Collective Dynamics of Electrons in Quantum Wells

The goal of this work is to explore the dynamics of electrons in quantum wells when driven by THz fields with weak and strong intensities. Though the system is apparently trivially simple--physicists solve the problem of the energy levels of an electron confined to a finite square well in their sophomore or junior year as undergraduates --there is a huge amount of fascinating, poorly-understood, and technologically important physics in real semiconductor quantum wells doped with electrons. Let us take as the characteristic energy scale E10, the spacing between the ground and first excited state which you would calculate based on undergraduate quantum mechanics. The new aspects of the problem are:

1. There are many electrons in the quantum wells we study. The Coulomb repulsion between electrons is comparable to E₁₀, so many-body effects cannot be treated perturbatively.
2. With the free-electron laser, we have access to THz photon energies and THz electric field energies which are comparable to E₁₀. ( The characteristic THz electric field energy is eE <z>, where e is the electronic charge, E is the strength of the THz field, and is the dipole matrix element between, for example, the ground and first excited state of a quantum well).
3. The linewidth of intersubband transitions, a measure of the strength of dissipative processes, is one to two orders of magnitude smaller than E₁₀.

Accomplishments:

• Electrons in quantum wells can emit harmonics when driven by THz radiation, and the nonlinear susceptibilities associated with this emission are up to eight orders of magnitude larger than those of bulk GaAs.¹
• The lifetime electrons in excited subbands in quantum wells can be as long as 1 ns, but decreases sharply with intensity and temperature.²
• The intersubband absorption can be "undressed" upon excitation with intense THz radiation.³
• The linewidth of intersubband transitions is determined by many-body effects, in agreement with a new theory based on time-dependent density functional theory.[submitted]

Current and future efforts--bifurcations and chaos in a manifestly quantum system

This research is sponsored, in part, by the NSF.

Visit our THz electro-optics page for more quantum well physics.

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