SciPost Submission Page
Spin-only dynamics of the multi-species nonreciprocal Dicke model
by Joseph Jachinowski, Peter B. Littlewood
Submission summary
| Authors (as registered SciPost users): | Joseph Jachinowski |
| Submission information | |
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| Preprint Link: | scipost_202508_00053v1 (pdf) |
| Date submitted: | Aug. 21, 2025, 8:23 p.m. |
| Submitted by: | Joseph Jachinowski |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
The Hepp-Lieb-Dicke model is ubiquitous in cavity quantum electrodynamics, describing spin-cavity coupling which does not conserve excitation number. Coupling the closed spin-cavity system to an environment realizes the open Dicke model, and by tuning the structure of the environment or the system-environment coupling, interesting spin-only models can be engineered. In this work, we focus on a variation of the multi-species open Dicke model which realizes mediated nonreciprocal interactions between the spin species and, consequently, an interesting dynamical limit-cycle phase. In particular, we improve upon adiabatic elimination and, instead, employ a Redfield master equation in order to describe the effective dynamics of the spin-only system. We assess this approach at the mean-field level, comparing it both to adiabatic elimination and the full spin-cavity model, and find that the predictions are sensitive to the presence of single-particle incoherent decay. Additionally, we clarify the symmetries of the model and explore the dynamical limit-cycle phase in the case of explicit $\mathcal{PT}$-symmetry breaking, finding a region of phase coexistence terminating at an codimension-two exceptional point. Lastly, we go beyond mean-field theory by exact numerical diagonalization of the master equation, appealing to permutation symmetry in order to increase the size of accessible systems. We find signatures of phase transitions even for small system sizes.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
1) The introduction presents a strong and clear overview of the field as it stands.
2) The appendix provides a clear and interesting derivation of a non-secular Redfield equation for a multi-species open Dicke Model.
3) The analysis, and benchmarking against exact results, is logical and clear.
4) The use of weak and strong symmetries to understand the results is intuitive.
Weaknesses
1) Some of the background 'derivation' could be clearer.
2) The impact and importance of the final simulation results could be more clear and transparent.
Report
Requested changes
1) Regarding the starting point of the (driven)-dissipative Dicke model, the authors say on lines 53-56:
" the Dicke model can be found in Ref. [16] including both equilibrium and driven-dissipative variations. For the rest of this paper, we focus on the dissipative Dicke model (without drive) and, therefore, drop the modifier."
The (driven)-dissipative dicke model is then given in equation 7. I would just ask the authors to clarify what they mean by ''without drive'', since, to my understanding, typically equation 7 is derived as an effective time-independent model from a driven time-dependent one. In the driven frame, we can have non-equilibrium local losses, list those equation 7, which don't respect detailed balance as the whole model is in a rotating frame. I would just ask the authors to clarify this, as it has led to confusion in other works.
On a related note, if what I am saying here is correct (perhaps the authors have a different justification in mind), does this effective frame introduce any issues in the derivation of the Redfield model? I expect not, but it would be good to keep in mind.
2) In deriving the Redfield model, the authors trace out the cavity, and (I believe) require that the cavity correlation functions decay faster than the spin time scales. This is fair, and standard. However, the derivation also usually relies on a Born approximation in that, unless one is in the exact delta-function limit (which would actually give a local Lindblad instead of a Redfield-style equation), we also require the coupling to be weak. It appears generally this is not the case in the analysis, so I find it interesting that the model still works so well (particularly compared to adiabatic elimination, which intuitively is more suited to this problem).
It would be useful for the authors to comment on this. In my experience the boundary between perturbative and non-perturbative regimes is a bit murky, particularly with the non-secular version of this type of master equation, so any light the authors could shed would be welcome.
3) In the introduction and conclusions the authors state 'We find signatures of phase transitions even for small system sizes.' However, in the main text (presumably in section 3.5), I did not find this result to be particularly clearly explained, and the results analysis in general, also in other sections, was sometimes quite complex and obtuse. If possible I would ask the authors to more clearly present this result, and slightly simplify some of the discussion of the other simulation results to emphasize which parts of most importance.
Recommendation
Ask for minor revision