  Atomic interferometry in optical lattices is a new trend of developing
practical quantum gravimeter. Here, we propose a compact and portable
gravimetry scheme with an ensemble of ultracold atoms in gravitationally tilted
spin-dependent optical lattices. The fast, coherent separation and
recombination of atoms can be realized via polarization-synthesized optical
lattices. The input atomic wavepacket is coherently split into two parts by a
spin-dependent shift and a subsequent $\frac{\pi}{2}$ pulse. Then the two parts
are held for accumulating a relative phase related to the gravity. Lastly the
two parts are recombined for interference by a $\frac{\pi}{2}$ pulse and a
subsequent spin-dependent shift. The $\frac{\pi}{2}$ pulses not only preclude
the spin-dependent energies in the accumulated phase, but also avoid the error
sources such as dislocation of optical lattices in the holding process. In
addition, we develop an analytical method for the sensitivity in multi-path
interferometry.
