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.