## 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, o , as opposed to the -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).

Original language | English (US) |
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Article number | 175001 |

Journal | Nanotechnology |

Volume | 34 |

Issue number | 17 |

DOIs | |

State | Published - Apr 23 2023 |

Externally published | Yes |

## Keywords

- cavity polaritons
- correlated photons
- lasing phase transition
- nano-plasmonic cavity
- parametric down-conversion

## ASJC Scopus subject areas

- Bioengineering
- Chemistry(all)
- Materials Science(all)
- Mechanics of Materials
- Mechanical Engineering
- Electrical and Electronic Engineering