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Communications in Theoretical Physics

Transient Intersubband Optical Absorption in Double Quantum Well Structure

Wu Bin-He

Published Apr 1, 2005• 5 citations
Publisher

Abstract

The microscopic equations of motion including many-body effects are derived to study the intersubband polarization in the double quantum well structure induced by an ultrafast pumping infrared light. Based on the self-consistent field theory, the transient probe absorption coefficient is calculated. These calculations are beyond the previous steady-state assumption. Transient probe absorption spectra are calculated under different pumping intensity and various pump probe delay.

DOI
10.1088/0253-6102/43/4/034

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The microscopic equations of motion including many-body effects are derived to study the intersubband polarization in the double quantum well structure induced by an ultrafast pumping infrared light. Based on the self-consistent field theory, the transient probe absorption coefficient is calculated. These calculations are beyond the previous steady-state assumption. Transient probe absorption spectra are calculated under different pumping intensity and various pump probe delay.
We study theoretically the time evolution of nonlinear optical phenomena of a probe electromagnetic field pulse in intersubband transitions of a semiconductor quantum well structure under the influence of a pump electromagnetic field. More specifically, we take into consideration the effects of electron-electron interactions and consider the interaction of a two-subband system with rectangular electromagnetic fields. The spectral form of the linear absorption, dispersion, and nonlinear optical Kerr effect is described, from the time that the external field is applied up until the dynamics of the system has reached a steady state. In order to describe the dynamics of the system, the effective nonlinear Bloch equations are used, in which renormalized terms for the transition energy and the applied field have been added, due to the effects of electron-electron interactions. These equations are properly combined, and the differential equations of the density matrix elements for the several optical phenomena up to third order are derived. These are solved numerically in the whole time range up to the steady state for a GaAs/AlGaAs quantum well structure. We show that the form of the several optical spectra studied here has a significantly altered evolution over time, according to the value of the frequency of the pump field and of electron sheet density. Even in the case in which the spectral form in the steady state case is almost identical for two different sets of parameters, their evolution can be quite different, according to the precise value of these parameters.
We give a local-field calculation of the dynamic response of a single quantum well (QW) inside a cavity pumped by a strong light beam. The starting point of our theory is the microscopic Maxwell-Lorentz equation combined with light-induced nonlinear current densities associated with intersubband transitions in the QW system. The frequency- and space-dependent current densities are derived from the density-matrix formalism in a nonperturbative manner. Assuming only the electromagnetic coupling from the pump beam to the probe beam is important, we solve the wave equation exactly for both the pump and probe fields. In turn we determine the probe absorption coefficient of the QW structure. For a GaAs/Al0.33{}_{0.33}0.33​Ga0.67{}_{0.67}0.67​As QW placed between vacuum and a GaAs/AlAs distributed Bragg reflector followed by a GaAs prism, we calculate the probe absorption spectra for different parameters such as the pump frequency, the incident intensity of the pump field, and the cavity quality. Our results show that the optical absorption and amplification for the probe field are strongly dependent of these parameters. It is also demonstrated that it is of importance to take into account the dynamic screening effect for the pump field in the calculation of the probe spectra.
The two-band effective semiconductor optical Bloch equations for a quantum well have been generalized to include multisubband effects. The ultrafast transient adiabatic-following solutions are obtained from the equations for interband polarizations, intersubband polarizations, and subband-carrier distribution functions of a ${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$Alx{\mathrm{Al}}_{\mathit{x}}Alx​As/GaAs quantum well, excited by an ultrafast optical pump field. Two conservation laws for the multisubband case are derived. The steady-state response and the \ensuremath{\pi}-pulse response are studied. It is found that these multisubband equations lead to quantitatively different results from the conventional two-band approximation, particularly for wide quantum wells and asymmetric quantum wells.
The transient and steady-state behaviour of the absorption and the dispersion of a probe field propagating at λ = 1.55 μm through an InGaAs\InP double coupled quantum well are studied. The effect of terahertz signal excitation, electron tunnelling and incoherent pumping on the optical properties of the probe field is discussed. The linear dynamical properties of the double coupled quantum well by means of perturbation theory and density matrix method are discussed. We show that the group velocity of a light pulse can be controlled from superluminal to subluminal or vice versa by controlling the rates of incoherent pumping field, terahertz signal and tunnelling between the quantum wells. The required switching time is calculated and we find it between 3 to 15 ps. In the terahertz (30 ~ 300 μm or 1 ~ 10THz) intersubband transition, the incoming photon energy is (4 ~ 41mev) and maybe in the order of electron thermal broadening (KT ~ 6 meV-25 meV for 77 K -300 K). Therefore in the conventional structure, the incoming photon can directly excite the ground state electrons to higher energy levels. It is shown that the absorption and the dispersion of the probe field can be controlled by the intensity of terahertz signal and incoherent pumping field.
The transient and steady-state behavior of the absorption and the dispersion of a probe pulse laser field propagating through an InGaAs\InP double coupled quantum well are studied. The effect of terahertz radiation excitation, electron tunnelling and incoherent pumping on the optical properties of the probe field is discussed. In the terahertz (30~300 μm or 1~10 THz) intersubband transition, the incoming photon energy is (4~41 mev) and maybe in the order of electron thermal broadening (KT~6 meV-25 meV for 77 K-300 K). Therefore in the conventional structure, the incoming photon can directly excite the ground state electrons to higher energy levels and this process inhabits the correct optical switching in terahertz applications. We show that the group velocity of a light pulse can be controlled from superluminal to subluminal or vice versa by controlling the rates of incoherent pumping field and tunnelling between the quantum wells. The required switching time is calculated and we find it between 3 to 26 picoseconds.
We report the measurement of the transient intersubband absorption in a coupled quantum well semiconductor structure. Pulsed interband excitation is used to prepare a coherent population in the two lowest states of a three level system of electronic subbands. The time-dependent absorption to the upper state is probed by midinfrared time-domain spectroscopy. For certain pump–probe delay times we observe in the intersubband absorption spectra typical signatures of quantum interference: regions with reduced or enhanced absorption.