Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Polaritons confined in dielectric structures

Amir Rahmani, Dogyun Ko, Maciej Dems, Andrzej Opala, Michał Matuszewski

TL;DR

This work develops a general, parameter-free framework to construct quantum models of polaritons in arbitrarily structured dielectrics. By solving the classical Maxwell–matter problem and applying Bogoliubov transformations for the conservative case, and third quantization for the dissipative case, it yields diagonal polariton bases in which both Hamiltonian and Liouvillian dynamics are simple and mode-separable. The approach provides a direct quantum–classical correspondence, avoids fitting parameters, and enables engineering of strong, nonlocal polariton interactions and nonclassical light generation in tailored nanostructures. The methods hold broad potential for quantum simulations and optimized polaritonic devices beyond the Hopfield paradigm.

Abstract

Light-matter interaction in the regime of strong quantum coupling is usually treated within the framework of the Hopfield model. However, the picture of coupling well-defined modes of light and matter is correct only as long as the shapes of these eigenmodes are not substantially modified by the interaction. Moreover, parameters of theoretical models are usually obtained by fitting to experimental data. To date, there has been no straightforward method to determine a quantum master equation corresponding to a system with specific dielectric structure, which may lead to incompatibility of theoretical descriptions and physical realizations. We present a recipe for obtaining a quantum model in the polariton eigenmode basis based on Bogoliubov transformation in the conservative case and third quantization technique in the dissipative case. We show how this method can be used for boosting interaction strength and engineering nonlocal many-body interactions in carefully designed nanostructures, resulting in strongly nonclassical correlations of emitted light.

Polaritons confined in dielectric structures

TL;DR

This work develops a general, parameter-free framework to construct quantum models of polaritons in arbitrarily structured dielectrics. By solving the classical Maxwell–matter problem and applying Bogoliubov transformations for the conservative case, and third quantization for the dissipative case, it yields diagonal polariton bases in which both Hamiltonian and Liouvillian dynamics are simple and mode-separable. The approach provides a direct quantum–classical correspondence, avoids fitting parameters, and enables engineering of strong, nonlocal polariton interactions and nonclassical light generation in tailored nanostructures. The methods hold broad potential for quantum simulations and optimized polaritonic devices beyond the Hopfield paradigm.

Abstract

Light-matter interaction in the regime of strong quantum coupling is usually treated within the framework of the Hopfield model. However, the picture of coupling well-defined modes of light and matter is correct only as long as the shapes of these eigenmodes are not substantially modified by the interaction. Moreover, parameters of theoretical models are usually obtained by fitting to experimental data. To date, there has been no straightforward method to determine a quantum master equation corresponding to a system with specific dielectric structure, which may lead to incompatibility of theoretical descriptions and physical realizations. We present a recipe for obtaining a quantum model in the polariton eigenmode basis based on Bogoliubov transformation in the conservative case and third quantization technique in the dissipative case. We show how this method can be used for boosting interaction strength and engineering nonlocal many-body interactions in carefully designed nanostructures, resulting in strongly nonclassical correlations of emitted light.
Paper Structure (18 sections, 42 equations, 3 figures)

This paper contains 18 sections, 42 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Conservative system
  3. Classical regime
  4. Quantization
  5. Diagonalization in polariton modes
  6. Quantum-classical correspondence
  7. Dissipative system
  8. Third quantization treatment
  9. Coherent states of dissipative modes
  10. Quantum-classical correspondence
  11. Lindbladian form of master equation
  12. Summary
  13. Applications
  14. Interactions
  15. Quantum fluctuations
  16. ...and 3 more sections

Figures (3)

  • Figure 1: Scheme of a microcavity structure with two dielectric Bragg mirrors (DBR) confining a photon mode. The cavity incorporates an active quantum well (QW) region hosting excitons. The cavity structure is assumed to extend indefinitely in the cavity plane, while the active region is constricted to a finite volume.
  • Figure 2: (a) Proposed vertical microcavity structure with exciton-only confinement. Blue area corresponds to InGaAs active layer with excitons resonant with the optical mode, and pink area is the Al$_{0.95}$Ga$_{0.05}$As layer with no resonant exciton transition. (b) Light intensity in the lowest energy polariton mode for the structure shown in panel (a). (c) Calculated polariton interaction U (blue triangles), loss rate $\gamma$ (red circles) and light-matter interaction strength $\Omega_{eff}$ (green squares) with varying lateral size of the active exciton volume marked in blue in panel (a). Lines are guides to the eye. (d) Proposed structure with active two-dimensional MoS$_2$ flake marked as in panel (a). (e) Lowest energy polariton mode calculated for the structure shown in (d). (f) An AlGaAs polariton waveguide structure with standing-wave polariton mode pinned to an active exciton region.
  • Figure 3: (a) Structure similar to that in Fig. \ref{['fig:confinement']} but designed for the realization of nonlocal interaction between two polariton modes. Inset shows amplitude cross-sections of symmetric and antisymmetric modes together with the schematic double well potential resulting from refractive index distribution. (b) Light intensity in the lowest symmetric polariton mode. (c) Second-order equal-time same-site correlation functions $g_{11}^{(2)}(0)=g_{22}^{(2)}(0)$ as a function of detuning in the case of resonant pumping with detuning $\delta$. (d) Cross-site correlation function $g_{12}^{(2)}(0)$ as a function of of detuning (solid line) compared to the case when cross-mode interaction $U_{12}$ is artificially set to zero (dashed line), demonstrating the effect of nonlocal interactions. Shaded area shows the region of the violation of the Cauchy-Schwartz inequality. Calculated parameters of the master equation are $\gamma=9.5 \mu$eV, $J = 47 \,\mu$eV, $U_{11} =U_{22} = 171 \,\mu$eV, and $U_{12} = 0.11 \,U_{11}$.