Ab-initio calculation of optical absorption in semiconductors: A density-matrix description

We show how to describe Coulomb renormalization effects and dielectric screening in semiconductors and semiconductor nanostructures within a first-principles density-matrix description. Those dynamic variables and approximation schemes which are required for a proper description of dielectric screening are identified. It is shown that within the random-phase approximation the direct Coulomb interactions become screened, with static screening being a good approximation, whereas the electron-hole exchange interactions remain unscreened. Differences and similarities of our results with those obtained from a corresponding GW approximation and Bethe-Salpeter equation Green's function analysis are discussed.Comment: 10 pages, to be published in Physical Review

Theory of exciton-exciton correlation in nonlinear optical response

We present a systematic theory of Coulomb interaction effects in the nonlinear optical processes in semiconductors using a perturbation series in the exciting laser field. The third-order dynamical response consists of phase-space filling correction, mean-field exciton-exciton interaction, and two-exciton correlation effects expressed as a force-force correlation function. The theory provides a unified description of effects of bound and unbound biexcitons, including memory-effects beyond the Markovian approximation. Approximations for the correlation function are presented.Comment: RevTex, 35 pages, 10 PostScript figs, shorter version submitted to Physical Review

Collective oscillations driven by correlation in the nonlinear optical regime

We present an analytical and numerical study of the coherent exciton polarization including exciton-exciton correlation. The time evolution after excitation with ultrashort optical pulses can be divided into a slowly varying polarization component and novel ultrafast collective modes. The frequency and damping of the collective modes are determined by the high-frequency properties of the retarded two-exciton correlation function, which includes Coulomb effects beyond the mean-field approximation. The overall time evolution depends on the low-frequency spectral behavior. The collective mode, well separated from the slower coherent density evolution, manifests itself in the coherent emission of a resonantly excited excitonic system, as demonstrated numerically.Comment: 4 pages, 4 figures, accepted for publication in Physical Review Letter

Ultrafast Coulomb-induced dynamics of 2D magnetoexcitons

We study theoretically the ultrafast nonlinear optical response of quantum well excitons in a perpendicular magnetic field. We show that for magnetoexcitons confined to the lowest Landau levels, the third-order four-wave-mixing (FWM) polarization is dominated by the exciton-exciton interaction effects. For repulsive interactions, we identify two regimes in the time-evolution of the optical polarization characterized by exponential and {\em power law} decay of the FWM signal. We describe these regimes by deriving an analytical solution for the memory kernel of the two-exciton wave-function in strong magnetic field. For strong exciton-exciton interactions, the decay of the FWM signal is governed by an antibound resonance with an interaction-dependent decay rate. For weak interactions, the continuum of exciton-exciton scattering states leads to a long tail of the time-integrated FWM signal for negative time delays, which is described by the product of a power law and a logarithmic factor. By combining this analytic solution with numerical calculations, we study the crossover between the exponential and non-exponential regimes as a function of magnetic field. For attractive exciton-exciton interaction, we show that the time-evolution of the FWM signal is dominated by the biexcitonic effects.Comment: 41 pages with 11 fig

Ultrafast Depopulation of a Quantum Dot by LA-phonon-assisted Stimulated Emission

We demonstrate ultrafast \emph{incoherent} depopulation of a quantum dot from above to below the transparency point using LA-phonon-assisted emission stimulated by a red-shifted laser pulse. The QD is turned from a weakly vibronic system into a strongly vibronic one by laser driving which enables the phonon-assisted relaxation between the excitonic components of two dressed states. The depopulation is achieved within a laser pulse-width-limited time of 20~ps and exhibits a broad tuning range of a few meV. Our experimental results are well reproduced by path-integral calculations

Renormalized Bosonic Interaction of Excitons

An effective bosonic Hamiltonian of $1s$ excitons with ``spin'' degrees of freedom in two dimension is obtained through a projection procedure, starting from a conventional electron-hole Hamiltonian ${\cal H}_{eh}$. We first demonstrate that a straightforward transformation of ${\cal H}_{eh}$ into a Hamiltonian of bosonic excitons does not give the two-body interaction between an ``up-spin'' exciton and a ``down-spin'' exciton, which are created by the left- and right-circularly polarized light beams, respectively. We then show that this interaction is generated through a projection procedure onto the subspace spanned by $1s$ excitons, as a renormalization effect coming from higher exciton states. The projection also renormalizes the interaction between $1s$ excitons with the same spins by a large amount. These renormalization effects are crucial for the polarization dependence of the optical responses from semiconductors. The present theory gives the microscopic foundation of the phenomenology that was successfully applied to the analysis of four-wave mixing experiments in GaAs quantum wells strongly coupled to the radiation field in a high-Q micro cavity.Comment: 2 figure

Resonant nature of phonon-induced damping of Rabi oscillations in quantum dots

Optically controlled coherent dynamics of charge (excitonic) degrees of freedom in a semiconductor quantum dot under the influence of lattice dynamics (phonons) is discussed theoretically. We show that the dynamics of the lattice response in the strongly non-linear regime is governed by a semiclassical resonance between the phonon modes and the optically driven dynamics. We stress on the importance of the stability of intermediate states for the truly coherent control.Comment: 4 pages, 2 figures; final version; moderate changes, new titl

Probing Interband Coulomb Interactions in Semiconductor Nanocrystals with 2D Double-Quantum Coherence Spectroscopy

Using previously developed exciton scattering model accounting for the interband, i.e., exciton-biexciton, Coulomb interactions in semiconductor nanocrystals (NCs), we derive a closed set of equations for 2D double-quantum coherence signal. The signal depends on the Liouville space pathways which include both the interband scattering processes and the inter- and intraband optical transitions. These processes correspond to the formation of different cross-peaks in the 2D spectra. We further report on our numerical calculations of the 2D signal using reduced level scheme parameterized for PbSe NCs. Two different NC excitation regimes considered and unique spectroscopic features associated with the interband Coulomb interactions are identified.Comment: 11 pages, 5 figure