  Ramsey interferometers have wide applications in science and engineering.
Compared with the traditional interferometer based on internal states, the
interferometer with external quantum states has advantages in some applications
for quantum simulation and precision measurement. Here, we develop a Ramsey
interferometry with Bloch states in S- and D-band of a triangular optical
lattice for the first time. The key to realizing this interferometer in
two-dimensionally coupled lattice is that we use the shortcut method to
construct $\pi/2$ pulse. We observe clear Ramsey fringes and analyze the
decoherence mechanism of fringes. Further, we design an echo $\pi$ pulse
between S- and D-band, which significantly improves the coherence time. This
Ramsey interferometer in the dimensionally coupled lattice has potential
applications in the quantum simulations of topological physics, frustrated
effects, and motional qubits manipulation.
