Macroscopic quantum entanglement between an optomechanical cavity and a continuous field

Probing quantum entanglement with macroscopic objects allows us to test quantum mechanics in new regimes. One way to realize such behavior is to couple a macroscopic mechanical oscillator to a continuous field through an optical cavity. In view of this, our system comprises an optomechanical cavity driven by a coherent optical field in the non-sideband-resolved regime where we assume Gaussian initial states for each degree of freedom. We develop a framework to quantify the amount of entanglement in the system numerically. Different from previous work, we take into account both the continuous optical field and the cavity mode. In order to apply our framework to real experimental data, we use the noise curves of the Laser Interferometer Gravitational-Wave Observatory (LIGO). Furthermore, we discuss the parameter regimes where entanglement exists, even in the presence of quantum and classical noises. Lastly, we compute the maximally entangled mode as a reference for future experiments.