The control of interactions among quantum emitters through nanophotonic structures offers significant opportunities for quantum technologies. However, a rigorous theoretical description of the interaction of multiple quantum emitters with complex, dispersive dielectric objects remains challenging. Here, we introduce an approach based on the modified Langevin noise formalism that unveils the roles of both the noise polarization currents of the dielectrics and the vacuum fluctuations of the electromagnetic field scattered by the dielectrics. This work extends Refs. \cite{miano_quantum_2025} and \cite{miano_spectral_2025} to the general case of an arbitrary number of emitters. The proposed approach allows us to describe the dynamics of the quantum emitters for arbitrary initial quantum states of the electromagnetic environment, consisting of two independent bosonic reservoirs, a medium-assisted reservoir and a scattering-assisted reservoir, each characterized by its own spectral density matrix. Specifically, we examine situations where both reservoirs are initially in thermal quantum states but have different temperatures. Understanding how these reservoirs shape the dynamics of the emitters is crucial for understanding light-matter interactions in complex electromagnetic environments and for improving intrinsic emitter properties within structured environments.
We consider sub- and superradiance of quantum emitters in a solid-state environment. This collective emission depends on the electromagnetic interaction between the emitters that can be engineered via the environment and described by the classical electromagnetic Green function. But also phonons may affect the collective emission. Phonons produce dephasing, both non-exponential fast initial dephasing and slower exponential dephasing. We compared several ways to account for both types of phonon interactions into the more standard optical master equation for an arbitrary number of quantum emitters that mutually interact via the electromagnetic field. In particular we present a concatenation method that incorporates phonon effects without adding computational complexity, suitable for arrays of emitters. Here we use it to study the effects of detunings on two-emitter spectra and on the corresponding population and entanglement dynamics.
Abstract Understanding the photon number statistics of a quantum emitter (QE) interacting with complex photonic environments is fundamental to advances in quantum optics and nanophotonics. We introduce a general theoretical framework for calculating the modal photon number density spectrum (MPNDS) in arbitrary dielectric structures with an embedded two-level QE. We validate our approach by investigating a system composed of a two-level QE and a photonic crystal (PhC) slab with an L3 cavity and a waveguide, finding that the MPNDS exhibits significant changes in both waveguide and background radiative channels as the interaction between the QE and modal field transitions from weak coupling to strong coupling. We observe that the number of photons guided along the waveguide shows a strong dependence on the QE’s transition frequency and transition dipole moment, but demonstrates robustness to the transition dipole moment when the transition frequency approaches the waveguide cutoff frequency. Our work allows for the determination and tailoring of light emission characteristics across diverse radiative channels in complex photonic environments.
Superradiance is a quantum phenomenon in which coherence between emitters results in enhanced and directional radiative emission. Many quantum optical phenomena can be characterized by the two-time quantum correlation function
g(2)(t,τ), which describes the photon statistics of emitted radiation. However, the critical task of determining
g(2)(t,τ) becomes intractable for large emitter ensembles due to the exponential scaling of the Hilbert space dimension with the number of emitters. Here, we analyse and benchmark two approximate numerical sampling methods applicable to emitter arrays embedded within electromagnetic environments, which generally provide upper and lower bounds for
g(2)(t,0). We also introduce corrections to these methods (termed offset corrections) that significantly improve the quality of the predictions. The optimal choice of method depends on the total number of emitters, such that taken together, the two approaches provide accurate descriptions across a broad range of important regimes. This work therefore provides new theoretical tools for studying the well-known yet complex phenomenon of superradiance in large ensembles of quantum emitters.