Signature of Electron-Plasmon Quantum Kinetics in GaAs

Abstract

We predict a carrier-density dependent oscillation, which is superimposed on the decay of the coherent control photon echo signal of a semiconductor. It reflects the oscillatory transfer of excitation back and forth between electrons and a mixed plasmon-phonon mode. This signature provides obvious and unique evidence for the finite duration of the interaction process, i.e., evidence for the collective Coulomb quantum kinetics. The theoretical predictions for the model semiconductor GaAs are reproduced in corresponding experiments. PACS numbers: 78.47. +p, 42.50.Md, 42.65.Re, 63.20.Kr Dissipation and relaxation processes in solid state physics can often be thought of as a transfer of excitation from a part of the problem, "the system," to the rest, "the bath." For the well-studied example of electron-phonon interaction in semiconductors, this separation into system and bath is obvious. Yet, it has only been recently that quantum kinetics has revealed the rich real-time quantum mechanical details of this transfer process [1][2][3]. The main new point of quantum kinetics -as compared to semiclassical Boltzmann kinetics -is that two time scales are involved: the mean time between collisions and the duration of an interaction process. One signature of this finite duration is a coherent oscillation which results from a combined electron-phonon coherence, i.e., the excitation oscillates back and forth between system and bath for a short time span, the memory time. The analog of this process for a molecule or a quantum dot, where one has discrete states rather than energy bands, would be a quantum beating between an electronic state and its vibrational sideband [4].These concepts of quantum kinetics reach far beyond solid state physics. They are currently also discussed for heavy-ion collisions, for nonequilibrium nuclear matter, and for plasmas in strong electromagnetic fields (for a recent survey, see, e.g., Ref.[5]).For the case of electron-electron interaction in semiconductors, a separation of the complete problem into system and bath contributions is not obvious at all. As a result, many groups have addressed various aspects of this fundamental problem in the dilute limit [6][7][8], where memory effects due to biexcitonic correlations do occur indeed [8], as well as for elevated carrier densities [9][10][11][12][13][14][15], where plasma screening becomes important. Intuitively, one would expect that the collective excitation of the electron gas, the plasmon, could play the role of the phonon in the above example. In analogy to the electron-phonon quantum kinetics, one should then be able to observe an oscillation corresponding to the transfer of excitation back and forth between individual electrons (the system) and the collective mode of the electrons, i.e., the plasmons (the bath). This combined electron-plasmon coherence, which must not be confused with coherent plasmons [16], has neither been observed experimentally, nor has any realistic theoretical suggestion been made as to how it could be measured.In t...

Delayed formation of coherent LO phonon-plasmon coupled modes inn- andp-type GaAs measured using a femtosecond coherent control technique

“…The transition from the photoexcited electron-hole plasma to collective response of the many-body system takes around one period of the plasmon (less than 100 fs). Moreover, both theories and experiments of quantum kinetics have demonstrated that the LOPC modes are not established instantaneously and the coupling of two longitudinal modes is a kinetic process controlled by time and carrier density [14][15][16]. It is not surprising, however, that the delayed formation of coupled modes has no considerable influence on the observed dynamics because most of the frequency-domain measurements are incapable to resolve such short time scale.…”

Light-Induced Gaps in Semiconductor Band-to-Band Transitions

“…[15] is numerically too demanding under these conditions. Hence, we employ a phenomenological description-with parameters based on earlier findings [15,16]. For the dephasing of the off-diagonal density matrix elements we take into account that the damping is the sum of a constant contribution due to LO-phonon scattering and a term proportional to the third root of the carrier density n [16].…”

“…A full quantum kinetic treatment along the lines of Ref. [15] is numerically too demanding under these conditions. Hence, we employ a phenomenological description-with parameters based on earlier findings [15,16].…”

“…At large excess energies, where the dephasing is stronger, only an irreversible increase of the inversion is left after the pulse has passed. Based on our experience with quantum kinetics [15,16], we expect that the window of coherent dynamics would be widened to a certain extent by the use of a non-Markovian retarded description of electron-electron scattering. We have checked that replacing the above electron-phonon scattering by electron-phonon quantum kinetics leads to no significant changes.…”

Ultrafast nonlinear optical response of strongly correlated systems: Dynamics in the quantum Hall effect regime

“…6,7,8,11,21,39 However, there are some important differences. In the undoped system, the electronic operators commute with the collec-tive excitation (phonon) operators, and the ground state correlations can be neglected.…”