We derive the stochastic Schrödinger equation for the limit of continuous weak measurement where the observables monitored are canonical position and momentum. To this end we extend an argument due to Smolianov and Truman from the von Neumann model of indirect measurement of position to the Arthurs and Kelly model for simultaneous measurement of position and momentum. We only require unbiasedne...

The quantum mechanics of position measurement of a macroscopic object is typically inaccessible because of strong coupling to the environment and classical noise. In this work, we monitor a mechanical resonator subject to an increasingly strong continuous position measurement and observe a quantum mechanical back-action force that rises in accordance with the Heisenberg uncertainty limit. For o...