Towards an order of magnitude improved sensitivity to the electron's EDM with trapped HfF$^{\mathrm{+}}$*

In 2017, our group completed the first measurement of the electron's electric dipole moment (eEDM, $d_{e})$ using trapped molecular ions, yielding a 90{\%} confidence upper bound of \textbar $d_{e}$\textbar \textless 1.3 x 10$^{\mathrm{-28}} \quad e$ cm. Our measurement [1], which was statistics-limited, provided confirmation of the upper bound on \textbar $d_{e}$\textbar set by the ACME Collaboration [2], and demonstrated coherence times over 1 second using trapped molecules -- a valuable feature for future eEDM searches. Here, we will present our progress towards an order of magnitude higher statistical sensitivity via increased sample size and coherence time, cooling of the rotational degree of freedom, and imaging of photodissociation products. [1] W. B. Cairncross \textit{et al}., Phys. Rev. Lett. \textbf{119}, 153001 (2017) [2] The ACME Collaboration, Science \textbf{343}, 269 (2014)