The supplementary materials for the article "Quantum entanglement and interference at 3 μm" by Zheng Ge et al. provide detailed information on the experimental setup and methods used in the study. The half-wave plate (HWP) is placed on a rotating translation stage, with its fast axis aligned parallel to the vibrational direction of the ordinary photons. The HWP rotation causes a change in the optical range, which in turn changes the phase of the photons. The phase modulation is calculated using the refractive indices of the signal and idle photons, and the total phase difference introduced by the interferometer is expressed mathematically. The article also explains the calculation of the Coincidence Analysis Ratio (CAR) and the interference visibility for both homodyne (HOM) and time-energy entangled states. The bandwidth of the photon pair is determined using a specific equation, and the selection of the coincidence window is discussed to ensure sufficient time resolution and avoid multiphoton recombination events. Additionally, the generation of the mid-infrared (MIR) laser at 3082 nm is described, including the use of a difference frequency generation (DFG) process and the tuning of the lasers to achieve the desired wavelengths. The MIR laser is used to pump the SPDC crystal and measure the second harmonic spectrum, which helps in determining the appropriate central wavelength and temperature for generating degenerate photon pairs.The supplementary materials for the article "Quantum entanglement and interference at 3 μm" by Zheng Ge et al. provide detailed information on the experimental setup and methods used in the study. The half-wave plate (HWP) is placed on a rotating translation stage, with its fast axis aligned parallel to the vibrational direction of the ordinary photons. The HWP rotation causes a change in the optical range, which in turn changes the phase of the photons. The phase modulation is calculated using the refractive indices of the signal and idle photons, and the total phase difference introduced by the interferometer is expressed mathematically. The article also explains the calculation of the Coincidence Analysis Ratio (CAR) and the interference visibility for both homodyne (HOM) and time-energy entangled states. The bandwidth of the photon pair is determined using a specific equation, and the selection of the coincidence window is discussed to ensure sufficient time resolution and avoid multiphoton recombination events. Additionally, the generation of the mid-infrared (MIR) laser at 3082 nm is described, including the use of a difference frequency generation (DFG) process and the tuning of the lasers to achieve the desired wavelengths. The MIR laser is used to pump the SPDC crystal and measure the second harmonic spectrum, which helps in determining the appropriate central wavelength and temperature for generating degenerate photon pairs.