  We propose an experimentally feasible method for enhancing the atom-field
coupling as well as the ratio between this coupling and dissipation (i.e.,
cooperativity) of two atoms in an optical cavity. Our method also enables the
generation of steady-state nearly-maximal quantum entanglement. Our approach
exploits optical parametric amplification to exponentially enhance the
atom-cavity interaction and, hence, the cooperativity of the system, with the
squeezing-induced fluctuation noise being completely eliminated. Thus, an
effective cooperativity much larger than $100$ can be achieved even for modest
values of a squeezing parameter. We demonstrate that the entanglement
infidelity (which quantifies the deviation of the generated state from a
maximally-entangled state) is exponentially smaller than the lower bound on the
infidelities obtained in other dissipative entanglement preparations without
applying squeezing. Thus, this infidelity can be arbitrarily small. Our generic
method for enhancing atom-cavity cooperativities can be implemented in a wide
range of physical systems, and it can provide diverse applications for quantum
information processing based on entanglement.
