Simultaneous Generation of Quantum Frequency Combs across Distinct Modal Families in a Single $Si_3 N_4$ Whispering Gallery Mode Resonator

Quantum frequency combs (QFCs) are versatile resources for multi-mode entanglement, such as cluster states, crucial for quantum communication and computation. On-chip whispering gallery mode resonators (WGMRs) can generate these states at ultra-low threshold power. This work demonstrates the simultaneous generation of multiple QFCs using a single on-chip silicon nitride WGMR across distinct modal families. It presents a micro-ring resonator with a radius of 240 $\mathrm{μm}$, capable of supporting four modal families within the 130 to 260 $\mathrm{THz}$ frequency range for consistency regulation. The results indicate that, by carefully designing the structure of silicon nitride WGMRs, it is possible to generate quantum entangled frequency combs across distinct modal families simultaneously using monochromatic pump light. It is achieved by modulating the pump mode profiles with a spatial light modulator (SLM) or an on-chip inverse-designed mode converter. This approach offers a simple and low-cost method to achieve higher-density entanglement integration on-chip.