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 magnetic field, rotation, geometric phase, etc. Here we report the experimental realization of a vortex matter-wave interferometer by coherently transferring the optical angular momentum to an ultracold Bose condensate. We use the angular interference technique to measure the relative phase of two vortex states. For a lossless interferometer with atoms only populating two spin states, the difference between the relative phases in the two spin states is locked to π . We also prove the robustness of this out-of-phase relation, not sensitive to the angular-momentum difference between two 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 based on the vortex matter-wave interference.