Quantum entanglement and Einstein-Podolsky-Rosen steering in ultrastrongly light-matter coupled system

This work presents a scheme for engineering quantum entanglement and Einstein-Podolsky-Rosen (EPR) steering with Gaussian measurements based on the quantum Hopfield model that incorporates a common thermal reservoir. We begin by examining quantum correlations, specifically quantum entanglement and EPR steering, in the ground state. These quantum correlations primarily stem from squeezing interactions in weak and normal strong coupling regimes. As the coupling strength increases, especially upon entering the ultrastrong coupling regime, the correlations emerge from the combined effect of squeezing and mix-mode interactions. Importantly, this scenario enables the realization of two-way EPR steering. Moreover, lower optical frequencies enhance both quantum entanglement and EPR steering. Further, when considering thermal effects, the ultrastrong and deep strong coupling regimes, paired with lower optical frequencies, lead to improved entanglement. The one-way EPR steering for resonant case can be effectively controlled in the ultrastrong and deep strong coupling regimes which originates from the asymmetry of subsystem and reservoir coupling induced by the diamagnetic term. Additionally, one-way EPR steering can also be produced for nonresonant case. In this case, the asymmetry of the subsystem and reservoir originates from the combined effect of nonresonant frequencies and diamagnetic term. Our findings have the potential to inspire further research into quantum information processing that leverages light-matter entanglement and EPR steering.