Schottky Barrier Diode

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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 Nanotechnology, Technical University of Denmark, DTU, DK-2800 Lyngby, Denmark. 2 COM - Department of Communications, Optics & Materials, Technical University of Denmark, DTU, DK-2800 Lyngby, Denmark. Introduction to slow light 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., Nature 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..

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Card Appendix Quantum Concepts
1 Physics 310 Card Appendix Quantum Concepts Table of Contents 0. Blackbody Radiation 2 3. Normalize 2 4. Angular Momentum 3 4. Hydrogen 4 5. Wavefunction 4 6. Photoelectric Effect 5 7. Lowering Operator 5 8. Schrodinger's Cat 6 9. Famous Physicists 6 9.1 Vera Rubin 6 9.2 Lene Hau 7 9.3 Fabiola Gianotti 7 9.4 Maria Goeppert-Mayer 8 10. Entanglement 8 11. Spooky Action at a Distance 9 12. Raising Operator 9 14. Tunneling 10 25. CERN 10 2 0. Blackbody Radiation: Blackbody radiation occurs when light waves hit a black body (such as a star) and releases a different type of light wave that depends on the particular black body. Classical physics expected that the intensity of radiation would increase as the wavelength of the emitted light was smaller, but in reality, the radiation followed the curves below it. Max Planck found out that energy can exist in a very small packet, and in doing so, he was able to adjust the theory so that the theoretical curves matched the actual curves 3. Normalize: A particle must be found somewhere in space. This relationship is represented by the above equation. This equation means that the probability of finding a wavefunction is 1, just as the probability of you rolling a 1,2,3,4,5 or 6 on a 6 sided die being 1. If you normalize a wave function at some time t0 , then it will be normalized for all t. 3 4. Angular Momentum: Angular momentum (L) is conversed just like classical linear momentum and it is the product of the moment of inertia and angular velocity.
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