  The interferometer is one of the most important devices for revealing the
nature of light and for precision optical metrology. Though lots of experiments
were performed for probing photons behaviors in various configurations, a
complete study of photons behavior in a birefringent interferometer has not
ever been performed. Based on an environmental turbulence immune Mach-Zehnder
interferometer, tunable photonic beatings by rotating a birefringent crystal
versus the temperature of the crystal for both single-photon and two-photon are
observed. Furthermore, the two-photon interference fringes beat two times
faster than the single-photon interference fringes. This beating effect is used
to determine the thermal dispersion coefficients of the two principal
refractive axes with a single measurement, the two-photon interference shows
super-resolution and high sensitivity. Obvious differences between two-photon
and single photon interference are also revealed in an unbalanced situations.
In addition, influences of the photon bandwidth to the beating behaviors that
come from polarization-dependent decoherence are also investigated. Our
findings will be important for better understanding the behavior of two-photon
interference in a birefringent interferometer and for precision optical
metrology with quantum enhancement.
