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.

A microscopic approach that is based on the multisubband semiconductor Bloch equations formulated in the basis of a 14-band k · p model is employed to compute the temporal dynamics of photocurrents in GaAs quantum wells following the excitation with femtosecond laser pulses. This approach provides a transparent description of the interband, intersubband, and intraband excitations, fully includes all resonant as well as off-resonant excitations, and treats the light-matter interaction non-perturbatively. For linearly polarized excitations the photocurrents contain contributions from shift and rectification currents. We numerically compute and analyze these currents generated by the excitation with femtosecond laser pulses for [110]-and [111]-oriented GaAs quantum wells. It is shown that the often employed perturbative χ (2) -approach breaks down for peak fields larger than about 10 kV/cm and that non-perturbative effects lead to a reduction of the peak values of the shift and rectification currents and to temporal oscillations which originate from Rabi flopping. In particular, we find a complex oscillatory photon energy dependence of the magnitudes of the shift and rectification currents. Our simulations demonstrate that this dependence is the result of mixing between the heavy-and light-hole valence bands. This is a surprising finding since the bandmixing has an even larger influence on the strength of the photocurrents than the absorption coefficient. For [110]-oriented GaAs quantum wells the calculated photon energy dependence is compared to experimental results and a good agreement is obtained which validates our theoretical approach.

Shift current transient are obtained for near band gap excitation of bulk GaAs by numerical solutions of the semiconductor Bloch equations in a basis obtained from a 14 band k·p model of the band structure. This approach provides a transparent description of the optically induced excitations in terms of interband, intersubband, and intraband excitations which enables a clear distinction between different contributions to the shift current transients and fully includes resonant as well as off-resonant processes. Using a geodesic grid in reciprocal space in our numerical solutions, we are able to include the electron-hole Coulomb attraction in combination with our anisotropic three-dimensional band structure. We obtain an excitonic absorption peak and an enhancement of the continuum absorption and demonstrate that the excitonic wave function contains a significant amount of anisotropy. Optical excitation at the excitonic resonance generates shift current transients of significant strength, however, due to the electron-hole attraction the shift distance is smaller than for above band gap excitation. We thus demonstrate that our approach is able to provide important information on the ultrafast electron dynamics on the atomic scale.

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