  We report the development of a superconducting acousto-optic phase modulator
fabricated on a lithium niobate substrate. A titanium-diffused optical
waveguide is placed in a surface acoustic wave resonator, where the electrodes
for mirrors and an interdigitated transducer are made of a superconducting
niobium titanium nitride thin film. The device performance is evaluated as a
substitute for the current electro-optic modulators, with the same fiber
coupling scheme and comparable device size. Operating the device at a cryogenic
temperature (T=8K), we observe the length-half-wave-voltage (length-$V_\pi$)
product of 1.78 V$\cdot$cm. Numerical simulation is conducted to reproduce and
extrapolate the performance of the device. An optical cavity with mirror
coating on the input/output facets of the optical waveguide is tested for
further enhancement of the modulation efficiency. A simple extension of the
current device is estimated to achieve an efficient modulation with $V_\pi=$
0.27 V.
