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We propose an experimentally feasible method for enhancing the atom-fieldcoupling as well as the ratio between this coupling and dissipation (i.e.,cooperativity) of two atoms in an optical cavity. Our method also enables thegeneration of steady-state nearly-maximal quantum entanglement. Our approachexploits optical parametric amplification to exponentially enhance theatom-cavity interaction and, hence, the cooperativity of the system, with thesqueezing-induced fluctuation noise being completely eliminated. Thus, aneffective cooperativity much larger than $100$ can be achieved even for modestvalues of a squeezing parameter. We demonstrate that the entanglementinfidelity (which quantifies the deviation of the generated state from amaximally-entangled state) is exponentially smaller than the lower bound on theinfidelities obtained in other dissipative entanglement preparations withoutapplying squeezing. Thus, this infidelity can be arbitrarily small. Our genericmethod for enhancing atom-cavity cooperativities can be implemented in a widerange of physical systems, and it can provide diverse applications for quantuminformation processing based on entanglement.

Exponentially-Enhanced Light-Matter Interaction, Cooperativities, and Steady-State Entanglement Using Parametric Amplification