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arXiv:1909.01619 · Physical Review Research

Nonequilibrium states of a plasmonic Dicke model with coherent and dissipative surface-plasmon–quantum-emitter interactions

Andrei Piryatinski, Oleksiy Roslyak, Hao Li, Eric R. Bittner

Published Feb 10, 2020• 6 citations
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Abstract

This paper presents a theoretical examination of the non-equilibrium phase diagram of quantum emitters in a plasmonic cavity. The authors generalize driven-dissipative Dicke model to account for the coherent and dissipative interactions between the quantum emitters and the surface plasmon cavity mode. Depending on the interaction strength, the normal, superradiant, regular lasing, and lasing without inversion states are identified. Their signatures in the photon emission spectra are demonstrated.

DOI
10.1103/physrevresearch.2.013141

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This paper presents a theoretical examination of the non-equilibrium phase diagram of quantum emitters in a plasmonic cavity. The authors generalize driven-dissipative Dicke model to account for the coherent and dissipative interactions between the quantum emitters and the surface plasmon cavity mode. Depending on the interaction strength, the normal, superradiant, regular lasing, and lasing without inversion states are identified. Their signatures in the photon emission spectra are demonstrated.
We present the non-equilibrium phase diagram of a model which can demonstrate both Dicke–Hepp–Lieb superradiance and regular lasing by varying the coherent and incoherent driving terms We find that the regions in the phase diagram corresponding to superradiance and standard lasing are always separated by a normal region. We analyse the behaviour of the system using a combination of exact numerics based on permutation symmetry of the density matrix for small to intermediate numbers of molecules, and second order cumulant equations for large numbers of molecules. We find that the nature of the photon distribution in the superradiant and lasing states are very similar, but the emission spectrum is very different. We also show that in the presence of both coherent and incoherent driving, a period-doubling route to a chaotic state occurs.
We theoretically study the dissipative dynamics of a quantum emitter placed near the planar surface of a metal supporting surface-plasmon excitations. The emitter-metal coupling regime can be tuned by varying some control parameters such as the qubit-surface separation and/or the detuning between characteristic frequencies. By using a Green's-function approach jointly with a time-convolutionless master equation, we analyze the non-Markovian dissipative features on the qubit time evolution in two cases of interest: (i) an undriven qubit initially prepared in its excited state and (ii) the evolution toward a steady state for a system driven by a laser field. For weak to moderate qubit-metal coupling strength, and on time scales large compared to the surface plasmon oscillation time, a Markovian approximation for the master-equation results to be adequate to describe the qubit main optical properties: surface enhancements of rate emission, optical spectra, and time-dependent photon-photon correlation functions. The qubit decay shows a crossover passing from being purely dissipative for small qubit-surface distances to plasmon emission for larger separations.
We present the non-equilibrium phase diagram of a model which can demonstrate both Dicke-Hepp-Lieb superradiance and regular lasing by varying the coherent and incoherent driving terms We find that the regions in the phase diagram corresponding to superradiance and standard lasing are always separated by a normal region. We analyse the behaviour of the system using a combination of exact numerics based on permutation symmetry of the density matrix for small to intermediate numbers of molecules, and second order cumulant equations for large numbers of molecules. We find that the nature of the photon distribution in the superradiant and lasing states are very similar, but the emission spectrum is very different. We also show that in the presence of both coherent and incoherent driving, a period-doubling route to a chaotic state occurs.
Control and manipulation of quantum engineered systems allows for the utilization of time-dependent parametric modulations for accessing novel out-of-equilibrium phenomena. In the absence of such driving, the dissipative Dicke model exhibits a fascinating out-of-equilibrium many-body phase transition as a function of a coupling between a driven photonic cavity and numerous two-level atoms. We study the effect of a parametric modulation of this coupling and discover a rich phase diagram as a function of the modulation strength. We find that in addition to the established normal and super-radiant phases, a new phase with pulsed superradiance, which we term dynamical normal phase, appears when the system is parametrically driven. Employing different methods, we characterize the different phases and the transitions between them. Specific heed is paid to the role of dissipation in determining the phase boundaries. Our analysis paves the road for the experimental study of dynamically stabilized phases of interacting light and matter.
We present the non-equilibrium phase diagram of a model which can demonstrate both Dicke--Hepp--Lieb superradiance and regular lasing by varying the coherent and incoherent driving terms. We find that the regions in the phase diagram corresponding to superradiance and standard lasing are always separated by a normal region. We analyse the behaviour of the system using a combination of exact numerics based on permutation symmetry of the density matrix for small to intermediate numbers of molecules, and second order cumulant equations for large numbers of molecules. We find that the nature of the photon distribution in the superradiant and lasing states are very similar, but the emission spectrum is very different. We also show that in the presence of both coherent and incoherent driving, a period-doubling route to a chaotic state occurs.
We develop a theory of cooperative emission of light by an ensemble of emitters, such as fluorescing molecules or semiconductor quantum dots, located near a metal nanostructure supporting surface plasmon. The primary mechanism of cooperative emission in such systems is resonant energy transfer between emitters and plasmons rather than the Dicke radiative coupling between emitters. We identify two types of plasmonic coupling between the emitters, (i) plasmon-enhanced radiative coupling and (ii) plasmon-assisted nonradiative energy transfer, the competition between them governing the structure of system eigenstates. Specifically, when emitters are removed by more than several nanometers from the metal surface, the emission is dominated by three superradiant states with the same quantum yield as a single emitter, resulting in a drastic reduction of ensemble radiated energy, while at smaller distances cooperative behavior is destroyed by nonradiative transitions. The crossover between two regimes can be observed in distance dependence of ensemble quantum efficiency. Our numerical calculations incorporating direct and plasmon-assisted interactions between the emitters indicate that they do not destroy the plasmonic Dicke effect.