Synchronizing quantum and classical clocks made of quantum particles up to ħ2

Abstract

Quantum corrections to the classical time of arrival arises if time is treated quantum mechanically, i.e. time is a dynamical observable. Here, we demonstrate how to eliminate these quantum corrections for a quantum object in a potential free region of space, as computed in Phys. Rev. A 80, 030102(R) (2009), can be eliminated up to ħ² using an appropriate position dependent phase. By doing so, we are able to synchronize classical and quantum clocks that tells time using the classical and quantum arrival time of the object, respectively. We provide an example for synchronizing such a clock.