Phase-locking matter-wave interferometer of vortex states

Matter-wave interferometer of ultracold atoms with different linear momenta has been extensively studied in theory and experiment. The vortex matter-wave interferometer with different angular momenta is applicable as a quantum sensor for measuring the rotation, interatomic interaction, geometric phase, etc. Here we report the first experimental realization of a vortex matter-wave interferometer by coherently transferring the optical angular momentum to an ultracold Bose condensate. After producing a lossless interferometer with atoms only populating the two spin states, we demonstrate that the phase difference between the interferences in the two spin states is locked on $\pi$. We also demonstrate the robustness of this out-of-phase relation, which is independent of the angular-momentum difference between the two interfering vortex states, constituent of Raman optical fields and expansion of the condensate. The experimental results agree well with the calculation from the unitary evolution of wave packet in quantum mechanics. This work opens a new way to build a quantum sensor and measure the atomic correlation in quantum gases.