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Physical review. B, Condensed matter

Coherent optics for pumping near the absorption edge

Stephan Glutsch, Ralf Zimmermann

Published Mar 15, 1992• 24 citations

Abstract

The optical properties of a semiconductor pumped near the 1s exciton resonance are studied. The equation of motion for the density matrix in the Hartree-Fock approximation is traced back to the Bloch equation, well known from two-level systems. The essential difference, however, is the coupling of different wave vectors via the Coulomb potential. Principal features of the different stationary solutions are discussed. For a closer inspection of stability, we calculate the response to a smooth switchon of the pump field. For pump frequencies above the 1s exciton, the system follows first adiabatically the pulse shape, showing a blueshift and a slight increase of the oscillator strength as in the off-resonant case. The system jumps later into a second solution characterized by optical gain below the pump frequency, related to complete saturation (excitonic insulator). The major objective of our paper is to provide a numerical solution to the equation of motion in the Hartree-Fock approximation and to compare the results to those obtained by stationary considerations.

DOI: 10.1103/physrevb.45.5857

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The optical properties of a semiconductor pumped near the 1s exciton resonance are studied. The equation of motion for the density matrix in the Hartree-Fock approximation is traced back to the Bloch equation, well known from two-level systems. The essential difference, however, is the coupling of different wave vectors via the Coulomb potential. Principal features of the different stationary solutions are discussed. For a closer inspection of stability, we calculate the response to a smooth switchon of the pump field. For pump frequencies above the 1s exciton, the system follows first adiabatically the pulse shape, showing a blueshift and a slight increase of the oscillator strength as in the off-resonant case. The system jumps later into a second solution characterized by optical gain below the pump frequency, related to complete saturation (excitonic insulator). The major objective of our paper is to provide a numerical solution to the equation of motion in the Hartree-Fock approximation and to compare the results to those obtained by stationary considerations.

An excitonic approach to the ultrafast optical response of confined semiconductors at elevated densities below the Mott transition is presented. The theory is valid from the coherent regime, where coherent excitonic transitions and biexcitons dominate, to the incoherent regime, where excitonic occupations dominate. Numerical simulations of the

1s

exciton dynamics during intense circularly polarized pump pulses in two different Coulomb-interaction regimes are performed for two-dimensional semiconductors: Moderate Coulomb interaction is compared with dominating Coulomb interaction with respect to the light-matter interaction strength. The different many-body contributions are disentangled and it is found, that excitonic Rabi oscillations in the Coulomb-dominated regime are considerably less strong. By also comparing circular and linear excitation in a MoSe

_2

monolayer, it is found, that linear excitation creates a regime, where excitonic Rabi oscillations are almost completely suppressed.

Ultrafast pump-probe measurements evidence the dynamical Stark splitting in the exciton absorption spectrum of a single semiconductor quantum well. The intensity of the Stark sidebands in the spectrum is comparable to the linear absorption and their separation scales as the pump field amplitude. In the time domain the Rabi oscillations are observed. The semiconductor Bloch equations solved in the Hartree-Fock approximation demonstrate that the coherent exciton-light coupling dominates over the many-body dephasing.

A comprehensive numerical study of the optical Stark effect and associated phenomena in semiconductors is presented. The results are obtained from numerical solutions of the full semiconductor Bloch equations for bulk and quantum-well structures. Coherent oscillations, the optical Stark effect, and adiabatic following, i.e., ultrafast bleaching and recovery of the exciton, are discussed. The relative importance of the different contributions in the semiconductor Bloch equations is identified. Optical-absorption spectra are computed for different exciton dephasing models and a large variety of pump-probe excitation parameters.

The form invariant coherent pulse propagation in semiconductors excited at 1s-exciton resonance is studied analytically using the reduced semiconductor Maxwell-Bloch equations. The sech-shaped pulse solution for excitonic self-induced transparency (SIT) is presented, showing significant difference in comparison with the well known SIT solution for non-interacting two-level systems. In contrast to 2π pulses in atomic systems, the phenomenon of SIT of interacting excitons in semiconductors occurs for the pulses of area 1.07π. Possible applications of the SIT solitons in semiconductor all-optical switching devices are discussed.