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Quasiequilibrium polariton condensates in the nonlinear regime and beyond
by Ned Goodman, Brendan C. Mulkerin, Jesper Levinsen, Meera M. Parish
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Submission summary
Authors (as registered SciPost users):  Brendan Mulkerin · Meera Parish 
Submission information  

Preprint Link:  https://arxiv.org/abs/2211.03321v1 (pdf) 
Date submitted:  20221114 00:58 
Submitted by:  Mulkerin, Brendan 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We investigate the manybody behavior of polaritons formed from electronhole pairs strongly coupled to photons in a twodimensional semiconductor microcavity. We use a microscopic meanfield BCS theory that describes polariton condensation in quasiequilibrium across the full range of excitation densities. In the limit of vanishing density, we show that our theory recovers the exact singleparticle properties of polaritons, while at low densities it captures nonlinear polaritonpolariton interactions within the Born approximation. For the case of highly screened contact interactions between charge carriers, we obtain analytic expressions for the equation of state of the manybody system. This allows us to show that there is a photon resonance at a chemical potential higher than the photon cavity energy, where the electronhole pair correlations in the polariton condensate become universal and independent of the details of the carrier interactions. Comparing the effect of different ranged interactions between charge carriers, we find that the RytovaKeldysh potential (relevant to transition metal dichalcogenides) offers the best prospect of reaching the BCS regime, where pairs strongly overlap and the minimum pairing gap occurs at finite momentum. Finally, going beyond thermal equilibrium, we argue that there are generically two polariton branches in the drivendissipative system and we discuss the possibility of a densitydriven exceptional point within our model.
Current status:
Reports on this Submission
Report 1 by Ryo Hanai on 2023316 (Invited Report)
 Cite as: Ryo Hanai, Report on arXiv:2211.03321v1, delivered 20230316, doi: 10.21468/SciPost.Report.6913
Strengths
 The authors were able to formulate a meanfield theory for electronhole photon condensate without introducing UV cutoff.
 This formalism enabled the authors to show that the BCS regime is enhanced for RytovaKeldysh potential compared to Coulomb or contact interaction.
Weaknesses
 The overall picture of what the authors obtained is not very different from the known results.
 The treatment of dissipation is problematic even at the phenomenological level.
Report
In this work, the authors present a meanfield theory of an electronholephoton mixture in a twodimensional semiconductor microcavity. While there have been several works that performed a similar analysis to the model considered in this manuscript, the novelty here is that they have employed an appropriate renormalization scheme. They considered three types of interactions: Coulomb interaction, contact interaction, and RytovaKeldysh potential, and found that the RytovaKeldysh potential offers the largest parameter regime of the BCS regime. This treatment allowed the authors to eliminate the ultraviolet cutoff dependence from the model.
The results are nontrivial, and the manuscript is wellwritten. I, therefore, recommend its publication in SciPost Physics once the following comments are addressed.
Requested changes
1. Is there an intuitive understanding of why the RytovaKeldysh potential provides a more significant BCS regime than the Coulomb interaction? I would have thought that the shorter range nature of the RytovaKeldysh potential would suppress the band renormalization that made it possible to exhibit the BCS regime.
2. In Sec. IV, the authors consider the effect of dissipation by introducing a gain and a loss to the exciton and photon component, respectively, in a phenomenological manner. However, I find some of their treatment problematic.
The chemical potential μ must not have an imaginary part since its presence implies damping or gain of the condensate. Note that, in the canonical ensemble, the condensate has an oscillating phase determined by the chemical potential, as Delta(t) = Delta_0 exp[I 2μt]; see Ref. [49]. This contradicts the assumption that the system is in a steadystate. In general, there would be a nonlinear imaginary term that gives rise to the saturation effect (as done in [Wouters and Carusotto, PRL 99, 140402 (2007)] for the onecomponent case and Ref. [49] and [Hanai and Littlewood, PRR 2, 033018 (2020)] for the twocomponent case) that automatically makes the steadystate condition (=μ being real) satisfied in the longtime limit.
This can be achieved by interpreting their gamma (RX in Ref. [49]) to include these nonlinear effects. In particular, gamma should be considered as a parameter that is determined by demanding μ to be real, as done in Ref. [49] (instead of assuming gamma = kappa as done in the manuscript).
On the other hand, there is no need to add an imaginary part to the electron density Eq. (37). In the Keldysh formalism, adding dissipation to the system would make the spectrum have a Lorentz distribution rather than the deltafunction of the meanfield approximation but would never give rise to an imaginary part of the density (See, e.g., Ref. [14].). Therefore, solving Eq. (49) is not necessary. What one should solve instead is the requirement that the chemical potential μ is real, WITHOUT assuming by hand that gamma = kappa, as mentioned above.
One of the reasons that I strongly recommend the authors to perform the above analysis is that assuming gamma = kappa would lead to a somewhat misleading conclusion that one always goes through an exceptional point by tuning the density. Instead, as pointed out in Ref. [49] (and more recently in [Fruchart, Hanai, Littlewood, Vitelli, Nature 592, 363 (2021)] from a symmetry perspective), one needs to finetune TWO parameters to go through an exceptional point in a U(1)broken system like excitonpolariton condensates.
3. I am confused by the authors’ comment “Reference [49] has proposed that … due to Pauli blocking or phase space filling effects [2, 3, 54]. However, we observe no such decrease of the Rabi splitting with increasing density ...” I am pretty sure that the Pauli blocking effect already appears at a meanfield level; see Eq. (S81) of the SI of Ref. [49]. Could the authors comment on why they could not see such effects in more detail?
Author: Brendan Mulkerin on 20230524 [id 3682]
(in reply to Report 1 by Ryo Hanai on 20230316)RESPONSE TO REFEREE:
We thank the Referee for his comments and detailed analysis of our manuscript and we appreciate his supportive report and recommendations.
We address his comments point by point in the attached document, which includes changes to the manuscript highlighted in blue.
Attachment:
respone_final_Ryo.pdf