  The text below was written during two visits that Daniel Segal made at
Universit{\'e} Paris 13. Danny stayed at Laboratoire de Physique des Lasers the
summers of 2008 and 2009 to participate in the exploration of a novel lead in
the field of ultra-high resolution spectroscopy. Our idea was to probe trapped
molecular ions using Quantum Logic Spectroscopy (QLS) in order to advance our
understanding of a variety of fundamental processes in nature. At that time,
QLS, a ground-breaking spectroscopic technique, had only been demonstrated with
atomic ions. Our ultimategoals were new approaches to the observation of parity
violation in chiral molecules and tests of time variations of the fundamental
constants. This text is the original research proposal written eight years ago.
We have added a series of notes to revisit it in the light of what has been
since realized in the field.
