Influence of Coulomb interactions on quantum coherence in quantum dots

Jakob Houmark-Nielsen1, Antti-Pekka Jauho1, Torben R. Nielsen2 and Jesper Mørk2 1 MIC - Department of Micro and , Technical University of , DTU, DK-2800 Lyngby, Denmark. 2 COM - Department of Communications, Optics & Materials, Technical University of Denmark, DTU, DK-2800 Lyngby, Denmark.

Introduction to Computational method The subject of slowing down light in a highly dispersive media The optical response is found by solving the Semiconductor has gained enormous attention since Lene Hau et al. reported on Bloch equations in the Hartree-Fock approximation using a light propagating at 17 m/s through a vapour of ultra cold Na fourth order Runge-Kutta routine. atoms[1]. Slow-down is achieved through a quantum interference phenomenon called Electromagnetically Induced Transparency (EIT) that occurs in three-level systems. The EIT principle relies on a coupling and probe laser driving separate atomic transitions. The medium is rendered transparent to the probe beam due to (Fano-like) destructive interference between the different decay channels of the system. According to the Kramers-Kronig relation a change in the imaginary part of the susceptibilty c (absorption) is also reflected in the real part.

Off-diagonal scattering terms Sn1n2 are approximated by a 12 -1 dephasing rate gd=1x10 s at 200 K. Diagonal terms representing collision induced particle exchange processes, are mimicked by a population relaxation towards quasiequilibrium Fermi-Dirac functions. The positive slope of Re(c) translates into a slower group velocity We investigate steady state situations; i.e., using a drive pulse through the relation: , temporally several times wider (FWHM) than the -1 dephasing time (gd ) of the where w is the frequency of the light, k is the wavevector, and system. is the refractive index.

Quantum dot model Results We investigate a ”ladder” scheme. Calculating the optical We consider conical InAs quantum dots (QD) on a wetting layer response using two models: The ”atomic” model, without many- (WL) sandwiched between GaAs slabs. The system consist of particle interactions, and the semiconductor model, where states bound to the QD and delocalized states extended in the Coulomb interactions are included. Continuum electron states quantum well comprised of the WL. These states are found as the Bound solution to the one band Schödinger eqution for the envelope electron states wpump wavefunction yn in the effective mass approximation:

wprobe

Bound hole Holes: Electrons: states

Continuum hole states

Ladder scheme Continuum states

Bound state

References In contrast to other findings[2] we do not see a shift in the drive [1]: L. V. Hau et al., 397, 594 (1999). power required to obtain slow light. Only the probe transition is [2]: S. Michael et al., App. Phys. Lett. 89, 181114 (2006). Coulomb enhanced, resulting in a larger slow-down factor.