We think that in the Big Bang, the universe began with equal parts matter and antimatter. So why is the universe today composed mostly of matter? A new measurement of the neutron electric dipole moment (nEDM) could help to address this question, and other important questions about the symmetry between particles and their antiparticle counterparts. It is the aim of the TRIUMF Ultra-Cold Advanced Neutron (TUCAN) collaboration to measure the nEDM with an uncertainty of 1 x 10-27 ecm, a factor of ten improvement over the previous best measurement. The most unique feature of our experiment is that it uses superfluid helium as the final step in the production of our ultracold neutrons. I will describe our exciting experiment, with a focus on the contributions of my group to the cryogenics, magnetic fields, and magnetometry for the experiment. The path forward beyond TUCAN will also involve the use of superfluid helium, and I will discuss other opportunities to use similar cryogenic techniques to improve the precision by another order of magnitude.
