The observation of hyperradiance accompanied by enhanced entanglement in a hybrid optomechanical system

We have theoretically investigated an optomechanical system and presented the scenario of significantly enhanced bipartite photon–phonon entanglement for two qubits coupled to the single mode of the cavity. The results are compared with the one qubit case for reference. The tripartite atom–photon–phonon interaction is considered as only three-body resonant interaction, while the two-body actions are ignored under some potential approximations. Furthermore, we have studied the phenomenon of hyperradiance in which the well-known Dicke superradiant (N2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N^2$$\end{document} scaling law) can be surpassed due to the inter-atomic correlations. Jointly, a parameter regime is explored to observe the entanglement of photon–phonon pairs and their hyperradiance simultaneously. As it is important to show that the generation of photons and phonons is antibunched, the equal time second-order correlation function g(2)(0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g^{(2)}(0)$$\end{document} is characterized as witness. This system can be realized in Circuit Cavity Quantum Electrodynamics (CCQED) in which the direct coupling of the atom and mechanical resonator is possible.