## Molecules for Precision Measurements

We proposed in PRL 100, 043201 (2008) and PRL 100, 043202 (2008) that ultracold moleculecules are good candidates for high-precision measurements. This is due to the complexity of the molecular electronic and rovibrational spectra, which provides a series of precision benchmarks from the radio frequencies to the visible spectrum.

An important application of a precision measurement with ultracold molecules is to test for possible time variation of fundamental constants. In particular, in above studies we focused on the variation of the proton-electron mass ratio. We theoretically analysed various factors that can affect frequency measurements in the ground state of Sr2 and Cs2 molecules.

In case of Sr2 we evaluated transition dipole moments between vibrational levels of the ground and metastable states, for determination of optimal pathways for Raman transitions. In addition, we analyzed the dynamic polarizability of ground state vibrational levels to identify Stark-cancellation optical lattice frequencies for vibrational transitions. Finally, we estimated the natural linewidths of the intermediate metastable vibrational levels, in order to obtain realistic estimates of trap losses. This analysis is described in detail in PRA 79, 012504 (2009).

For Cs2 we have performed calculations of the electronic and vibrationally-averaged dipole moments between the triplet and singlet ground states. These transitions are allowed due to hyperfine interactions between the potentials. We have found four pairs of vibrational levels that coincide, which are proposed to be most sensitive to variation of the proton-electron mass ratio. A more detailed description on the mixing of the triplet/singlet ground states in Cs2 is given in PRA 86, 022513 (2012).