Arkhipov, Ievgen 
Submitted to:  SciPost Physics 
Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
Phase transitions in nonHermitian systems are at the focus of cutting edge theoretical and experimental research. On the one hand, paritytime ($\cal PT$) and anti$\cal PT$symmetric physics have gained evergrowing interest, due to the existence of nonHermitian spectral singularities called exceptional points (EPs). On the other, topological and localization transitions in nonHermitian systems reveal new phenomena, e.g., the nonHermitian skin effect and the absence of conventional bulkboundary correspondence. The great majority of previous studies exclusively focus on nonHermitian Hamiltonians, whose realization requires an {\it a priori} finetuned extended lattices to exhibit topological and localization transition phenomena. In this work, we show how the nonHermitian localization phenomena can naturally emerge in the synthetic field moments space of zerodimensional bosonic anti$\cal PT$ and $\cal PT$symmetric quantum dimers. This offers an opportunity to simulate localization transitions in lowdimensional systems, without the need to construct complex arrays of, e.g., coupled cavities or waveguides. Indeed, the field moment equations of motion can describe an equivalent (quasi)particle moving in a onedimensional (1D) synthetic lattice. This synthetic field moments space can exhibit a nontrivial localization phenomena, such as nonHermitian skin effect, induced by the presence of highlydegenerate EPs. We demonstrate our results on the example of an exactly solvable nonHermitian 1D model, emerging in the moments space of an anti$\cal PT$symmetric twomode system. Our results can be directly verified in stateoftheart optical setups, such as superconducting circuits and toroidal resonators, by measuring photon moments or correlation functions.
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Submission & Refereeing History
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Reports on this Submission
Anonymous Report 2 on 2022614 (Invited Report)
Strengths
1. The paper is very clearly written and the images support the text very well
2. The subject of the paper is very interesting and presents novel ideas
3. The authors propose a clear path towards realising nonHermitian phenomena in truly quantum setups
Report
The authors introduce what they call a nonHermitian quantum simulator, which is a Lindbladian system that can reproduce the dynamics of nonHermitian lattices. The advantage of this method is that it requires no finetuning. They illustrate their method with a minimal example of an antiPTsymmetric bosonic dimer coupled to a Markovian bath consisting of two quantum fields. They show that the synthetic space of the dimer higherorder field moments is equivalent to the nonHermitian Hamiltonian of a onedimensional PTsymmetric chain, and identify a localisation transition induces by the presence of an exceptional point.
This paper is very well written and very interesting. It presents a novel method to simulate nonHermitian dynamics on a quantum level, while circumventing techniques like postselection. I believe this paper meets all the criteria for publishing in SciPost. As such, I recommend this paper for publication.
Requested changes
1. The citation to Fig.1(d) below Eq.(3) should be Fig.1(e). Fig.1(d) should be cited elsewhere in the text.
2. I am a bit puzzled why references [110] and [111] are cited at the end of section VI. To my knowledge, they do not discuss lattices of N coupled cavities.
3. The authors focus on bosonic systems in their work. Could they comment on if and, if yes, how their work could be translated to the fermionic case?
Author: Ievgen Arkhipov on 20220623 [id 2605]
(in reply to Report 2 on 20220614)
We thank the Referee for his/her careful reading of our work and for the overall appreciation of the manuscript, finding it "very well written and very interesting" and recommending it for publication.
The Referee asks two minor changes and poses important and interesting questions.
We provide our answers on the Referee's comments (13) below.
**The referee writes:**
>The citation to Fig.1(d) below Eq.(3) should be Fig.1(e). Fig.1(d) should be cited elsewhere in the text.
**Our reply:**
We thanks the Referee for spotting that typo. We have fixed it the revised version of the manuscript.
**2. The referee writes:**
>I am a bit puzzled why references [110] and [111] are cited at the end of section VI. To my knowledge, they do not discuss lattices of N coupled cavities.
**Our reply:**
We apologize for any possible confusion. Indeed, [110] and [111] do not treat directly lattice models, but one of the motivations behind their investigation is the emergent nonHermitian Hamiltonian describing singleparticle physics of Ddimensional lattices [110] and Lieblike lattices [111].
The revised manuscript now reads:
*Thus, to obtain a NHH akin to those emerging in higherdimensional lattice architectures [36,110,111] one has to tune the few parameters of the dimer instead of finetuning all the parameters of the lattice.*
**3. The referee writes:**
>The authors focus on bosonic systems in their work. Could they comment on if and, if yes, how their work could be translated to the fermionic case?
**Our reply:**
We thank the Referee for the very interesting question. The use of higherorder moments and the mapping to the singleparticle NHH is based on the bosonic operator algebra, and as such a direct extension to the fermionic problem is not possible. Nonetheless, it is an interesting question what is the structure of the moment space of quadratic fermionic systems, and it could constitute an interesting future research direction.
We added a corresponding paragraph at the end of Sec. V of the revised manuscript:
*Another interesting direction of future research will be the investigation of higherorder moments spaces of quadratic fermionic fields, and their possible similar mapping to higherdimensional lattice systems.
A foreseeable challenge towards this extension is the mathematical construction of the fermionic higherorder moments space and the associated mapping to the singleparticle NHHs.
Indeed, the Kronecker sum algebra, that we employed in the bosonic case, cannot be directly applied to fermionic particles.*
Author: Ievgen Arkhipov on 20220623 [id 2606]
(in reply to Report 2 on 20220614)We thank the Referee for his/her careful reading of our work and for the overall appreciation of the manuscript, finding it "very well written and very interesting" and recommending it for publication. The Referee asks two minor changes and poses important and interesting questions. We provide our answers on the Referee's comments (13) below.
Our reply: We thanks the Referee for spotting that typo. We have fixed it the revised version of the manuscript.
Our reply: We apologize for any possible confusion. Indeed, [110] and [111] do not treat directly lattice models, but one of the motivations behind their investigation is the emergent nonHermitian Hamiltonian describing singleparticle physics of Ddimensional lattices [110] and Lieblike lattices [111]. The revised manuscript now reads: Thus, to obtain a NHH akin to those emerging in higherdimensional lattice architectures [36,110,111] one has to tune the few parameters of the dimer instead of finetuning all the parameters of the lattice.
Our reply: We thank the Referee for the very interesting question. The use of higherorder moments and the mapping to the singleparticle NHH is based on the bosonic operator algebra, and as such a direct extension to the fermionic problem is not possible. Nonetheless, it is an interesting question what is the structure of the moment space of quadratic fermionic systems, and it could constitute an interesting future research direction. We added a corresponding paragraph at the end of Sec. V of the revised manuscript: Another interesting direction of future research will be the investigation of higherorder moments spaces of quadratic fermionic fields, and their possible similar mapping to higherdimensional lattice systems. A foreseeable challenge towards this extension is the mathematical construction of the fermionic higherorder moments space and the associated mapping to the singleparticle NHHs. Indeed, the Kronecker sum algebra, that we employed in the bosonic case, cannot be directly applied to fermionic particles.