Proposed search for $T$-odd, $P$-even interactions in spectra of chaotic atoms

Violation of fundamental symmetries in atoms is the subject of intense experimental and theoretical interest. $P$-odd, $T$-even transitions have been observed and are in excellent agreement with electroweak theory. Searches for permanent electric dipole moments have placed bounds on $T$-odd, $P$-odd interactions, constraining proposed extensions to the standard model of elementary particles. Here we propose a search for $T$-odd, $P$-even (TOPE) interactions in atoms. We consider open-shell atoms, such as rare-earth-metal atoms, which have dense, chaotic excitation spectra with strong level repulsion. The strength of the level repulsion depends on the underlying symmetries of the atomic Hamiltonian. TOPE interactions lead to enhanced level repulsion. We demonstrate how a statistical analysis of many chaotic spectra can determine the strength of level repulsion; in particular, the variance of the number of levels in an energy range has been shown to be a useful measure. We estimate that, using frequency comb spectroscopy, a sufficient number of chaotic levels could be measured to match or exceed the current experimental bounds on TOPE interactions.