Precision spectroscopy of the molecular ion HD+: Control of Zeeman shifts

Precision spectroscopy on cold molecules can potentially enable novel tests of fundamental laws of physics and alternative determination of some fundamental constants. Realizing this potential requires a thorough understanding of the systematic effects that shift the energy levels of molecules. We have performed a complete ab initio calculation of the magnetic field effects for a particular system, the molecular hydrogen ion HD+. Different spectroscopic schemes have been considered, and several transitions, all accessible by modern radiation sources and exhibiting well controllable or negligible Zeeman shift, have been identified. Thus, HD+ is a candidate for the determination of the ratio of electron-to-nuclear reduced mass, and for tests of its time independence.