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Physical Review A

Collective dissipation of oscillator dipoles strongly coupled to one-dimensional electromagnetic reservoirs

Shekhar Guha, I. Bar, Bijay Kumar Agarwalla, B. Prasanna Venkatesh

Published Sep 16, 2025• 2 citations
Publisher

Abstract

We study the collective dissipative dynamics of dipoles modeled as harmonic oscillators coupled to one-dimensional electromagnetic reservoirs. The bosonic nature of the dipole oscillators as well as the reservoir modes allows an exact numerical simulation of the dynamics for arbitrary coupling strengths. At weak coupling, apart from essentially recovering the dynamics expected from a Markovian Lindblad master equation, we also obtain non-Markovian effects for spatially separated two-level emitters. In the so-called ultrastrong coupling regime, we find the dynamics and steady state depends on the choice of the reservoir which is chosen as either an ideal cavity with equispaced, unbounded dispersion or a cavity array with a bounded dispersion. Moreover, at even higher coupling strengths, we find a decoupling between the light and matter degrees of freedom attributable to the increased importance of the diamagnetic term in the Hamiltonian. In this regime we find that the dependence of the dynamics on the separation between the dipoles is not important and the dynamics is dominated by the occupation of the polariton mode of lowest energy.

DOI
10.1103/dnnn-5b5p

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We study the collective dissipative dynamics of dipoles modeled as harmonic oscillators coupled to one-dimensional electromagnetic reservoirs. The bosonic nature of the dipole oscillators as well as the reservoir modes allows an exact numerical simulation of the dynamics for arbitrary coupling strengths. At weak coupling, apart from essentially recovering the dynamics expected from a Markovian Lindblad master equation, we also obtain non-Markovian effects for spatially separated two-level emitters. In the so-called ultrastrong coupling regime, we find the dynamics and steady state depends on the choice of the reservoir which is chosen as either an ideal cavity with equispaced, unbounded dispersion or a cavity array with a bounded dispersion. Moreover, at even higher coupling strengths, we find a decoupling between the light and matter degrees of freedom attributable to the increased importance of the diamagnetic term in the Hamiltonian. In this regime we find that the dependence of the dynamics on the separation between the dipoles is not important and the dynamics is dominated by the occupation of the polariton mode of lowest energy.
We study the collective dissipative dynamics of dipoles modeled as harmonic oscillators coupled to 1-D electromagnetic reservoirs. The bosonic nature of the dipole oscillators as well as the reservoir modes allows an exact numerical simulation of the dynamics for arbitrary coupling strengths. At weak coupling, apart from essentially recovering the dynamics expected from a Markovian Lindblad master equation, we also obtain non-Markovian effects for spatially separated two-level emitters. In the so called ultrastrong coupling regime, we find the dynamics and steady state depends on the choice of the reservoir which is chosen as either an ideal cavity with equispaced, unbounded dispersion or a cavity array with a bounded dispersion. Moreover, at even higher coupling strengths, we find a decoupling between the light and matter degrees of freedom attributable to the increased importance of the diamagnetic term in the Hamiltonian. In this regime, we find that the dependence of the dynamics on the separation between the dipoles is not important and the dynamics is dominated by the occupation of the polariton mode of lowest energy.
Phenomenological approaches to photon loss have long been the workhorse of cavity-QED, but prove inadequate in the presence of sufficiently broadband light-matter interactions. We present a rigorous and ab initio derivation of a quantum master equation for a quantized optical cavity mode coupled to a dipole, using a quasinormal mode (QNM) quantization procedure for plasmonic and dielectric open-system cavity-QED, which is valid in broadband light-matter interaction regimes, including ultrastrong coupling (USC). The theory supports general three-dimensional resonators with arbitrary dispersion and loss, and thus can be applied to a wide range of realistic open cavities. Our ab initio and gauge-invariant approach fully recovers a recent result for the spectral density of a quantized cavity with a single dipole and reveals important departures from previous heuristic assumptions about system-reservoir coupling. We identify a new criterion for what we term the "broadband dissipative" regime of cavity-QED, where phenomenological models require corrections in accordance with the intrinsic and spatially-dependent complex phase of the QNM, and also shed light on fundamental limits to single-mode models in extreme coupling regimes. Using experimentally motivated plasmonic and dielectric cavity examples, we show validity ranges of our QNM master equation and spectral USC calculations, and discuss prospects for near-term experimental observation of the broadband dissipative effects.
In this article we extend the results presented in Ref. [Phys. Rev. A 76, 032101 (2007)] to treat quantitatively the effects of reservoirs at finite temperature in a bosonic dissipative network: a chain of coupled harmonic oscillators whichever its topology, i.e., whichever the way the oscillators are coupled together, the strength of their couplings and their natural frequencies. Starting with the case where distinct reservoirs are considered, each one coupled to a corresponding oscillator, we also analyze the case where a common reservoir is assigned to the whole network. Master equations are derived for both situations and both regimes of weak and strong coupling strengths between the network oscillators. Solutions of these master equations are presented through the normal ordered characteristic function. We also present a technique to estimate the decoherence time of network states by computing separately the effects of diffusion and the attenuation of the interference terms of the Wigner function. A detailed analysis of the diffusion mechanism is also presented through the evolution of the Wigner function. The interesting collective diffusion effects are discussed and applied to the analysis of decoherence of a class of network states. Finally, the entropy and the entanglement of a pure bipartite system are discussed.
We have investigated theoretically a dissipative polariton system in the ultrastrong light-matter coupling regime without using the rotating-wave approximation on system-reservoir coupling. Photons in a cavity and excitations in matter respectively couple two large ensembles of harmonic oscillators (photonic and excitonic reservoirs). Inheriting the quantum statistics of polaritons in the ultrastrong coupling regime, in the ground state of the whole system, the two reservoirs are not in the vacuum states but they are squeezed and correlated. We presume the reservoirs to be in this nonvacuum state in the master equation and in the input-output formalism with Langevin equations. Both approaches consistently guarantee the decay of the polariton system to its ground state; no photon detection is also obtained when the polariton system is in the ground state.
We investigate how to model Markovian evolution of coupled harmonic oscillators, each of them interacting with a local environment. When the coupling between the oscillators is weak, dissipation may be modeled using local Lindblad terms for each of the oscillators in the master equation, as is commonly done. When the coupling between oscillators is strong, this model may become invalid. We derive a master equation for two coupled harmonic oscillators that are subject to individual heat baths modeled by a collection of harmonic oscillators and show that this master equation in general contains nonlocal Lindblad terms. We compare the resulting time evolution with that obtained for dissipation through local Lindblad terms for each individual oscillator and show that the evolution is different in the two cases. In particular, the two descriptions give different predictions for the steady state and for the entanglement between strongly coupled oscillators. This shows that when describing strongly coupled harmonic oscillators, one must take great care in how dissipation is modeled and that a description using local Lindblad terms may fail. This may be particularly relevant when attempting to generate entangled states of strongly coupled quantum systems.
We investigate the dynamical properties of the finite-size Dicke model coupled to a photon reservoir in the dispersive regime. The system-reservoir coupling in our Hamiltonian includes counter-rotating terms, which are relevant in the strong atom-cavity coupling. Because the dispersive regime is considered, the dynamics of low-energy states are described sufficiently accurately within the finite-dimensional subspace of the dressed states. Using the separation of the time scales between the system and the reservoir, we derive the Markovian quantum master equation in the subspace without ignoring the counter-rotating terms. The temporal evolution of the expectation of the cavity mode shows that the bifurcation of the long-lived state corresponds to the superradiant transition in the isolated model. The master equation explicitly gives the steady state solution. The numerical results for the first-order correlation function on the steady state indicate that the strong atom-cavity coupling enhances the coherence and softens the dephasing in the superradiant region.