Feasible Optical Weak Measurements of Complementary Observables via a Single Hamiltonian

Date: 2012-02-23
Authors Shengjun Wu and Marek ┼╗ukowski
Journal No. Phys. Rev. Lett. 108, 080403 (2012)
Abstract A general formalism for joint weak measurements of a pair of complementary observables is given. The standard process of optical three-wave mixing in a nonlinear crystal (such as in parametric down-conversion) is suitable for such tasks. To obtain the weak value of a variable A one performs weak measurements twice, with different initial states of the meter field. This seems to be a drawback, but as a compensation we get for free the weak value of a complementary variable B. The scheme is tunable and versatile: one has access to a continuous set of possible weak measurements of a pair of observables. The scheme increases signal-to-noise ratio with respect to the case without postselection.