Quantum Enhanced Precision and Stability of Atomic Clocks

The goal of this work was to study theoretically the prospect of enhancing the precision and stability of atomic clocks though the use of collective effects in ensembles of atoms and through the use of alternatives to the usual observable, namely the population of the excited state of the atoms. We assumed that each atom possess only two relevant levels (such as the two hyperfine levels of cesium-133) where the transitions between these levels are driven by resonant (or near resonant) classical coherent radiation fields. Lessons learned form our work in quantum optical interferometry were brought to bear on this work. Quantum optical interferometry is similar to Ramsey spectroscopy, also known at population spectroscopy. In the present work we considered the Ramsey method with collections of unentangled atoms where the monitored observable was the probability that all the atoms are in their excited states at the end of the Ramsey sequence of pulses and free evolution. We found that this technique narrows the central Ramsey fringe due to collective effects. It is the narrowing of the central fringe that can result in enhanced precision and stability. We also studied cases where the atoms are entangled, but we discovered that a different observable must be use, namely the atomic parity, this being -1 raised to the number of atoms in the excited state.