  Using a general Hamiltonian treatment, we theoretically study the generation
of degenerate quadrature squeezing in a dual-pumped integrated microring
resonator coupled to a waveguide. Considering a dual-pump four-wave mixing
configuration in an integrated $\text{Si}_3\text{N}_4$ platform, and following
the coupled-mode theory approach, we investigate the effects of parasitic
quantum nonlinear optical processes on the generation of squeezed light.
Considering five resonance modes in this approach allows us to include the most
important four-wave mixing processes involved in such a configuration. We
theoretically explore the effects of the pump detunings on different nonlinear
processes and show that the effects of some of the parasitic processes are
effectively neutralized by symmetrically detuning the two pumps. This yields a
significant enhancement in the output squeezing quality without physically
changing the structure, but suffers from the trade-off of requiring
substantially higher pump power for a fixed target level of squeezing.
