Quantum Resonance Beyond Direct Measurement: Insights from Weak Measurement

Aharonov's weak value amplification realized via weak measurement provides a versatile means to measure physical parameters with high accuracy, similar to quantum resonance epitomized by the Rabi and Ramsey resonances. The similarity between the two is not accidental: in fact, these two methods of precision measurement have recently been shown to be interconnected for the particular case of direct weak measurement. Here we show that this connection also holds in the case of indirect weak measurement, which is the standard scheme used mostly for studies of weak value amplification. We present a unified framework of weak measurements in which direct measurement appears as a special case of indirect measurement. This allows us to compare the measurement precision of different methods on a common basis, as demonstrated explicitly for the Rabi and Ramsey resonances, showing how the precision of the latter surpasses that of the former in the context of weak value amplification.