Signatures of transient Wannier-Stark localization in bulk gallium arsenide

Many properties of solids result from the fact that in a periodic crystal structure, electronic wave functions are delocalized over many lattice sites. Electrons should become increasingly localized when a strong electric field is applied. So far, this Wannier-Stark regime has been reached only in artificial superlattices. Here we show that extremely transient bias over the few-femtosecond period of phase-stable mid-infrared pulses may localize electrons even in a bulk semiconductor like GaAs. The complicated band structure of a three-dimensional crystal leads to a strong blurring of field-dependent steps in the Wannier-Stark ladder. Only the central step emerges strongly in interband electro-absorption because its energetic position is dictated by the electronic structure at an atomic level and therefore insensitive to the external bias. In this way, we demonstrate an extreme state of matter with potential applications due to e.g., its giant optical non-linearity or extremely high chemical reactivity.