Complex signal measurement based on weak measurements

In the application of weak measurements, such as the estimation of magnetic parameters, the purely real weak coupling of standard weak measurement (SWM) does not correspond to the true physical parameters. To accommodate more complex application scenarios, we further explore three different weak measurement models in which both complex weak coupling and complex weak values coexist. This paper theoretically analyzes pointer variations and applicable ranges in SWM, double pointer weak measurement (DPWM), and almost-balanced weak measurement (ABWM) under specific conditions. Notably, only ABWM can successfully distinguish the real and imaginary components of weak values under complex weak-coupling conditions. While SWM and DPWM can also solve for weak values, they fail to obtain a unique and correct test value. The ABWM technique provides a higher sensitivity than SWM when measuring extremely small parameters. Furthermore, we apply ABWM to the magneto-optical Kerr effect measurement of a Ni-Fe film. This research deepens the understanding of weak measurement techniques and introduces new methods for multiparameter measurements.