Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1401.5776 · Physical Review A

Spontaneous collective coherence in driven dissipative cavity arrays

J. Ruiz-Rivas, Elena del Valle, Christopher Gies, P. Gärtner, Michael J. Hartmann

Published Sep 4, 2014• 30 citations
arXivHTMLPDF

Abstract

We study an array of dissipative tunnel-coupled cavities, each interacting with an incoherently pumped two-level emitter. For cavities in the lasing regime, we find correlations between the light fields of distant cavities, despite the dissipation and the incoherent nature of the pumping mechanism. These correlations decay faster than any power of the distance for arrays in any dimension but become increasingly long ranged with increasing photon tunneling between adjacent cavities. The interaction-dominated and the tunneling-dominated regimes show markedly different scaling of the correlation length which always remains finite due to the finite photon trapping time. We propose a series of observables to characterize the spontaneous buildup of collective coherence in the system.

DOI
10.1103/physreva.90.033808

Related papers

Phase diagram of incoherently driven strongly correlated photonic lattices

Alberto Biella, Florent Storme, José Lebreuilly +4 more

We explore theoretically the nonequilibrium photonic phases of an array of coupled cavities in presence of incoherent driving and dissipation. In particular, we consider a Hubbard model system where each site is a Kerr nonlinear resonator coupled to a two-level emitter, which is pumped incoherently. Within a Gutzwiller mean-field approach, we determine the steady-state phase diagram of such a system. We find that, at a critical value of the intercavity photon hopping rate, a second-order nonequilibrium phase transition associated with the spontaneous breaking of the $\text{U}(1)$ symmetry occurs. The transition from an incompressible Mott-like photon fluid to a coherent delocalized phase is driven by commensurability effects and not by the competition between photon hopping and optical nonlinearity. The essence of the mean-field predictions is corroborated by finite-size simulations obtained with matrix product operators and corner-space renormalization methods.

arXiv:1704.08978•Physical Review A•Aug 17, 2017•69 citations

Strongly correlated photons in arrays of nonlinear cavities

Alexandre Le Boité

In recent years, the control of photon-photon interactions in optical nonlinear media has led to the realization of quantum fluids of light. One of the current challenges is to increase the strength of these interactions and enter the so-called strongly correlated regime. To achieve this goal, arrays of nonlinear cavities are a very promising candidate. In this thesis, theoretical results on arrays of nonlinear cavities described by a driven-dissipative Bose-Hubbard model are presented. In particular, a general method to compute the mean-field phase diagram of this model is described. Due to the finite life time of photons, the system is intrinsically dissipative: cavity losses must be compensated by an external driving field. This nonequilibrium nature gives rise to interesting features, such as a transition between monostable and bistable phases induced by tunneling. In the limit of weak dissipation and weak driving, analytical results describing generalized Mott insulating phases are derived. These states survive up to a critical tunneling strength, above which a crossover to a classical coherent state takes place. Finally, the issue of how to go beyond the mean-field approximation is addressed by performing exact numerical simulations. Large arrays of cavities were simulated by implementing a new method specifically tailored for driven-dissipative systems.

•May 6, 2015•1 citation

Collective quantum coherent oscillations in a globally coupled array of superconducting qubits

Pavel A. Volkov, M. V. Fistul

We report a theoretical study of coherent collective quantum dynamic effects in an array of $N$ qubits (two-level systems) incorporated into a low-dissipation resonant cavity. Individual qubits are characterized by energy level differences ${\ensuremath{\Delta}}_{i}$ and a spread of ${\ensuremath{\Delta}}_{i}$ is taken into account. Noninteracting qubits display coherent quantum beatings with $N$ different frequencies, i.e., ${\ensuremath{\omega}}_{i}={\ensuremath{\Delta}}_{i}/\ensuremath{\hbar}$. Virtual emission and absorption of cavity photons provides a long-range interaction between qubits. In the presence of such interaction we analyze quantum correlation functions of individual qubits ${C}_{i}(t)$ to obtain two collective quantum-mechanical coherent oscillations, characterized by frequencies ${\ensuremath{\omega}}_{1}=\overline{\ensuremath{\Delta}}/\ensuremath{\hbar}$ and ${\ensuremath{\omega}}_{2}={\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}_{R}$, where ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}_{R}$ is the resonant frequency of the cavity renormalized by interaction. The amplitude of these oscillations can be strongly enhanced in the resonant case when ${\ensuremath{\omega}}_{1}\ensuremath{\simeq}{\ensuremath{\omega}}_{2}$. These collective quantum oscillations can be directly observed, e.g., by measurements of frequency dependent transmission coefficient $D(\ensuremath{\omega})$ of electromagnetic field propagating in a transmission line coupled to the system.

arXiv:1305.7370•Physical Review B•Feb 18, 2014•18 citations

Correlator expansion approach to stationary states of weakly coupled cavity arrays

Elena del Valle, Michael J. Hartmann

We introduce a method for calculating the stationary state of a translation invariant array of weakly coupled cavities in the presence of dissipation and coherent as well as incoherent drives. Instead of computing the full density matrix our method directly calculates the correlation functions which are relevant for obtaining all local quantities of interest. It considers an expansion of the correlation functions and their equations of motion in powers of the photon tunneling rate between adjacent cavities, leading to an exact second order solution for any number of cavities. Our method provides a controllable approximation for weak tunneling rates applicable to the strongly correlated regime that is dominated by nonlinearities in the cavities and thus of high interest.

arXiv:1304.3659•Journal of Physics B Atomic Molecular and Optical Physics•Nov 7, 2013•8 citations

The Quantum Dynamics of Two Coupled Cavities Containing Pumped Atomic Ensembles

Sergiu Carlig, Viorel Ciornea, Corneliu Gherman +1 more

Abstract We investigate a hybrid quantum system consisting of two coupled optical cavities, each containing an ensemble of coherently pumped artificial or real two-level atoms. The system is modelled within the dressed-state formalism, accounting for coherent driving and dissipative interactions with independent electromagnetic reservoirs. Focusing on the regime where the Rabi frequency greatly exceeds the collective spontaneous emission and cavity decay rates, respectively, we derive the equations of motion characterizing the system and analyse its steady-state behaviours. Special attention is given to the scenario in which only one cavity contains a pumped multi-atom ensemble, and as a consequence, coherent excitation transfer to the second cavity occurs via cavity–cavity coupling. In this case, the mean photon number in the second cavity mode scales proportional to the squared number of atoms, i.e., N2 from the first cavity. The proposed model offers insight into light–matter interaction in composite systems and suggests viable mechanisms for engineering collective interactions and non-local excitation transport in quantum optical platforms.

Physics of the Solid State•Oct 1, 2025•0 citations

Few emitters in a cavity: from cooperative emission to individualization

Alexia Auffèves, Dario Gerace, S. Portolan +2 more

We study the temporal correlations of the field emitted by an electromagnetic resonator coupled to a mesoscopic number of two-level emitters that are incoherently pumped by a weak external drive. We solve the master equation of the system for increasing number of emitters and as a function of the cavity quality factor, and we identify three main regimes characterized by well-distinguished statistical properties of the emitted radiation. For small cavity decay rates, the emission events are uncorrelated and the number of photons in the emitted field becomes larger than one, resembling the build-up of a laser field inside the cavity. At intermediate decay rates (as compared with the emitter–cavity coupling) and for a few emitters, the statistics of the emitted radiation is bunched and strikingly dependent on the parity of the number of emitters. The latter property is related to the cooperativity of the emitters mediated by their coupling to the cavity mode, and its connection with steady-state subradiance is discussed. Finally, in the bad cavity regime the typical situation of emission from a collection of individual emitters is recovered. We also analyze how the cooperative behavior evolves as a function of pure dephasing, which allows us to recover the case of a classical source made of an ensemble of independent emitters, similar to what is obtained for a very leaky cavity. State-of-the-art techniques of Q -switch of resonant cavities, allied with the recent capability of tuning single emitters in and out of resonance, suggest this system to be a versatile source of different quantum states of light.

arXiv:1106.0836•New Journal of Physics•Sep 9, 2011•91 citations
We study an array of dissipative tunnel-coupled cavities, each interacting with an incoherently pumped two-level emitter. For cavities in the lasing regime, we find correlations between the light fields of distant cavities, despite the dissipation and the incoherent nature of the pumping mechanism. These correlations decay faster than any power of the distance for arrays in any dimension but become increasingly long ranged with increasing photon tunneling between adjacent cavities. The interaction-dominated and the tunneling-dominated regimes show markedly different scaling of the correlation length which always remains finite due to the finite photon trapping time. We propose a series of observables to characterize the spontaneous buildup of collective coherence in the system.
We explore theoretically the nonequilibrium photonic phases of an array of coupled cavities in presence of incoherent driving and dissipation. In particular, we consider a Hubbard model system where each site is a Kerr nonlinear resonator coupled to a two-level emitter, which is pumped incoherently. Within a Gutzwiller mean-field approach, we determine the steady-state phase diagram of such a system. We find that, at a critical value of the intercavity photon hopping rate, a second-order nonequilibrium phase transition associated with the spontaneous breaking of the U(1)\text{U}(1)U(1) symmetry occurs. The transition from an incompressible Mott-like photon fluid to a coherent delocalized phase is driven by commensurability effects and not by the competition between photon hopping and optical nonlinearity. The essence of the mean-field predictions is corroborated by finite-size simulations obtained with matrix product operators and corner-space renormalization methods.
In recent years, the control of photon-photon interactions in optical nonlinear media has led to the realization of quantum fluids of light. One of the current challenges is to increase the strength of these interactions and enter the so-called strongly correlated regime. To achieve this goal, arrays of nonlinear cavities are a very promising candidate. In this thesis, theoretical results on arrays of nonlinear cavities described by a driven-dissipative Bose-Hubbard model are presented. In particular, a general method to compute the mean-field phase diagram of this model is described. Due to the finite life time of photons, the system is intrinsically dissipative: cavity losses must be compensated by an external driving field. This nonequilibrium nature gives rise to interesting features, such as a transition between monostable and bistable phases induced by tunneling. In the limit of weak dissipation and weak driving, analytical results describing generalized Mott insulating phases are derived. These states survive up to a critical tunneling strength, above which a crossover to a classical coherent state takes place. Finally, the issue of how to go beyond the mean-field approximation is addressed by performing exact numerical simulations. Large arrays of cavities were simulated by implementing a new method specifically tailored for driven-dissipative systems.
We report a theoretical study of coherent collective quantum dynamic effects in an array of NNN qubits (two-level systems) incorporated into a low-dissipation resonant cavity. Individual qubits are characterized by energy level differences ${\ensuremath{\Delta}}_{i}$ and a spread of ${\ensuremath{\Delta}}_{i}$ is taken into account. Noninteracting qubits display coherent quantum beatings with NNN different frequencies, i.e., ${\ensuremath{\omega}}_{i}={\ensuremath{\Delta}}_{i}/\ensuremath{\hbar}$. Virtual emission and absorption of cavity photons provides a long-range interaction between qubits. In the presence of such interaction we analyze quantum correlation functions of individual qubits Ci(t){C}_{i}(t)Ci​(t) to obtain two collective quantum-mechanical coherent oscillations, characterized by frequencies ${\ensuremath{\omega}}_{1}=\overline{\ensuremath{\Delta}}/\ensuremath{\hbar}$ and ${\ensuremath{\omega}}_{2}={\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}_{R}$, where ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}_{R}$ is the resonant frequency of the cavity renormalized by interaction. The amplitude of these oscillations can be strongly enhanced in the resonant case when ${\ensuremath{\omega}}_{1}\ensuremath{\simeq}{\ensuremath{\omega}}_{2}$. These collective quantum oscillations can be directly observed, e.g., by measurements of frequency dependent transmission coefficient $D(\ensuremath{\omega})$ of electromagnetic field propagating in a transmission line coupled to the system.
We introduce a method for calculating the stationary state of a translation invariant array of weakly coupled cavities in the presence of dissipation and coherent as well as incoherent drives. Instead of computing the full density matrix our method directly calculates the correlation functions which are relevant for obtaining all local quantities of interest. It considers an expansion of the correlation functions and their equations of motion in powers of the photon tunneling rate between adjacent cavities, leading to an exact second order solution for any number of cavities. Our method provides a controllable approximation for weak tunneling rates applicable to the strongly correlated regime that is dominated by nonlinearities in the cavities and thus of high interest.
Abstract We investigate a hybrid quantum system consisting of two coupled optical cavities, each containing an ensemble of coherently pumped artificial or real two-level atoms. The system is modelled within the dressed-state formalism, accounting for coherent driving and dissipative interactions with independent electromagnetic reservoirs. Focusing on the regime where the Rabi frequency greatly exceeds the collective spontaneous emission and cavity decay rates, respectively, we derive the equations of motion characterizing the system and analyse its steady-state behaviours. Special attention is given to the scenario in which only one cavity contains a pumped multi-atom ensemble, and as a consequence, coherent excitation transfer to the second cavity occurs via cavity–cavity coupling. In this case, the mean photon number in the second cavity mode scales proportional to the squared number of atoms, i.e., N2 from the first cavity. The proposed model offers insight into light–matter interaction in composite systems and suggests viable mechanisms for engineering collective interactions and non-local excitation transport in quantum optical platforms.
We study the temporal correlations of the field emitted by an electromagnetic resonator coupled to a mesoscopic number of two-level emitters that are incoherently pumped by a weak external drive. We solve the master equation of the system for increasing number of emitters and as a function of the cavity quality factor, and we identify three main regimes characterized by well-distinguished statistical properties of the emitted radiation. For small cavity decay rates, the emission events are uncorrelated and the number of photons in the emitted field becomes larger than one, resembling the build-up of a laser field inside the cavity. At intermediate decay rates (as compared with the emitter–cavity coupling) and for a few emitters, the statistics of the emitted radiation is bunched and strikingly dependent on the parity of the number of emitters. The latter property is related to the cooperativity of the emitters mediated by their coupling to the cavity mode, and its connection with steady-state subradiance is discussed. Finally, in the bad cavity regime the typical situation of emission from a collection of individual emitters is recovered. We also analyze how the cooperative behavior evolves as a function of pure dephasing, which allows us to recover the case of a classical source made of an ensemble of independent emitters, similar to what is obtained for a very leaky cavity. State-of-the-art techniques of Q -switch of resonant cavities, allied with the recent capability of tuning single emitters in and out of resonance, suggest this system to be a versatile source of different quantum states of light.