SciPost Submission Page
Space-time first-order correlations of an open Bose Hubbard model with incoherent pump and loss
by Martina Zündel, Leonardo Mazza, Léonie Canet, Anna Minguzzi
Submission summary
| Authors (as registered SciPost users): | Martina Zündel |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202405_00048v1 (pdf) |
| Date submitted: | 2024-05-30 11:56 |
| Submitted by: | Zündel, Martina |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We investigate the correlation properties in the steady state of driven-dissipative interacting bosonic systems in the quantum regime, as for example non-linear photonic cavities. Specifically, we consider the Bose-Hubbard model on a periodic chain and with spatially homogeneous one-body loss and pump within the Markovian approximation. The steady state corresponds to an infinite temperature state at finite chemical potential with diagonal spatial correlations. Nonetheless, we observe a nontrivial behaviour of the space-time two-point correlation function in the steady state, obtained by exact diagonalisation. In particular, we find that the decay width of the propagator is not only renormalised at increasing interactions, as it is the case of a single non-linear resonator, but also at increasing hopping strength. We then compute the full spectral function, finding that it contains both a dispersive free-particle like dispersion at low energy and a doublon branch at energy corresponding to the on-site interactions. We compare with the corresponding calculation for the ground state of a closed quantum system and show that the driven-dissipative nature - determining both the steady state and the dynamical evolution - changes the low-lying part of the spectrum, where noticeably, the dispersion is quadratic instead of linear at small wavevectors.
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 steady state of this model was already know to be the infinite temperature state with a given fugacity. The novelty of this paper is the study of the first order correlations. The system is studied both with exact diagonalization (ED) and with the Keldysh field formalism. It is only within the ED approach that new results on the correlations are obtained.
2- The paper is well written and easy to follow. The introduction gives a good overview of the field of open many body systems and the theoretical techniques to deal with them.
Weaknesses
1- The problem I have with the manuscript is related to the perspective the results are put in. In the abstract and conclusions, the difference with the correlations in the ground state of the Bose-Hubbard model are emphasised. It is a bit a strange choice to put the emphasis on these differences, because the steady state is rather the infinite temperature one. Actually in Sec. 5.4 the comparison with the infinite temperature closed system is made and a good correspondence is observed. At least, this is what I get from Fig. 7 and the describing text. It is said in the abstract that “the dispersion is quadratic instead of linear at small wave vectors”. But in Fig. 7, the dispersion also looks quadratic to me for the closed system.
I would therefore tend to say that the driving and dissipation has a small effect on the first-order correlations. I agree that this conclusion may be a bit disappointing and that the authors therefore put the emphasis on the difference with the zero-temperature state. But that conclusion would also hold for comparing the infinite and zero temperature closed systems and no one would be surprised by that.
Given the close similarities between the left and right hand panels in Fig. 7, I could imagine that it is possible to develop a perturbative treatment of the driving and dissipation, but it is hardly the task of the referee to suggest new research.
Report
The manuscript by Zündel et al. presents a theoretical analysis of the first order correlation function of a driven-dissipative Bose-Hubbard model with incoherent pumping and losses.
The current manuscript leaves me a bit wondering whether there is something interesting to be said about the first order coherence for this system with respect to the closed system. This leaves one with a nice piece of work where the conclusions seem to be unfortunately a bit trivial. But of course the authors are very much welcome to point out my oversights.
Requested changes
1- Unless I have missed it, the manuscript actually does not point out a big impact of the nonequilibrium condition on the first order correlation function. If the authors cannot convince me that I am wrong, I am afraid that the manuscript lacks a clear message that warrants publication in SciPost.
2- As a side remark, I would like to mention that I did not appreciate very much the discussion of the work in perspective of the NISQ era in the conclusions. There does not seem to be any potential of the presented driven-dissipative Bose-Hubbard model in this respect. It is my opinion that these boiler plate texts should be avoided as much as possible in the ChatGPT era.
Recommendation
Ask for major revision