  Investigation on the relative phase evolution between two bounded optical
solitons is essential for its potential applications in development of larger
telecommunication capacity of optical fiber transmission lines, resolution
improvement in advancing ultrafast characterization approaches and development
of all-optical information storage. Here we characterized relative comb-line
phase jitter power spectral density (PSD) of a soliton molecule pair generated
from a passively mode-locked Er:fiber laser. Through tracking the intensity
difference between two selected wavelengths in one certain spectral
interference fringe, the relative comb-line phase noise PSD is measured by
balanced detection. The estimated measurement resolution is at 10^(-14) rad2/Hz
level and the estimated integrated phase noise from 10 MHz to 100 Hz is 2.04
mrad. The estimated relative linewidth is far below 1 mHz. Comparison between
phase noise PSD and intensity noise PSD indicates that AM-PM conversion plays
an important role in relative phase jitter dynamics between the two solitons.
Our spectral interference fringe tracking technique is attractive for its
simplicity and shows potential in ultra-high resolution in phase noise
measurement, providing an ultra-sensitive alternative approach for relative
phase noise stabilization of optical soliton molecules, between two independent
mode-locked lasers and optical length stabilization of interferometers.
