Improving the Q factor of an optical atomic clock using quantum non-demolition measurement

Quantum non-demolition (QND) measurement is a remarkable tool for the manipulation of quantum systems. It allows specific information to be extracted while still preserving fragile quantum observables of the system. Here we apply cavity-based QND measurement to an optical lattice clock---a type of atomic clock with unrivalled frequency precision---preserving the quantum coherence of the atoms after readout with 80\% fidelity. We apply this technique to stabilise the phase of an ultrastable laser to a coherent atomic state via a series of repeated QND measurements. We exploit the improved phase-coherence of the ultrastable laser to interrogate a separate optical lattice clock, using a Ramsey spectroscopy time extended from 300~ms to 2~s. With this technique we maintain 95\% contrast and observe a seven-fold increase in the clock's \emph{Q} factor to $1.7\times10^{15}$.