Precision metrology using weak measurement

Weak measurement can dramatically amplify a small effect, therefore has received increasing interest in metrology [1, 2]. Yet the amplification effect of weak measurement comes at the cost of a reduction in the rate at which data can be acquired, due to the requirement to select almost orthogonal pre- and post-selected states. Therefore whether weak measurement can really enhance the measurement precision or even beat the classical limit has been under debate for long time [3-5]. Here we investigate two precision metrology schemes using weak measurement. The first one can be viewed as a weak measurement in the phase space. By coupling a single photon with an intense coherent beam, we demonstrate a measurement precision at the Heisenberg limit with the proper pre- and post-selection on the superposition state of the single photon. For the second scheme we study the performance of weak measurement in tracking light beam displacements with a scientific CCD. We show that, with the presence of classical noise and detector saturation that are ubiquitous in CCD arrays, weak measurement outperforms conventional measurement in terms of measurement precision. Our results foreshadow the applications of weak measurement in quantum-enhanced metrology.