What can we know from weak measurements? - Shengjun Wu

The idea of weak measurement was introduced by Aharonov, Albert and Vaidman in 1988. It not only provides a theoretical framework for addressing counterintuitive quantum phenomena and fundamental questions, but also gives a practical tool for amplifying very tiny signals that would not be observed in the conventional measurement schemes. In this talk, I shall review the basic idea of weak measurement, and show explicitly how it can be used for signal amplification. I shall present an extension of weak measurement to general preselection and postselection with corrections to high order terms, and give a general formalism for weak measurement of a pair of complementary observables. I shall also discuss the limitation on amplification of the signal-to-noise ratio and how this limitation can be overcome by simultaneous weak measurements of a pair of complementary observables. An experimental scheme based on parametric down conversion will be presented. This scheme could also work in other processes such as the opto-mechanical interaction in the strong coupling regime and the four-wave mixing process in cold atoms.