Towards a Molecular Lattice Clock: Magic-Wavelength Vibrational Spectroscopy of Sr$_{\mathrm{2}}$

Homonuclear diatomic molecules tightly confined at ultracold temperatures allow for high-precision spectroscopy and coherent control over their quantum states. These qualities offer novel pathways for tests of fundamental physics, such as searches for temporal drifts in the fundamental constants and ``fifth forces'', in addition to probing quantum chemistry in the ultracold regime. Here we report the progress in building a molecular lattice clock with ultracold $^{\mathrm{88}}$Sr$_{\mathrm{2}}$ molecules trapped in an optical lattice, with the goals of testing molecular QED, improving constraints on nanometer-scale gravity, and potentially providing a model-independent test of the temporal variation of the electron-proton mass ratio. These involve precise metrology of the binding energies of vibrational states spanning the ground-state potential. We locate several vibrational states by employing two-photon spectroscopy. To eliminate differential light shifts and decoherence due to the lattice, we demonstrate a new type of magic wavelength based on narrow polarizability resonances. Additionally, we present results on ultracold photodissociation where we demonstrate magnetic field control of matter-wave interference in the emerging photofragment angular distributions, and probe the quantum-quasiclassical transition behavior at increasing photofragment energies, finding excellent agreement with a multi-channel quantum chemistry model.