  The quantum states of light in an integrated photonics platform provide an
important resource for quantum information processing and takes advantage of
the scalability and practicality of silicon photonics. Integrated resonators
have been well explored in classical and quantum optics. However, to encode
multiple information through integrated quantum optics requires broader
utilization of the available degrees of freedom on a chip. Here, we studied the
quantum interference between photon pairs of the same higher order whispering
gallery modes populated by spontaneous four-wave mixing in an integrated
silicon micro-disk resonator. The quantum interference between the photon pairs
of the first two quasi-TE0 and quasi-TE1 radial modes was measured to be Vnet ~
98 + 0.8 % and Vnet ~ 94 + 2.6 %, respectively. The results are promising for
achieving higher-dimensional quantum states using the higher-order radial modes
of a micro-disk resonator coupled with an integrated waveguide.
