Quantum-Plasmonic Dynamics Modeled via a Modified Langevin Noise Formalism: Numerical Studies of Single-Photon Emission and Two-Photon Interference

TL;DR

This work develops and validates a first-principles framework for quantum plasmonics in open, dissipative environments by combining the modified Langevin-noise (M--LN) formalism with boundary-assisted (BA) and medium-assisted (MA) field modes. It demonstrates two key quantum-plasmonic phenomena: (i) two-photon interference on a plasmonic beam splitter, where Hong–Ou–Mandel-type behavior is shown to be computable from classical time-domain EM simulations through BA-mode envelopes, and (ii) non-Markovian atom–plasmon dynamics with directional control of out-coupled single photons, realized via a computationally efficient multimode Jaynes–Cummings (MMJC) model that integrates BA–MA coupling without explicitly sampling the full continuum. The paper also introduces an efficient reduced description using a frequency-resolved variable $E_{\omega}(t)$ tied to the imaginary part of the Green’s function, enabling scalable simulations in realistic plasmonic geometries and validation against spectral-function approaches. Collectively, the results offer a rigorous, scalable tool for designing on-chip quantum plasmonic devices—ranging from single-photon sources to beam splitters and directional emitters—in open, lossy environments, with broad applicability to photonic integrated circuits and cavity QED problems.

Abstract

Recent studies have established and rigorously validated a modified Langevin noise formalism that enables first-principles quantization of electromagnetic fields in open and dissipative environments [1,2,3]. Building on this foundation, a fully quantum-mechanical multimode Jaynes-Cummings framework has been developed and verified, providing an accurate description of atom--field interactions in lossy and radiative systems [4]. In this work, we explore the potential of this formalism for nanophotonic applications by modeling representative quantum-plasmonic dynamics. In particular, we present detailed numerical examples for (i) two-photon interference mediated by a quantum plasmonic beam splitter, and (ii) non-Markovian dynamics of an atom located in plasmonic antennas and directional control of out-coupled single-photon fields. These results demonstrate that the proposed modeling approach can be directly used to guide the design and optimization of plasmonic single-photon sources and beam-splitting structures. Moreover, the framework is broadly applicable to the analysis of linear optical components and cavity quantum electrodynamics problems in open and dissipative photonic integrated circuits.

Figures (9)

• Figure 1: The new Langevin noise formalism Drezet2017quantizingStefano2001Modena2023numerical employ two different fields for the quantization of open and dissipative EM systems : (i) boundary-assisted (BA) and (ii) medium-assisted (MA) fields to balance the radiation and medium losses. Monochromatic BA and MA fields form the infinite degeneracy in terms of ($\mathbf{k}\in S_{k}$, $s\in\left\{H,V\right\}$) and ($\mathbf{r}'\in V_{m},\xi\in\left\{x,y,z\right\}$), respectively.
• Figure 2: A plasmonic platform for observing quantum plasmonic Hong--Ou--Mandel effects. The inset SEM image (right) of the photon-to-surface-plasmon-polariton launcher was reproduced from Dheur2016Single. The black dashed contour indicates the "homomorphic" two-dimensional platform used in our simulations.
• Figure 3: Numerical simulation scenario for observing the quantum plasmonic Hong--Ou--Mandel effect in two dimensions.
• Figure 4: Single-photon detection probability at successive time instants $t=t_0,t_1,t_2,t_3,t_4$ in the presence of the plasmonic beam splitter. The sequence shows photon-to-SPP conversion, SPP propagation and interference, and reconversion into out-coupled photons.
• Figure 5: Second-order correlation versus delay $\tau$ for three cases: (i) plasmonic BS with coincidence of out-coupled fields; (ii) plasmonic BS with coincidence of SPP fields; (iii) absence of the BS with coincidence of out-coupled fields.