Laser cooling Rydberg molecules -- a detailed study of the helium dimer

The helium dimer in its metastable triplet state is a promising candidate to be the first laser-cooled homonuclear molecule. An ultracold gas of He$_2^*$ would enable a new generation of precision measurements to test quantum electrodynamics for three- and four-electron molecules through Rydberg spectroscopy. Nearly diagonal Franck-Condon factors are obtained because the electron employed for optical cycling occupies a Rydberg orbital that does not take part in the chemical bond. Three possible laser cooling transitions are identified and the spin-rovibronic energy-level structure of the relevant states as well as electronic transition moments, linestrengths, and lifetimes are determined. The production of He$_2^*$ molecules in a supersonic beam is discussed, and a laser slowing scheme to load a magneto-optical trap under such conditions is simulated using a rate equation approach. Various repumping schemes involving one or two upper electronic states are compared to maximize the radiative force. Loss mechanisms such as spin-forbidden transitions, predissociation, and ionization processes are studied and found to not introduce significant challenges for laser cooling and trapping He$_2^*$. The sensitivity of the vibrational levels of He$_2^+$ with respect to the static polarizability of atomic helium is determined and its implications for a new quantum pressure standard are discussed.