Two-parameter estimation in a matter-wave Sagnac interferometer

Xu Yu,Hong-Bin Liang,Xiao-Guang Wang

Figure 1. Schematic diagram of the parameter measurement process in a Sagnac interferometry. The Sagnac system is simplified as a clockwise rotating disc with a uniform angular velocity ω. The input state that is prepared by trapping N spin-1/2 particles in a harmonic potential with frequency ω is injected into the Sagnac system. Then the particles with different spin directions are coherently split and countertransport along the disc with sweeping angular frequency ${\omega }_{p}(t)$ in the rotating frame. The output state containing the information of ω and ω is formed when the particles recombine again. One can readout the information of these parameters by detecting the output state.