#### Condensed Matter Theory

### Martin Holthaus: Bloch oscillations and Zener breakdown in an optical lattice

**Author(s)**:**Martin Holthaus****Title**:**Date of Upload**: 2002-09-03
**Article**:**Keywords**:
Bloch-Zener dynamics, weak-binding approximation, adiabatic theorem, optical lattices, Bose-Einstein condensates, mean-field approximation
**Abstract**:- We study the dynamics of ultracold atoms in an optical lattice under constant bias. After recapitulating the ideas underlying Bloch oscillations and Zener's formula for interband transitions, the Bloch-Zener scenario is tested by means of accurate numerical solutions to the time-dependent Schroedinger equation. It is shown how two shortcomings of the traditional Zener formula can be removed: the common weak-binding approximation can be circumvented by combining Kohn's insight into the structure of complex energy bands with the Dykhne-Davis-Pechukas description of transitions in terms of adiabatic excursions on analytically continued eigenvalue surfaces, and a usually neglected Stokes phenomenon comes into play when accounting for the finite width of the Brillouin zone. Treating Bose-Einstein condensates in optical lattices within the standard mean-field approximation at zero temperature, the ideal Bloch-Zener scenario turns out to be remarkably stable against the condensate's nonlinear self-interaction. Yet, under appropriate conditions a Bloch-oscillating Gross-Pitaevskii wavepacket reveals characteristic signatures of that nonlinearity, such as sudden phase jumps, slight shifts of the oscillation frequency or non-classical breathing modes. It is suggested that such experimentally detectable signatures will play an important role in future high-precision experiments aiming at the exploration of many-body dynamics in periodic potentials with condensates in optical lattices.
**URL: http://www.physik.uni-oldenburg.de/condmat/Papers/p_zener.ps (application/postscript, 3.8 MByte)**

**Bloch oscillations and Zener breakdown in an optical lattice**

**J. Opt. B: Quantum Semiclass. Opt. 2 (October 2000) 589-604, IOP**

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