Rotational symmetry breaking on the Rydberg energy spectrum of indirect excitons in diamond studied by terahertz time-domain spectroscopy

We investigated the $1S\text{\ensuremath{-}}2P$ transitions of the indirect excitons in diamond around 70 meV in the high-frequency terahertz region via time-resolved Lyman spectroscopy. We discovered significant splitting of the $2P$ levels and attributed it to the rotational-symmetry-breaking effect owing to the cubic crystal environment. The maximum energy separation of 14.9 meV reached 18% of the excitonic Rydberg constant---83.5 \ifmmode\pm\else\textpm\fi{} 2.9 meV---which deviated from the binding energy of the $1S$ ground state: 93.3 \ifmmode\pm\else\textpm\fi{} 2.0 meV. In addition to the anisotropy of the valence bands, we found the impact of the rotational symmetry breaking of the conduction band valleys, which leads to a significant deviation from the case with direct excitons. Detailed knowledge of the ground and excited states of long-lifetime excitons provides an unprecedented opportunity to develop the study of quantum many-body physics and quantum chaos.