The gravitational redshift effect of quantum matter waves passing a binary black hole

We simulate the gravitational redshift of quantum matter waves with a long de Broglie wavelength by tracing particle beams along geodesics, when they propagate within the rotation plane of binary black holes. The angular momentum of the binary black hole causes an asymmetric gravitational redshift distribution around the two black holes. The gravitational redshift changes the frequency of quantum matter waves and their wavelength, resulting in the different interference patterns of quantum matter waves with respect to different wavelengths. The interference pattern demonstrates strong contrast intensity and spatial order with respect to different wavelengths and the rotational angle of the binary black hole. A bright semicircular arc emerges from the interference pattern to bridge the two black holes, when they rotate to certain angles, which provides a theoretical understanding on the gravitational lensing effect of quantum matter waves.