Timing in quantum measurements of position and momentum

The prototype for a simultaneous measurement of two conjugate variables was originally introduced by Arthurs and Kelly in 1965. It relies on coupling the quantum particle to be probed to two additional systems, which serve as measurement pointers. In this contribution we investigate an extended scheme to measure position and momentum of a massive particle. By considering an explictly time-dependent coupling we can quantify the timing of the measurement. We investigate how the noise resulting from such a measurement process depends on the interaction strength and the size of the pointers. In particular, we focus on the question of which measurement timing minimizes the corresponding uncertainty product.