Small-tilt measurement based on weak-value-amplification with balanced homodyne detection

We experimentally realize a great precision enhancement in the small-tilt measurement by using a Sagnac interferometer and balanced homodyne detection (BHD) of high-order optical modes, together with the weak-value amplification (WVA) technique. Smaller minimum measurable tilt and higher signal-to-noise ratio can be obtained by using BHD, compared with the split detection. The precision of 3.8 nrad can be obtained under our present experimental condition. It is shown that combining WVA technique and BHD can strengthen each other's advantages and can behave better for some special application scenarios, such as extremely weak output, wider measurement bandwidth, etc. Moreover, the precision can be further enhanced by experimental parameter optimization.