Quantitative detection of the respective concentrations of chiral compounds with weak measurements

In this letter, we determine the respective concentrations of glucose and fructose in the mixed chiral solution by simultaneously measuring the optical rotation angle (ORA) and the refractive index change (RIC) with weak measurements. The photonic spin Hall effect (PSHE) serves as a probe in our scheme. The measurement of ORA is based on the high sensitivity of the amplification factor to the polarization state in weak measurements. The measurement of RIC is based on the rapid variation of spin splitting of the PSHE. The measurement precision of the respective concentrations can be achieved to be 0.02 mg/ml. This method can detect traces of enantiomeric impurities and has a potential application in chiral sensing.