Quantum Coherence of Continuum States in the Valence Band of GaAs Quantum Wells

Abstract

Quantum beats of heavy and light holes in GaAs quantum wells are investigated in femtosecond time-resolved four-wave mixing and transmission experiments as a function of optical excitation energy. Under nonexcitonic excitation conditions, the four-wave mixing signal disappears due to the immediate loss of the interband coherence of continuum states. In the transmission experiment, the quantum beats are observed up to excess energies of 75 meV above the exciton resonances.The experimental data clearly demonstrate the coherence of continuum states in the valence band. Changes of the beat frequency with the excitation energy are due to the dispersion of the valence bands.[ S0031-9007(96) Time-resolved investigations of quantum beats in semiconductor quantum wells have received considerable attention in the last few years, since they provide insight into the scattering and coupling mechanisms between light, excitons, free carriers, and phonons in these systems. Most of this work deals with quantum coherence of excitonic states, which may have dephasing rates up to some picoseconds at low lattice temperatures in GaAs based heterostructures. The most commonly used tool for the time-resolved detection of optically excited coherence in semiconductors is four-wave mixing (FWM) spectroscopy [1]. In self-diffracted degenerate FWM, the third order nonlinear interband polarization is detected, which gives a selective sensitivity for the excitonic coherence based on two facts: (i) The signal is proportional to the eighth order of the transition matrix elements [2], which is significantly enhanced at the exciton energy, and (ii) continuum states lose their interband coherence on a time scale of 100 fs resulting in the dominance of the long-living excitonic contribution [3]. The immediate loss of the interband coherence of continuum states arises from the k-space band dispersion, which is equivalent to an "inhomogeneous" broadening of interband transitions with the energetic width of the exciting laser spectrum. Furthermore, the excitation of continuum states with excess energy above the band minimum provides additional scattering channels for momentum and energy relaxation so that a decreased interband dephasing time is expected. Several different techniques have been applied for the time-resolved investigation of coherent electronic states in semiconductors, e.g., THz emission spectroscopy [4][5][6], time-resolved transmission spectroscopy [2,7], and time-resolved resonant luminescence up-conversion [8]. All these techniques provide distinctly different information on coherent states than FWM. In THz emission spectroscopy, the detected THz radiation arises from the real space oscillation of coherent wave packets and is thus not necessarily restricted to excitonic transitions. Therefore, under appropriate excitation conditions, the detected signal may give information on the intraband coherence of the excited states. These observations have been made for the case of nonexcitonic excitation of Bloch oscillations in superlattice...

Effects of non-exciton components excited by broadband pulses on quantum beats in a GaAs/AlAs multiple quantum well

“…Coherent exciton oscillations, such as quantum beats and Bloch oscillations, have been extensively studied to understand the ultrafast exciton dynamics 1 2 3 4 5 6 7 8 9 , the interaction of excitons with phonons 10 11 12 13 14 15 16 17 18 , the determination of the splitting energies in inhomogeneous systems 19 20 21 , and applications of ultrafast devices 22 23 24 . However, one problem has been the difficulty of generating a clear and long-lived oscillation.…”

“…For instance, several four-wave-mixing spectra under exciton excitation conditions have exhibited the broad tail around the exciton lines 25 26 . These components may act as free carriers and lead to exciton quantum beat dephasing 27 28 .…”

Coupled mode of the coherent optical phonon and excitonic quantum beat in GaAs∕AlAs multiple quantum wells

“…6,7 Quantum beats (QB's) of excitons in quantum wells (QW's) are extensively investigated from the standpoints of physical interesting and application to terahertz radiation. [8][9][10][11][12][13][14] When an electric field is applied to a QW, the excitonic QB leads to a longitudinal polarization along the growth direction of the QW. [11][12][13] Since the coherent LO phonon in the well layer of the QW has also a longitudinal polarization, we can expect the coupled oscillation of the excitonic QB and the coherent LO phonon (LO phonon-QB coupled mode) through their longitudinal polarizations when both are brought into resonance.…”

Influence of carrier–carrier scattering on intraband dephasing

“…One example is the observation of distinctly different dephasing in narrow miniband superlattices [22]. The different contributions of hole-hole scattering to the dephasing of interband and intraband dephasing has also been demonstrated by the observation of coherence of continuum states exhibiting heavy hole/light hole beats in the intraband dynamics while the interband dynamics traced by FWM already are dephased [23]. To our knowledge the different influence of scattering between coherent carriers and scattering with an incoherent carrier background has not yet been addressed.…”