The Two-time green functions for some two-level system

Nikolay M. Plakida

Megha Gopalakrishna, Y. Pavlyukh, Claudio Verdozzi

Due to their conceptual appeal and computational convenience, two‐level systems (TLSs) and generalizations are used to investigate nonlinear behavior in quantum optics and assess the applicability of theoretical methods. Herein, the focus is on second‐harmonic generation (SHG) and, as system of interest, on the Dicke model, which consists of several TLSs inside an optical cavity. The main aspect addressed is the scope of nonequilibrium Green's function (NEGF) to describe the effect of inhomogeneities and electron–electron (e–e) interactions on the SHG signal. For benchmarking purposes, exact diagonalization (ED) results are also presented and discussed. SHG spectra obtained with NEGF and ED are found to be in very good mutual agreement in most situations. Furthermore, inhomogeneity in the TLS and e–e interactions reduce the SHG signal, and the reduction is stronger with inhomogeneity than with interactions. This trend is consistently noted across different (small to large) system sizes. Finally, a modified NEGF approach is proposed to account for cavity leakage, where the quantum photon fields are coupled to a bath of classical oscillators. As expected, within this mixed quantum‐classical scheme, a decrease in the intensity of the fluorescent spectra takes place depending on the entity of leakage.

Rodney J. Gush, Herbert P. Gush

A general expression is found for the Green's function of a two-level system interacting with a classical monochromatic field of arbitrary frequency and intensity. The Green's function is first used to calculate the transition probability from the lower to the upper state as a function of the frequency and intensity of the field and a comparison of the results is made with experiment. It is then used to study the problem of scattering. It is found that the spectrum of the scattered radiation consists of a line at the frequency of the field (Rayleigh line) and two satellites symmetrically displaced from the Rayleigh line by an amount depending both on the intensity and frequency of the field. In addition there are emissions at three, five, etc., times the frequency of the field, and accompanying satellites. The cross sections for the production of the Rayleigh line and its satellites, and for the third-harmonic line and its satellites have been calculated for a range of values of the frequency and intensity of the incident field.

Hyunwoo Choi, Jisang Seo, Weng C. Chew +1 more

In this work, we present a numerical framework for modeling single photon emission from a two level system in open and dissipative systems beyond the Markovian approximation. The method can be readily integrated into standard computational electromagnetic (CEM) solvers such as finite difference time domain (FDTD) and finite element method (FEM). We numerically verify the completeness of boundary and medium assisted modes in the modified Langevin noise formalism by reconstructing the imaginary part of the dyadic Greens function through modal expansion in three dimensions. This reconstruction enables a first principles description of atom field interaction via the multi mode Jaynes Cummings model in open and dissipative environments. Within the single excitation manifold, we show that the memory kernel of a two level system is determined by the imaginary part of the Greens function, implying that radiative modes alone govern the relevant dynamics. The proposed framework thus provides a Greens function based approach for describing atomic population and single photon dynamics, directly compatible with Maxwell solvers. We then present concrete strategies for implementing our method in both FDTD and FEM frameworks, demonstrating its practical applicability. We further verify numerical results for a lossy Lorentz Drude type mirror, including both the case of a TLS near a finite sized metallic mirror and that of a TLS centered in a Fabry Perot cavity. This work establishes a rigorous foundation for incorporating quantum emitter dynamics into computational electromagnetics, thereby extending classical solvers toward quantum light matter interactions.

Nikolay M. Plakida

Robert van Leeuwen, Nils Erik Dahlen