Constraining the Evolution of the Fundamental Constants with a Solid-State Optical Frequency Reference Based on the ²²⁹Th Nucleus

We describe a novel approach to directly measure the energy of the narrow, low-lying isomeric state in ²²⁹Th. Since nuclear transitions are far less sensitive to environmental conditions than atomic transitions, we argue that the ²²⁹Th optical nuclear transition may be driven inside a host crystal with a high transition Q. This technique might also allow for the construction of a solid-state optical frequency reference that surpasses the short-term stability of current optical clocks, as well as improved limits on the variability of fundamental constants. Based on analysis of the crystal lattice environment, we argue that a precision (short-term stability) of 3×10^-17<Δf/f<1×10^-15 after 1 s of photon collection may be achieved with a systematic-limited accuracy (long-term stability) of Δf/f∼2×10^-16. Improvement by 10²-10³ of the constraints on the variability of several important fundamental constants also appears possible.