We present a microscopic many-particle theory for the dephasing of coherent intersubband excitations in semiconductor quantum wells including carrier-carrier and carrier-phonon scattering and light propagation effects. The contributions of many-particle processes are nonadditive and thus cannot be treated separately. It is shown that due to nondiagonal correlation contributions, scattering rates alone cannot be taken as a measure for the dephasing of the intersubband polarization. Surprisingly, radiative damping is found to be important even at moderate carrier densities. Calculated absorption spectra are in excellent agreement with experiments on a high-quality sample.

Radiative coupling of resonantly excited intersubband transitions in GaAs/ AlGaAs multiple quantum wells can have a strong impact on the coherent nonlinear optical response, as is shown by phase and amplitude resolved propagation studies of ultrashort electric field transients. Upon increasing the driving field amplitude, strong radiative coupling leads to a pronounced self-induced absorption, followed by a bleaching due to the onset of delayed Rabi oscillations. A many-particle theory including light propagation effects accounts fully for the experimental results.

The interaction of electrons with LO phonons provides an important mechanism of optical dephasing and carrier scattering for the two-dimensional electron gas in semiconductor quantum wells. In this paper, the corresponding ultrafast nonlinearities for off-resonant and resonant intersubband excitations are investigated. Quantum kinetic effects of the electron-phonon interaction and the corresponding violation of the microscopic energy conservation yield a qualitative different picture compared to the standard Markovian theory, if the phonon energy is larger than the intersubband-gap energy.In ultrafast optics, a two-level system is a well-known model system for nonlinear effects ranging from an instantaneous response of the induced dipole to the shape of the light pulse ͑adiabatic following or Kerr nonlinearity͒ for offresonant excitation to saturation effects ͑Pauli blocking͒ and Rabi flopping for resonant excitation. 1 Similar effects can also be observed for transitions between two bands in semiconductors. 2 However, compared to an atomic system such coherent optical nonlinearities in a semiconductor can be modified or completely suppressed by many-body effects, such as electron-phonon ͑el.-ph.͒ and electron-electron interaction. 3-5 For example, modified Rabi oscillations have been observed in semiconductor bulk material 6,7 as well as in semiconductor nanostructures, like quantum dots 8,9 and quantum wells. 10 Recently, experimental progress in the infrared and terahertz ͑THz͒ regime allows the extension of these studies to intersubband ͑ISB͒ transitions in a twodimensional electron gas in a semiconductor quantum well ͑QW͒. 11,12 More experimental observations of ultrafast optical nonlinearities in this low energy regime are expected to be published in the near future.In this paper, we aim at the importance of the quantum kinetics of the el.-ph. interarction for ISB nonlinearities and evaluate a theory of the optically induced ISB response in a deep semiconductor QW. The analysis includes the energetically lowest two subbands. Due to doping the subbands are populated with a two-dimensional electron gas forming a Fermi-distribution in the ground state, compare. Fig. 1. The optical field can be used to induce ISB transitions between both subbands ͑solid arrow͒. Material parameters, such as the subband energy ͑k͒ were taken from a GaAs/ AlGaAs QW. Nonparabolicity effects of the conduction band lead to different effective masses of each subband. 13 The masses can be calculated according to Ref. 16. As a first approach to manyparticle scattering and dephasing mechanisms for ISB transitions in nonlinear optics we discuss the coupling of the electronic system to a bath of optical bulk phonons, which are not confined by the QW, on a quantum kinetic ͑non-Markovian͒ and on a semiclassical ͑Markovian͒ level. Such a treatment of the phonons has already been used for quantum dots. 14,15 Quantum kinetic ͑el.-ph.͒ scattering was found to be important for ultrafast nonlinear optical excitations in bulk material and nanostruc...

We present a theory of the optical line shape of coherent intersubband transitions in a semiconductor quantum well, considering non-Markovian LO-phonon scattering as major broadening mechanism. We show that a quantum kinetic approach leads to additional polaron resonances and a resonance enhancement for gap energies close to the phonon energy.Non-Markovian electron-phonon scattering was found to dominate in bulk material on short time scales [1,2] and in the tails of the optical spectra [3]. Over the last years, the optical properties of intersubband transitions in semiconductor quantum wells were subject of research [4,5], however, the quantum kinetics of the electron-phonon interaction has not been investigated so far. Our quantum kinetic calculations of the line shape of semiconductor quantum well intersubband transitions are carried out in a density matrix formalism, where 12 k ρ , is the intersubband coherence between subband 1 and 2, while 1 k f , and 2 k f , are the occupations in the lower and upper subband. As the discussion is restricted to linear optics, i k f , in both subbands are given by static Fermi-Dirac distributions. The optical line shape is determined by the contribution of the transitions at all wavenumbers k . We use material parameters of a GaAs/Al 0 35 . Ga 0 65. As quantum well with a carrier concentration 11 e 6 10 n = × cm 2 − . The potential is assumed to be infinitely deep, further details like the Hamiltonian are given in Ref. [6]. The effective masses of the subbands and the gap energy gap ε between the subbands were calculated according to Ref. [7]. For the phonons a bath approximation is made, where the Bose-Einstein distribution q n is determined by the sample temperature T and a phonon energy of 36 meV. Using the Heisenberg equations of motion and a correlation expansion for higher many particle correlations [8], one obtains the equation of motion for the intersubband coherence. In the coherent part of the equation of motion, the intersubband dispersion

ErratumLight propagation-and many-particle-induced non-Lorentzian lineshapes in semiconductor nanooptics [phys. stat. sol. (b) 234, 155 (2002)]

We outline a theoretical description of the absorption linewidth of quantum well intersubband transitions by solving Maxwell's equations for a non-local susceptibility including many particle effects. We show that the intersubband absorption results from a complex interplay between mean-field effects, dephasing contributions and light propagation effects, all being very sensitive to subband dispersion.1 Introduction Optical absorption results from the interplay of light propagation and energy dissipation in the material. In coherent optics, dissipation is caused by the optical dephasing of the dipole density. In this paper, we discuss the absorption of a two-band intersubband transition [1] (interband and intersubband transitions are compared in Fig. 1a, b) in a multiple quantum well system (cf. Fig. 1c). The calculation of the absorption lineshape is composed of two parts: the first involves the determination of the source of electromagnetic emission, i.e. the dipole density P given by the contributions of all quantum wells, the second consists of finding the generated fields in the geometry of interest by solving Maxwell's equations (Fig. 1c). In the following, the absorption is defined as the part of the spectral intensity which remains inside the sample, where E in (E out ) is the inward (outward) travelling field:

Dedicated to Professor Dr. Roland Zimmermann on the occasion of his 60th birthdayThe occurrence of non-Lorentzian lineshapes is analyzed for a variety of nanooptical semiconductor systems such as quantum wells and quantum dots. Their origin is traced back to light-matter interaction (light propagation) and many-particle correlations (electron-electron and electronphonon interaction). 157

No abstract