Midbandgap electro-optic detection of Bloch oscillations

Abstract

Bloch oscillations excited in a biased GaAs/Al x Ga 1Ϫx As superlattice are investigated in a time-resolved two-color electro-optic detection scheme. The detection of resonantly excited Bloch oscillations is based on the Pockels effect probed at a wavelength in the center of the band gap. The observed birefringence is induced by the macroscopic polarization of the electronic wave packets relative to the localized holes. The off-resonant detection away from optical transitions directly monitors the spatial dynamics of the electrons in amplitude and phase. The dependence of the amplitudes of the Bloch oscillating electrons on the applied electric fields are in good agreement with the electron-hole dipole lengths calculated by a quantum-mechanical model. Bloch1 and Zener 2 have proposed in their theoretical studies on the dynamics of electronic wave packets in periodic potentials a temporal and spatial oscillation of the carriers in the presence of a static electric field. The frequency and the spatial amplitude L of these Bloch oscillations ͑BO's͒ are ϭeFd/h and Lϭ⌬/eF, ͑1͒respectively, where F is the applied electric field, d the potential period, h Planck's constant, and ⌬ the electronic bandwidth. As proposed by Esaki and Tsu, this intriguing phenomenon can be realized in a biased semiconductor superlattice ͑SL͒.3 Here, BO's are excited by the coherent superposition of several electronic Wannier-Stark ͑WS͒ states 4,5 with a common hole state by short laser pulses. The localization lengths of the electronic wave packets deviate from the semiclassical picture of BO's ͓Eq. ͑1͔͒ if a fully quantum-mechanical calculation of the wave functions in the artificial semiconductor structure is used.6 Additionally, the amplitude of optically excited BO's depends on the exciting laser pulse width and energy that determine the initial conditions of the wave packets. Pathbreaking investigations on BO's have been performed in four-wave-mixing, 8,9 THz emission, 10 and resonant transmittive electro-optic sampling ͑TEOS͒ experiments.11 In recent years, the experimental determination of the spatial amplitude of the oscillating electronic wave packets has become an objective of the studies. The amplitude determination of BO's in a SL has been reported in a THz emission experiment.12 The amplitudes were calculated from the detected THz radiation power by applying a superradiance theory. Subsequently, the BO amplitude has been carefully determined in spectrally and time-resolved four-wave mixing experiments.13 Using this technique, the dependence of the amplitudes on the spectral position of the exciting laser pulses was investigated.14 Resonant TEOS experiments performed with optical detection spectrally integrated over WS transitions can only provide a qualitative analysis of the electronic dynamics due to nonlinearities of the electro-optic effect at the interband resonances.In this paper, we present the off-resonant electro-optic detection of Bloch oscillations in a GaAs/Al x Ga 1Ϫx As SL. BO's are excited resonantly, but detecte...

Generation of a DC Fiske current by coupling of Bloch and in‐plane cyclotron oscillations in a semiconductor superlattice

“…Neglecting many-particle effects [15,16], it essentially gives selective access to field changes along the growth axis of the superlattice (direction of the Bloch oscillations) for (100)-oriented crystals like the ones investigated here. As a consequence, the magneto-Bloch oscillations are visible, but not the in-plane cyclotron oscillations.…”

Bloch Oscillations and Ultrafast Coherent Optical Phenomena

“…Therefore, TEOS can be used to measure the internal oscillating field caused by the BOs and thus obtain the amplitude of the Bloch wave packet at resonant near-bandgap (Dekorsy et al, 1994) and off-resonant (Forst et al, 2000) excitations. Therefore, TEOS can be used to measure the internal oscillating field caused by the BOs and thus obtain the amplitude of the Bloch wave packet at resonant near-bandgap (Dekorsy et al, 1994) and off-resonant (Forst et al, 2000) excitations.…”

LDRD final report on Bloch Oscillations in two-dimensional nanostructure arrays for high frequency applications.

“…Esaki and Tsu [3] predicted that negative differential conductance can be observed in semiconductor superlattices without applying a huge electric field due to their large lattice periods, small Brilloin zones, and narrow bandwidths. Investigations of Bloch oscillations have been carried out in THz emission [46][47][48][49], electro-optic detection [49,50], and four-wave mixing experiment [51].…”