  We introduce a high performance differential dilatometer based on an
all-fiber Michelson interferometer at cryogenic temperature with $10^{-10}$
resolution in $\delta L/L$. It resolve the linear thermal expansion coefficient
by measuring the oscillating changes of sample thickness and sample temperature
with the interferometer and in-situ thermometer, respectively. By measuring the
linear thermal expansion coefficient $\alpha$ near the antiferromagnetic
transition region of BaFe$_2$As$_2$ as a demonstration, we show our dilatometer
is able to measure thin samples with sub-pm-level length change resolution and
mK-level temperature resolution. Despite there is residual background thermal
expansion of a few nm/K in measurement result, our new dilatometer is sitll a
powerful tool for study of phase transition in condensed matter physics,
especially significant advantages in fragile materials with sub-100$\mu$m
thickness and being integrated with multiple synchronous measurements and
tuning thanks to the extremely high resolution and contactless nature. The
prototype design of this setup can be further improved in many aspects for
specific applications.
