All of coincidence

Sometimes, I feel lots of things happened on me are of coincidence. In the today’s team building, we got to LONG QING XIA to have a short traveling. This is the second time for me to tranvel here. Four years before I tranvelled here with the previous colleagues. And the almost same time I got to the same place again. However, I changed a lot, including my life and my work. I became more mature and social. It exactly is a coincidence for me. And it gives more stuffs to my life and experience. And I hope the tranvelling will be a good beginning here for me.

Entangled photon pairs in the path degree-of-freedom (DoF) are generated using two identical high-quality-factor (high-Q) microring resonators. Each microring facilitates spontaneous four wave mixing (SFWM) for the photon pair generation. Owing to cavity enhancement, the generated photon pairs exhibit high brightness and coincidence-to-accident ratio (CAR). Through thermal annealing and optimized ICP-RIE etching, microrings with quality factors exceeding 1 million can be reliably fabricated (Fig. S2A). The high-Q here not only enhances nonlinear SFWM, but also reduces the pump power required to achieve adequate source brightness. Additional improvements in fabrication, such as adopting higher thermal annealing temperature or incorporating chemicalmechanical polishing (CMP) on top surface, can further increase the quality factor. Efficient SFWM requires satisfying both momentum and energy conservation conditions: 2𝑘𝑘𝑝𝑝 = 𝑘𝑘𝑠𝑠 + 𝑘𝑘𝑖𝑖 (S1a) 3 2𝜔𝜔𝑝𝑝 = 𝜔𝜔𝑠𝑠 + 𝜔𝜔𝑖𝑖 (S1b) Here, the subscripts 𝑝𝑝, 𝑠𝑠, 𝑖𝑖 correspond to the pump, signal, idler photons, respectively; 𝑘𝑘 denotes the wavevector of the whispering-gallery-mode (WGM), and 𝜔𝜔 is the angular frequency of the whispering gallery mode (WGM) in the microring. Due to the discrete nature of WGM modes in a microring, momentum conservation can be easily satisfied when: 𝑚𝑚𝑝𝑝 − 𝑚𝑚𝑠𝑠 = 𝑚𝑚𝑖𝑖 − 𝑚𝑚𝑝𝑝 = Δ𝑚𝑚 (S2) where 𝑚𝑚 denotes the WGM mode order. However, the nonlinear dispersion of optical modes in microrings imposes constraints on energy conservation, which can only be met if the frequency mismatch fulfills (28): 𝛿𝛿𝛿𝛿= 􀸫2𝜔𝜔𝑝𝑝 − 𝜔𝜔𝑠𝑠 − 𝜔𝜔𝑖𝑖􀸫 ≤ 𝜔𝜔𝑝𝑝 𝑄𝑄 (S3) Eq. S3 emphasizes the need to maintain frequency mismatch within the resonance linewidth. Following this criterion, our microring waveguide dimensions are carefully chosen to be 700 nm in height and 1500 nm in width. Fig. S2B displays the simulated 𝛿𝛿𝛿𝛿 = 2𝜋𝜋𝜋𝜋𝜋𝜋 as a function of 𝑑𝑑𝑑𝑑= 𝑓𝑓𝑠𝑠 − 𝑓𝑓𝑝𝑝 = 𝑓𝑓𝑝𝑝 − 𝑓𝑓𝑖𝑖, assuming a pump wavelength at 1550 nm. The red dashed line depicts the 𝑓𝑓𝑝𝑝/2𝑄𝑄 limit, representing a 3 dB bandwidth condition. Based on these simulations, we conclude that our source has a 3 dB photon pair bandwidth of approximately 13 THz centered at 1550 nm. Apart from the careful design of the waveguide dimension, the microring radius was also carefully chosen. Experimentally, to align fabricated microring resonances with commercial wavelength-division multiplexing (WDM) systems, the ring radius is specifically designed to be 113 μm. This radius ensures that resonance frequencies match the International Telecommunication Union (ITU) dense WDM (DWDM) frequency grids, featuring a
09-13
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