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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
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Anna Minguzzi · Martina Zündel |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202405_00048v3 (pdf) |
| Date accepted: | 2025-02-18 |
| Date submitted: | 2025-02-14 20:44 |
| 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 is non-thermal and is formally equivalent to an infinite-temperature state with finite chemical potential set by the dissipative parameters. While there is no effect of interactions on the steady state, we observe a nontrivial behaviour of the space-time two-point correlation function, 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. Furthermore, we numerically predict at large interactions a plateau value of the decay rate which goes beyond perturbative results in the interaction 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. Finally, we compare to a high temperature grand-canonical equilibrium state and show the difference with respect to the open system stemming from the additional degree of freedom of the dissipation that allows one to vary the width of the dispersion lines.
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
Author comments upon resubmission
Dear Editors,
We warmly thank the Referees for the positive assessments. We have implemented all the minor modifications suggested by the Referee 3, highlighted in red in the resubmitted version. An answer to the report of Referee 3 is given below.
Best regards, Martina Zündel and Anna Minguzzi on behalf of the authors
-------------- Answers to the Referee 3 -------------------- We thank for the careful reading, the suggestions and the positive feedback. 1) We added a half sentences in the conclusion concerning the linear excitation branch at low temperatures in equilibrium. 2) We tempered the expression from "remarkable" to "at first glance this seems astonishing" and we point out what is the difference to the equilibrium case: In the equilibrium density matrix the interaction does appear explicitly, compared to the open system steady state. 3) We thank for the question regarding the one-loop correction to the oscillation frequency: We could not make a quantitative comparison as it is hard to extract the correct oscillation frequency from the data with accuracy.
List of changes
- added a half-sentence in the conclusions
- changed a sentences in section 6.1
- corrected an expression in the headline of fig. 9
Published as SciPost Phys. 18, 095 (2025)