Hong-Ou-Mandel interference of entangled photons generated under pump-tight-focusing condition

Hong-Ou-Mandel (HOM) interference is a non-classical effect of photons and plays an important role in quantum optics. The beta-barium borate (BBO) has a high nonlinear efficiency, and is commonly used to generate biphoton states, thereby exhibiting HOM interference. However, in previous experiments, researchers often used band-pass filters, so the resulting spectrum was directly determined by the band-pass filter. As a result, the original spectrum of the BBO crystal, especially the spectrum under tight focusing, was lack of systematic research. In this paper, the biphoton spectral distribution and HOM interference generated by the BBO crystal under the condition of tight focusing are systematically studied for the first time. Theoretical calculations show that using a lens with 50-mm focusing length, the spectral width of the down-converted photons is increased by 7.9 times that of the non-focused case; the width of the HOM interference fringe is reduced to 1/8, and the visibility of the interference fringe increases from 53.0% to 98.7%. We experimentally prepare the energy-time entanglement state by using type-II BBO crystal and perform HOM interference, thereby obtaining the interference visibility of (86.6 +/- 1.0) %. The increasing of the HOM visibility is due to the improvement of biphoton's spectral symmetry. In addition, the proposed technique by which different spectral distributions are obtained at different incident angles is expected to be applied to the preparation of high-dimensional qudits in the future.