Greenaway, Mark Thomas
(2010)
Single particle and collective dynamics in periodic potentials.
PhD thesis, University of Nottingham.
Abstract
In this thesis, we describe, both semiclassically and quantum mechanically, the single-particle and collective dynamics of electrons and ultracold atoms moving through periodic potentials.
Firstly, we explore collective electron dynamics in superlattices with an applied voltage and tilted magnetic field. Single electrons in this system exhibit non-KAM chaotic dynamics. Consequently, at critical field values, coupling between Bloch and cyclotron motion causes delocalisation of the electron orbits, resulting in strong resonant enhancement of the drift velocity. We show that this dramatically affects the collective electron behaviour by inducing multiple propagating charge domains and, consequently, GHz-THz current oscillations with frequencies ten times higher than with no tilted field.
Secondly, we study the effect of applying an acoustic wave to the superlattice and find that we can induce high-frequency single electron dynamics that depend critically on the wave amplitude. There are two dynamical regimes depending on the wave amplitude and the electron's initial position in the acoustic wave. Either the electron can be dragged through the superlattice and is allowed to perform drifting periodic orbits with THz frequencies far above the GHz frequencies of the acoustic wave; or, by exerting a large enough potential amplitude, Bloch-like oscillations can be induced, which can cause ultra-high negative differential velocity. We also consider collective electron effects and find that, generally, the acoustic wave drags electrons through the lattice. Additionally, high negative differential drift velocity at the transition between these two single-electron dynamical regimes, induces charge domains in the superlattice that generates extra features in the current oscillations.
Finally, we investigate cold atoms in optical lattices driven by a moving potential wave, directly analogous to acoustically-driven superlattices. In this case, we find the same dynamical regimes found in the acoustically driven superlattice. In addition, there are a number a sharp resonant features in the velocity of the atom at critical wave amplitudes and speeds. This could provide a flexible mechanism for transporting atoms to precise locations in a lattice.
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