Generation of time-frequency entangled photon pairs propagating in separate waveguides in circuit QED setup

Time-frequency entangled photons constitute an important resource for a plethora of applications across the diverse quantum technology landscape. Thus, efficient and tunable setups generation are requisite modern technologies. In this work, we propose generic cavity QED setup designed on-demand time-frequency photon pairs, with each propagating in separate waveguide. We outline potential incarnation microwave superconducting circuit architecture. derive numerically solve set equations motion governing evolution state system, allowing us to examine emission dynamics. Using Schmidt decomposition joint spectral amplitude emitted pair, compute entanglement entropy analyzing its dependence on system parameters. extension proposed scheme multiphoton states.