  SU(1,1) interferometer (SUI) is a novel type of interferometer that uses
directly entangled quantum fields for sensing phase change. For rotational
sensing, Sagnac geometry is usually adopted. However, because SUI depends on
the phase sum of the two arms, traditional Sagnac geometry, when applied to
SUI, will result in null signal. In this paper, we modify the traditional
Sagnac interferometer by nesting SU(1,1) interferometers inside. We show that
the rotational signal comes from two parts labeled as "classical" and
"quantum", respectively, and the quantum part, where quantum entangled fields
are used for sensing, has rotational signal enhanced by a factor related to the
gain of the SUI.
