Effective Hamiltonian for Excitons with Spin Degrees of Freedom

Starting from the conventional electron-hole Hamiltonian ${\cal H}_{eh}$, we derive an effective Hamiltonian $\tilde{\cal H}_{1s}$ for $1s$ excitons with spin degrees of freedom. The Hamiltonian describes optical processes close to the exciton resonance for the case of weak excitation. We show that straightforward bosonization of ${\cal H}_{eh}$ does not give the correct form of $\tilde{\cal H}_{1s}$, which we obtain by a projection onto the subspace spanned by the $1s$ excitons. The resulting relaxation and renormalization terms generate an interaction between excitons with opposite spin. Moreover, exciton-exciton repulsive interaction is greatly reduced by the renormalization. The agreement of the present theory with the experiment supports the validity of the description of a fermionic system by bosonic fields in two dimensions.Comment: 12 pages, no figures, RevTe

Kinetics of four-wave mixing for a 2D magneto-plasma in strong magnetic fields

We investigate the femtosecond kinetics of an optically excited 2D magneto-plasma at intermediate and high densities under a strong magnetic field perpendicular to the quantum well (QW). We assume an additional weak lateral confinement which lifts the degeneracy of the Landau levels partially. We calculate the femtosecond dephasing and relaxation kinetics of the laser pulse excited magneto-plasma due to bare Coulomb potential scattering, because screening is under these conditions of minor importance. In particular the time-resolved and time-integrated four-wave mixing (FWM) signals are calculated by taking into account three Landau subbands in both the valance and the conduction band assuming an electron-hole symmetry. The FWM signals exhibit quantum beats mainly with twice the cyclotron frequency. Contrary to general expectations, we find no pronounced slowing down of the dephasing with increasing magnetic field. On the contrary, one obtains a decreasing dephasing time because of the increase of the Coulomb matrix elements and the number of states in a given Landau subband. In the situation when the loss of scattering channels exceeds these increasing effects, one gets a slight increase at the dephasing time. However, details of the strongly modulated scattering kinetics depend sensitively on the detuning, the plasma density, and the spectral pulse width relative to the cyclotron frequency.Comment: 13 pages, in RevTex format, 10 figures, Phys. Rev B in pres

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

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

Polariton propagation in weak confinement quantum wells

Exciton-polariton propagation in a quantum well, under centre-of-mass quantization, is computed by a variational self-consistent microscopic theory. The Wannier exciton envelope functions basis set is given by the simple analytical model of ref. [1], based on pure states of the centre-of-mass wave vector, free from fitting parameters and "ad hoc" (the so called additional boundary conditions-ABCs) assumptions. In the present paper, the former analytical model is implemented in order to reproduce the centre-of-mass quantization in a large range of quantum well thicknesses (5a_B < L < inf.). The role of the dynamical transition layer at the well/barrier interfaces is discussed at variance of the classical Pekar's dead-layer and ABCs. The Wannier exciton eigenstates are computed, and compared with various theoretical models with different degrees of accuracy. Exciton-polariton transmission spectra in large quantum wells (L>> a_B) are computed and compared with experimental results of Schneider et al.\cite{Schneider} in high quality GaAs samples. The sound agreement between theory and experiment allows to unambiguously assign the exciton-polariton dips of the transmission spectrum to the pure states of the Wannier exciton center-of-mass quantization.Comment: 15 pages, 15 figures; will appear in Phys.Rev.

Excitonic and free-carrier polarizations of bulk GaAs studied by femtosecond coherent spectroscopy

The transient third-order polarization at the band gap of undoped and p-doped GaAs is investigated by spectrally and temporally resolved four-wave mixing. Excitonic and free-carrier contributions simultaneously excited within the bandwidth of the 100-fs pulses are clearly distinguished by their different spectral envelopes. The excitonic part dominates at carrier densities below 1016 cm-3 and shows a time evolution governed by exciton-free-carrier scattering and by many-body effects. At higher density, the free-carrier polarization has a strength similar to the exciton contribution and exhibits a spectrum resonant to the femtosecond pulses with a photon-echo-like temporal behavior. The data are analyzed by a numerical solution of the semiconductor Bloch equations including an ensemble Monte Carlo simulation of the scattering dynamics of the carriers. The theoretical model is in good agreement with the experimental results