In the spirit of Quantum Non-Demolition Measurements, we show that exploiting suitable vibronic couplings and repeatedly measuring the atomic population of a confined ion, it is possible to distill center of mass vibrational states with well defined square of angular momentum or, alternatively, angular momentum projection Schr\"odinger cat states.
@article{arxiv.quant-ph/0405079,
title = {Distilling angular momentum nonclassical states in trapped ions},
author = {B. Militello and A. Messina},
journal= {arXiv preprint arXiv:quant-ph/0405079},
year = {2018}
}