The realization of the ultrastrong coupling between Josephson plasma waves (JPWs) and terahertz (THz) photons in the subwavelength microcavity array is of interest for manipulating the THz cavity quantum electrodynamics (cQED), ultrahigh-resolution sensing and imaging, and quantum information processing. Here, we describe the engineering of ultrastrong light-matter interactions in a deeply subwavelength microcavity array based on the hybrid silicon and high-temperature superconductor (HTS) ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ (BSCCO) van der Waals (vdW) heterostructure. We perform numerical modeling and analytical calculation to describe Josephson THz cQED and the ultrastrong coupling process between THz radiation and the JPWs in Josephson medium which is naturally present in BSCCO vdW. The resonance frequency of microcavities is swept through the Josephson plasma frequency by altering their width. THz reflection demonstrates the anticrossing behavior of ultrastrong coupling with a normalized Rabi frequency (coupling strength) $2{\mathrm{\Omega }}_{\mathrm{R}}/f_{\mathrm{c}}=0.29$ for the BSCCO thickness $t=200$ nm, which increases to the value of 0.87 for $t=800$ nm. Furthermore, the thermal behavior of coupling strength shows modulation of Rabi splitting $2{\mathrm{\Omega }}_{\mathrm{R}}$ with temperature. We show that the normalized Rabi splitting $2{\mathrm{\Omega }}_{\mathrm{R}}/f_{\mathrm{c}}$ is independent of the temperature in the BSCCO superconducting regime, while a weak coupling can be observed above the superconducting transition temperature. The proposed chip-scale THz photonic integrated circuit with subwavelength microcavity metamaterial array shall guide the effort in the development of power-efficient coherent THz sources, quantum sensors, ultrasensitive detectors, parametric amplifiers and tunable bolometers based on BSCCO HTS quantum material.

• Received 28 August 2022
• Revised 17 November 2022
• Accepted 21 November 2022

DOI:https://doi.org/10.1103/PhysRevB.106.245140