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Polarization driven exciton dynamics in asymmetric nanostructures

Polarization driven exciton dynamics in asymmetric nanostructures. Margaret Hawton, Lakehead University Marc Dignam, Queens University Ontario, Canada. Outline. Excitons with a dipole moment are created by a laser pulse, giving polarization P inter .

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Polarization driven exciton dynamics in asymmetric nanostructures

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  1. Polarization driven exciton dynamics in asymmetric nanostructures Margaret Hawton, Lakehead University Marc Dignam, Queens University Ontario, Canada

  2. Outline • Excitons with a dipole moment are created by a laser pulse, giving polarization Pinter. • This results in a diffraction grating and an internal electric field, E (Pintra). • Simulation retains inter and intraband coherence, results shown are for a BSSL.

  3. SWM Signal, etc x 2k2- k1 z FWM Signal y k2 (probe) k1 (pump) THz emission Ultrafast experiments PP Signal

  4. Edc CB - wc Laser pulse G (dipole mom.) + QW made asymmetric by Edc Energy or frequency n=2 n=1 Egap VB

  5. G22 - + md Biased SC Superlattice (BSSL) energy or frequency m=2 w2 w0 Edc d

  6. - - - wB wc Laser pulse <G> + Biased SC Superlattice (BSSL) frequency (Stark ladder) m=2 m=1 m=0 m=-1 Edc d

  7. Bloch Oscillations of dipole moment (QM interference)

  8. wB G-1 -1 G22 G22 wB G00

  9. x,y K z H-like binding lowers below free e-h pair. Exciton: bound e and h in 2D H-like state, C of M wave vector K m=1 1s - + 2a0

  10. Linear response (note H-like binding) wc=w0

  11. x,y 2k2-k1= K-3 FWM Signal z k2 2p/|k2-k1| + harmonics k1/k2interference: the polarization grating

  12. thus Ks are discrete

  13. Inter and intraband polarization

  14. PZW (multipolar) Hamiltonian which we write as:

  15. Dipole approximation Hamiltonian is exact, P is approximate, includes self-energy.

  16. EM field

  17. x ------- +++++++ Kz Kz p/L L longitudinal/transverse Pintra K L ~.2mm l >1mm Kz >> K z Pintra For GaAs/Ga.7Al0.3As (67A/17A) 30 period superlattice

  18. - + -k k - + eh-pair H-like exciton PSF H-like excitons are(approximate) quasibosons.

  19. HP exciton dynamics To solve numerically, must take expectation value.

  20. PSF~ n/n0 n= exciton areal density =109 to 1010 cm-2 n0 = 1/pa02= 2x1011 cm-2 n/n0 < 0.1 Will omit PSF in numerical calculations here.

  21. Can solve to any definite order in Eopt etc, etc

  22. but solving to any finite order isn’t good enough - experiments show m peaks oscillate Lyssenko et al PRL 79, 301 (1997)

  23. Need infinite order, factored, like SBEs Retains exciton-exciton correlations, no biexcitons.

  24. with phenomenological decay

  25. Convergence: n0=3 (dash), 5(dot) and 13 (solid) FWM SWM EWM

  26. Origin of peak oscillations is quantum interference + higher order processes

  27. back to PSF Work on PSF in the exciton basis is in progress.

  28. Summary • Our model is a system of excitons described by m and K, driven and scattered by eE=D-P. • Infinite order calculations retain exciton-exciton correlations and show observed oscillations due to internal field, P/e. • The chief merit of our approach is sufficient simplicity for numerical work and a direct connection to the physics.

  29. Acknowledgements • Collaborator: Marc Dignam, Queens University • Financial support: NSERC Canada

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