Famous experiments which have been performed in JILA include measurements of parity violation, electric dipole moments (EDM) and variation of the fundamental constants. I will discuss new possibilities in these areas.
Molecular EDM experiments (including that in HfF+) may be used to measure time (T) and parity (P) violating nuclear magnetic quadrupole moment (MQM) produced by P,T-violating nuclear forces, nucleon and quark EDM and chromo-EDM, and QCD theta term. This will provide an important test of unification theories.
Parity violating effects produced by the tensor component of the weak interaction between deformed nucleus and electron are strongly enhanced in such molecules as HfF+. This should allow one to measure for the first time weak quadrupole moments and quadrupole moments of the neutron distribution in nuclei.
Low-mass boson dark matter particles produced after Big Bang form classical field and/or topological defects. In contrast to traditional dark matter searches, effects produced by interaction of an ordinary matter with this field and defects may be first power in the underlying interaction strength rather than the second power or higher (which appears in a traditional search for the dark matter). This may give an enormous advantage since the dark matter interaction constant is extremely small. The sensitivity improves by up to 15 orders of magnitude.
The interaction with axion dark matter produces oscillating EDM and parity violating effects in atoms and molecules.
Interaction between the scalar dark matter (e.g. dilatons) and ordinary matter produces oscillating variations of the fundamental constants including the fine structure constant alpha and particle masses, which may be searched for using atomic clocks. There are also astrophysical manifestations of such interaction.