Degenerate parametric down-conversion facilitated by exciton-plasmon polariton states in a nonlinear plasmonic cavity
Abstract
We study the effect of degenerate parametric down-conversion (DPDC) in an ensemble of two-level quantum emitters (QEs) coupled via near-field interactions to a single surface plasmon (SP) mode of a nonlinear plasmonic cavity. For this purpose, we develop a quantum driven-dissipative model capturing non-equilibrium dynamics of the system in which incoherently pumped QEs have transition frequency tuned near the second-harmonic response of the SPs. Considering the strong coupling regime, i.e. the SP-QE interaction rate exceeds system dissipation rates, we find a critical SP-QE coupling attributed to the phase transition between normal and lasing steady states. Examining fluctuations above the system's steady states, we predict new elementary excitations, namely, the exciton-plasmon polaritons formed by the two-SP quanta and single-exciton states of QEs. The contribution of two-SP quanta results in the linear scaling of the SP-QE interaction rate with the number of QEs, ${{ \mathcal N }}_{o}$ , as opposed to the $\sqrt{{{ \mathcal N }}_{o}}$ -scaling known for the Dicke and Tavis-Cummings models. We further examine how SP-QE interaction scaling affects the polariton dispersions and power spectra in the vicinity of the critical coupling. For this purpose, we compare the calculation results assuming a finite ensemble of QEs and the model thermodynamic limit. The calculated power spectra predict an interplay of coherent photon emission by QEs near the second-harmonic frequency and correlated photon-pair emission at the fundamental frequency by the SPs (i.e. the photonic DPDC effect).
- Publication:
-
Nanotechnology
- Pub Date:
- April 2023
- DOI:
- 10.1088/1361-6528/acb5a8
- arXiv:
- arXiv:2208.03929
- Bibcode:
- 2023Nanot..34q5001P
- Keywords:
-
- parametric down-conversion;
- nano-plasmonic cavity;
- lasing phase transition;
- cavity polaritons;
- correlated photons;
- Physics - Optics;
- Quantum Physics
- E-Print:
- 8 pages, 3 figures