Project 5

Quantum Wave Packets in One and Two Dimensions

Introduction

This project explores tunneling of quantum wave packets in one dimension through a single potential barrier or a double barrier structure where resonant tunneling can be observed at special energies. In quasi-one-dimensional wire with the spin-orbit coupling one can observe spin precession and spin decoherence studied in current research on spintronics [1].

Part I for both PHYS460 and PHYS660 students

By numerically solving the time-dependent Schrödinger equation in one spatial dimension,

Failed to parse (unknown function "\fraction"): {\displaystyle \frac{\hbar^2}{2m} \frac{\partial^2 \Psi}{\partial x^2} + V(x) \Psi(x) = i\hbar \fraction{\partial \Psi}{\partial t} }

study reflection and transmission of a quantum wave packet from a barrier for which the potential energy is greater than the kinetic energy of the incident wave packet.

References

• [1] D. D. Awschalom and M. E. Flatté, Challenges for semiconductor spintronics, Nature Physics 3, 153 (2007).
• [2] B. K. Nikolić, L. P. Zarbo, and S. Welack, Transverse spin-orbit force in the spin Hall effect in ballistic quantum wires, Phys. Rev. B 72, 075335 (2005).[PDF]
• [3] * B. K. Nikolić, L. P. Zarbo, and S. Souma, Spin currents in semiconductor nanostructures: A nonequilibrium Green function approach, Chapter 24, page 814-866 in Volume I of The Oxford Handbook of Nanoscience and Technology: Frontiers and Advances, edited by A. V. Narlikar and Y. Y. Fu (Oxford University Press, Oxford, 2010); also available as arXiv:0907.4122.
• [4] S. A. Crooker and D. L. Smith, Imaging spin flows in semiconductors subject to electric, magnetic, and strain fields, Phys. Rev. Lett. 94, 236601 (2005). [PDF]