Light-matter interaction with a squeezed vacuum has received much interest for the ability to increase the native interaction strength between an atom and a photon with a reservoir assumed to have an infinite bandwidth. Here we study a model of parametrically driven cavity quantum electrodynamics (QED) for enhancing light-matter interaction while subjected to a finite-bandwidth squeezed vacuum drive. Our method is capable of unveiling the effect of relative bandwidth as well as squeezing required to observe the anticipated anticrossing spectrum and enhanced cooperativity without the ideal squeezed bath assumption. Furthermore, we analyze the practicality of said models when including intrinsic photon loss due to resonator imperfection. With these results, we outline the requirements for experimentally implementing an effectively squeezed bath in solid-state platforms such as $\mathrm{In}\mathrm{As}$ quantum dot cavity QED such that in situ control and enhancement of light-matter interaction could be realized.

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• Cavity quantum electrodynamics
• Light-matter interaction
• Nonlinear optics
• Photonics
• Quantum information with solid state qubits
• Squeezing of quantum noise
• Optical parametric oscillators & amplifiers
• Jaynes-Cummings model