A. Leitenstorfer (1), T. Elsaesser (2), F. Rossi (3), T. Kuhn (4), W. Klein (5),

1. Physik Department E 11, Technische Universität München, D-85748 Garching, Germany
2. Max-Born-Institut für Nichtlineare Optik und Kurzzeitspektroskopie, D-12489 Berlin, Germany
3. Fachbereich Physik, Phillips-Universität Marburg, D-35032 Marburg, Germany
4. Lehrstuhl für Theoretische Physik, Brandenburgische Technische Universität, D-03013 Cottbus, Germany
5. Walter-Schottky-Institut, Technische Universität München, D-85748 Garching, Germany

Nonequilibrium electrons generated by coherent optical excitation of GaAs are studied in a wide range of carrier density. The electron distribution is monitored via spectrally resolved band-to-acceptor luminescence after continuous-wave, picosecond, or femtosecond laser excitation. Our data demonstrate that the coherent coupling between the laser radiation and the interband polarization and its dephasing strongly influence the initial carrier distribution. The energetic width of carrier generation is broadened due to rapid phase-breaking scattering events during carrier generation. Theoretical results form a Monte Carlo solution of the semiconductor Bloch equations including on the same kinetic level coherent and incoherent phenomena show that the broadening of the electron distribution is introduced mainly in the generation process whereas the recombination of electrons with bound holes makes a minor contribution. The theoretical results are in quantitative agreement with the experimental data.

S. Haas (1), F. Rossi (1), and T. Kuhn (2)

1. Fachbereich Physik und Zentrum für Materialwissenschaften, Phillips-Universität Marburg, Renthof 5, 35032 Marburg, Germany
2. Lehrstuhl für Theoretische Physik, Brandenburgische Technische Universität, Postfach 101344, 03013 Cottbus, Germany

A generalized Monte Carlo method for the solution of the coupled set of kinetic equations for the distribution functions and the interband polarization is presented. The aim of this method is to combine the advantages of the description within a fully quantum mechanical picture with the power of the Monte Carlo technique for the treatment of stochastic processes. It is based on a decomposition of the kinetic equations in a coherent and an incoherent part. The former is integrated directly while the latter is sampled by means of a Monte Carlo simulation. This allows us to treat on the same kinetic level carrier thermalization and relaxation as well as dephasing processes. In particular, the problem of photogeneration and its theoretical description is discussed. The equations of motion including the relevant scattering contributions are derived and presented in a way that emphasizes the symmetry between distribution functions and polarization. The scattering terms for the polarization are discussed in detail. We show that some of the approaches commonly used fail in describing correctly the effect of carrier-carrier interaction in the low-density limit. By including terms that have the structure of "in-scattering" terms for the interband polarization, the experimentally observed features in the carrier dynamics are well described in the whole density range.

1. Institut für Technische Physik, Deutsche Forschungsanstalt für Luft- und Raumfahrt, Pfaffenwaldring 38-40, 70569 Stuttgart, Germany
2. Lehrstuhl für Theoretische Physik, Brandenburgische Technische Universität, Postfach 101344, 03013 Cottbus, Germany; Institut für Theoretische Physik II, Westfälische Wilhelms-Universität, Wilhelm-Klemm-Str. 10, 48149 Münster, Germany

The spatio-temporal dynamics of semiconductor lasers is studied theoretically on the basis of semiclassic laser theory. The carrier dynamics is described in a density-matrix approach and the coupled set of equations of motion for the active medium and the light field are derived. Several approximations related to separations of length and time scales are discussed, resulting in a hierarchy of model equations leading from microscopic to macroscopic levels of description. By numerically solving space-dependent coupled partial differential equations for the (complex) optical fields, the interband polarization and the charge carrier distribution functions on the various levels of the hierarchy the formation and longitudinal propagation of unstable transverse optical filamentary structures is analyzed in a model configuration for typical double-heterostructure multi-stripe and broad-area lasers. Spectral and spatial hole burning which is observed in the simulated carrier distributions reflects the interplay between stimulated emission and the relaxation dynamics of the carrier distributions as well as the polarization. Its details are strongly influenced by the momentum and density dependence of the microscopic relaxation rates. The transverse hole burning leads to complex spatio-temporal patterns in the macroscopic intensity picture. This complex spatio-temporal dynamic behavior in multi-stripe and broad-area lasers is analyzed by various theoretical tools which allows one to quantify the degree of complexity.

1. Max-Born-Institut für Nichtlineare Optik und Kurzzeitspektroskopie, D-12489 Berlin, Germany
2. Physik Department E11, Technische Universität München, D-85748 Garching, Germany
3. Institut für Theoretische Physik, Universität Stuttgart, D-70550 Stuttgart, Germany
4. Fachbereich Physik, Universität Marburg, D-35032 Marburg, Germany

1. Prog. Crystal Growth and Charact. 33, 41 (1996)

Coherent nonlinear polarizations and on-equilibrium distributions of hot electrons are studied in femtosecond experiments with bulk GaAs. Both excitonic and free-carrier components contribute to the third-order polarization close to the bandgap and show a distinctly different time behavior. Phase relaxation during the femtosecond photogeneration process leads to a significant broadening of the initial carrier distribution in comparison to the power spectrum of the optical pulses. The experimental results are in excellent agreement with a Monte Carlo solution of the semiconductor Bloch equations.

1. Institut für Technische Physik, Deutsche Forschungsanstalt für Luft- und Raumfahrt e.V., Pfaffenwaldring 38-40, 70569 Stuttgart, Germany
2. Lehrstuhl für Theoretische Physik, Brandenburgische Technische Universität, Postfach 101344, 03013 Cottbus, Germany

1. Phys. Rev. A 54, 3347 (1996)

Space-dependent Maxwell-Bloch equations are derived for the description of spatiotemporal dynamics of spatially inhomogeneous semiconductor lasers. The dynamics of the charge carriers is described in a density-matrix approach using a Wigner function representation. On this basis, the coupled set of equations of motion for the active medium and the space-dependent light field is derived. Based on typical length and time scales, approximations are performed to obtain a numerically tractabel problem. The many-body interactions give rise to space-dependent energy renormalizations. Coulomb enhancement, and scattering processes. The latter ones are considered in the form of momentum- and density-dependent microscopic relaxation rates due to carrier-carrier and carrier-phonon interaction for the carrier distribution functions and the polarization. For the spatial transport or the carriers an ambipolar diffusion diffusion model is derived.

O. Hess (1) and T. Kuhn (2)

1. Institut für Technische Physik, Deutsche Forschungsanstalt für Luft- und Raumfahrt e.V., Pfaffenwaldring 38-40, 70569 Stuttgart, Germany
2. Lehrstuhl für Theoretische Physik, Brandenburgische Technische Universität, Postfach 101344, 03013 Cottbus, Germany

The spatiotemporal dynamics of broad-area lasers is analyzed on the basis of a space- and momentum-dependent density-matrix approach. To this means the space-dependent Maxwell-Bloch equations for the semiconductor laser (derived in our preceding paper I) are solved by direct numerical integration. The space and momentum resolved dynamics of the active semiconductor medium, described by microscopic charge-carrier distributions and nonlinear polarization functions, are treated self-consistently with the spatiotemporal dynamics of the light field. Carrier transport dynamics are approximated on the basis of an ambipolar diffusion approximation consistent with the microscopic processes. Boundary-influenced macroscopic waveguiding properties of typical conventional as well as tapered broad-area laser cavities are taken into account. The dynamics of the formation and longitudinal propagation of unstable transverse optical filamentary structures are analyzed. Simultaneous spectral and spatial hole burning with dynamical spatiospectral variations on ultrashort (ps and sub-ps) time scales are observed in the charge-carrier distributions, reflecting the interplay between stimulated emission and the relaxation dynamics of the carrier distributions as well as the polarization. The transverse hole burning leads to complex spatiotemporal patterns in the macroscopic intensity picture with different optical frequencies associated with various locations of the modelike near field patterns.

1. Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
2. Institut für Theoretische Physik II, Westfälische Wilhelms-Universität, Wilhelm-Klemm-Straße 10, 48149 Münster, Germany

The dynamics of intersubband transitions in quantm wires due to Coulomb interaction is studied in a quantum kinetic model. We find a significant enhancement of the transition rate at short times due to energy-time uncertainty which enables non-resonant transitions in the femtosecond region.

1. Institut für Theoretische Physik und Synergetik, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
2. Institut für Technische Physik, DLR Stuttgart, Pfaffenwaldring 38-40, 70569 Stuttgart, Germany
3. Institut für Theoretische Physik II, Westfälische Wilhelms-Universität, Wilhelm-Klemm-Straße 10, 48149 Münster, Germany

We present a theoretical analysis of different aspects associated with the microwave generation due to charge oscillations in an asymmetric doubel quantum well structure. The generation of the electron wave packet is described in terms of a multiband version of the semiconductor Bloch equations. The signal decays due to carrier-carrier and carrier-phonon scattering processes, which are taken into account by a microscopic model. Coherent phonons lead to a density dependent frequency shift.

A. P. Heberle (1), J. J. Baumberg (1), E. Binder (2), T. Kuhn (3),
K. Köhler (4), and K. H. Ploog (5)

1. Hitachi Cambridge Laboratory, Cambridge CB 3 0HE, U.K.
2. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
3. Institut für Theoretische Physik II, Westfälische Wilhelms-Universität, 48149 Münster, Germany
4. Fraunhofer-Institut für Angewandte Festkörperphysik, 79108 Freiburg, Germany
5. Paul-Drude-Institut für Festkörperelektronik, 10117 Berlin, Germany

We demonstrate femtosecond coherent control of excitons in quantum wells with phase-locked pairs of 100 fs infrared pulses. Copolarized pump pulses allow coherent control of exciton density and coherent destruction of excitons within a few hundred femtoseconds of their creation. This technique thus promises to avoid speed penalties in devices associated with long-lived persistent carrier populations. Cross-polarized pump pulses allow coherent control of spin dynamics and conversion of unpolarized excitons into spin polarized ones. Carrier density and spin are determined, respectively, from the differential reflection and from the Faraday rotation of a third probe pulse. The experimental results are in good agreement with calculations based on the semiconductor Bloch equations.

1. Istituto Nazionale di Fisica della Materia, Dipartimento di Scienza dei Materiali, Università di Lecce, Via Arnesano, 73100 Lecce, Italy
2. Istituto Nazionale di Fisica della Materia, Dipartimento di Fisica, Università di Modena, Via Campi 213/a, 42200 Modena, Italy
3. Centre d'Electronique et de Micro-optoélectronique de Montpellier, (CNRS UMR 5507) Université Montpellier II, 34095 Montpellier Cedex 5, France
4. Institut für Theoretische Physik II, Westfälische Wilhelms-Universität, Wilhelm-Klemm-Str. 10, 48149 Münster, Germany

Thermal conductivity and Lorenz number of charge carriers are investigated by using the correlation function approach. At thermodynamic equilibrium, the case of one-dimensional ballistic regime under degenerate conditions is found to exhibit a universal thermal conductance . The ballistic regime under classical conditions exhibits dispersion curves for the thermal conductivity and the Lorenz number associated with different time scales proper of the classical microscopic system. Under hot-carrier conditions and in the diffusive regime, the definition of thermal conductivity and Lorenz number is generalized through the noise temperature concept. In its range of validity, it provides exact values and predicts and anisotropic behaviour of the above kinetic coefficient with respect to the direction of the applied field. Calculations for the case of n-Si at 300 K evidence a dramatic decrease, for more than two orders of magnitude, of the longitudinal values at the highest fields of 100 kV/cm.

1. Istituto Nazionale di Fisica della Materia, Dipartimento di Scienza dei Materiali, Università die Lecce - via Arnesano, 73100 Lecce, Italy
2. Institut für Theoretische Physik II, Westfälische Wilhelms-Universität, 48149 Münster, Germany
3. Centre d' Electronique et de Micro-optoélectronique de Montpellier (CNRS UMR 5507) Université Montpellier II - 34095 Montpellier, Cedex 5, France

A universal thermal conductance of charge carriers is rigorously derived within a correlation-function formalism. Similar to the case of the universal electrical conductance this result pertains to one-dimensional, ballistic, and degenerate conditions for non-interacting particles.

V. M. Axt, K. Victor, and A. Stahl

Institut für Theoretische Physik B, Rheinisch Westfälische Technische Hochschule Aachen, Sommerfeldstraße. 52056 Aachen, Germany

The influence of a phonon bath on the dynamics of the many-body density matrice relevant for the nonlinear optical response of semiconductors ist studied. It ist shown that, as in the phonon-free case, only a finite set of electronic density matrice is needed to describe the optical response in a experiment. However, to obtain a closed set of equations of motion on the level additional truncation concepts habe to be introduced in order ro decouple the infinite hierarchy of phonon-assisted density matrices. Relations characteristic of intrinsic systems, that have previously been derived to reduce the number of independent dynamical varables in the phonon-free case, are generalized. While in a coherent system the optical response is completely determined by transition-type varibales, under the influense of a phonon bath occupation desities can also become independent dynamical quantities. Numerical results for a simple one-dimensional model are presented. Memory effects and dephasing induced by the electron-phonon coupling are discussed for all relevant electronic density matrices. The pump-probe signal for excitation in the spectral region of the biexcition is analvzed. The respective contributions of two processes for the generation of biexcitons, via twophoton transitions (TPT's) or from previously generated exciton densities, to the microscopic dynamics are identified. The second process yields a signal only due to the coupling to the phonon bath and turns out to contribute considerably less than the TPT under all conditions studied in this paper.

1. M. Axt, G. Bartels, and A. Stahl

Institut für Theoretische Physik B, Rheinisch Westfälische Hochschule Aachen, Sommerfeldstrasse, 52056 Aachen, Germany

The validity of the semiconductor Bloch equations (SBE) depends on the approximate decomosition of an intraband correlation function into a product of interband transition densities. We analyze the consequences of this approximation on the intraband dynamics of an optically excited semiconductor. As a special example where the SBE treatment becomes questionable we consider the THz emission of a narrow band superlattics in a static bias field. A comparison of the second order SBE solution with arigorous second order treatment of this system helps one identify the weak points of the SBE approach and understand the physical background of its failure.

K. Victor (1), V. M. Axt (1), G. Bartels (1), A. Stahl (1). K. Bott (2), and P. Thomas (2)

1. Institut für Theoretische Physik B, Rheinisch Westfälische Technische Hochschule Aachen, Sommerfeldstrasse, 52056 Aachen, Germany
2. Fachbereich Physik und Wissenschaftliches Zentrum für Materialwissenschaften, Philipps-Universität Marburg, Renthof 5, 35032 Marburg, Germany

It is shown how a phenomenological few-level descrition of coherent semiconductor optics is related to microscopic density-matrix theory. It turns out that the few-level dynamics is not obtained by simply projecting the microscopic dynamics onto a suitable chosen set of energy eigenstates. Therefore, a new hierarchy of microscopic densities is introduced with the property that their expansion in terms of energy eigenstates yields the level dynamics. The transformation rules between the few-level variables and the traditional density matrices are established. The problem of incorporating the coupling to continua into a few-level model ist discussed. A refined few-level model approximating the influence of the continua by modified couplings between the levels ist presented. The modified couplings turn out to be similar in structure to phenomenologically introduced refinements like local fields. The analysis makes clear that intuitively similar approximations have a different meaning when applied in the context of a few-level model or a truncated microscopic hierarchy.