Optical transitions between entangled electron–phonon states in silicon

Abstract

Silicon crystallizes in the diamond structure with two atoms per unit cell and supports three optical phonon modes. However, due to the centrosymmetric nature of the lattice, these modes do not induce a net dipole moment and are therefore inactive in infrared absorption. Even in polar semiconductors, where optical phonons can be IR-active, conventional techniques such as infrared absorption and Raman spectroscopy are restricted to probing phonons at the Brillouin zone center (Γ-point). In this work, we demonstrate that time- and spectrally resolved pump–probe ellipsometry enables access to the coherent response of electron–phonon coupled states involving both valence and conduction bands. Following two-photon absorption induced by the femtosecond pump pulse, the electronic excitation relaxes and drives the generation of coherent longitudinal optical phonons along the X-direction of the Brillouin zone, followed by optical transitions of entangled electron–phonon states along the Λ-direction. This process results in a transient, strongly correlated electron–phonon state that persists for up to ≈ 300 fs. Within this coherent time window, the silicon crystal exhibits optical resonances at electronic transition energies modulated by quantized phonon contributions. Finally, we detect further sidebands in the ellipsometric spectrum, which are 81 meV apart and assign these to two-phonon-assisted electronic transitions.