Spectroscopy of the forbidden $^1S_0 \rightarrow \,^3P_0$ transition on ultra-cold ytterbium atoms

Cold atoms in optical lattices are often considered a rich playground for emulating condensed matter systems, since they make it possible to engineer many-body Hamiltonians with tunable parameters. However, one missing feature is the ability to emulate orbital magnetism. Recent proposals for simulating orbital magnetism with neutral atoms rely on a state-dependent optical lattice with laser-driven hopping.\footnote{D. Jaksch and P. Zoller, NJP \textbf{5}, 56 (03)}$^,$\footnote{F. Gerbier and J. Dalibard, NJP \textbf{12}, 033007 (10)} Ytterbium, with its long lived metastable state ($^3P_0$), is a well-suited candidate for the implementation of such schemes. Addressing the forbidden transition between ytterbium ground ($^1S_0$) and meta-stable ($^3P_0$) states is experimentally challenging, and requires the use of a laser with stability close to the standards of atomic clocks. I will report on the building of a ultra-narrow laser locked on a high-finesse low-expansion cavity.\footnote{Dareau \textit{et al.}, arXiv:1412.5751} I will then show how the absolute frequency of the cavity modes can be calibrated by performing high-resolution spectroscopy on molecular iodine, allowing us perform Doppler spectroscopy on the $^1S_0\rightarrow\,^3P_0$ transition of an ytterbium BEC.