  Ultra-cold atoms provide ideal platforms for interferometry. The macroscopic
matter-wave property of ultra-cold atoms leads to large coherent length and
long coherent time, which enable high accuracy and sensitivity to measurement.
Here, we review our efforts to improve the performance of the interferometer.
We demonstrate a shortcut method for manipulating ultra-cold atoms in an
optical lattice. Compared with traditional ones, this shortcut method can
reduce manipulation time by up to three orders of magnitude. We construct a
matter-wave Ramsey interferometer for trapped motional quantum states and
significantly increase its coherence time by one order of magnitude with an
echo technique based on this method. Efforts have also been made to enhance the
resolution by multimode scheme. Application of a noise-resilient
multi-component interferometer shows that increasing the number of paths could
sharpen the peaks in the time-domain interference fringes, which leads to a
resolution nearly twice compared with that of a conventional double-path
two-mode interferometer. With the shortcut method mentioned above, improvement
of the momentum resolution could also be fulfilled, which leads to atomic
momentum patterns less than 0.6 $\hbar k_L$. To identify and remove systematic
noises, we introduce the methods based on the principal component analysis
(PCA) that reduce the noise in detection close to the $1/\sqrt{2}$ of the
photon-shot noise and separate and identify or even eliminate noises.
Furthermore, we give a proposal to measure precisely the local gravity
acceleration within a few centimeters based on our study of ultracold atoms in
precision measurements.
