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Physical Review Letters

Lifetime of Wannier-Stark States

Markus Glück, Andrey R. Kolovsky, H. J. Korsch

Published Aug 2, 1999• 40 citations
Publisher

Abstract

The lifetime of a Bloch particle in a homogeneous field is calculated numerically as a function of the field amplitude. A simple model explaining the characteristic features of the field dependence of the lifetime is introduced. The theoretical results are compared with the experimental data of C. F. Bharucha et al. [Phys. Rev. A 55, R857 (1997)] obtained for cold sodium atoms in an accelerated optical lattice.

DOI
10.1103/physrevlett.83.891

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The lifetime of a Bloch particle in a homogeneous field is calculated numerically as a function of the field amplitude. A simple model explaining the characteristic features of the field dependence of the lifetime is introduced. The theoretical results are compared with the experimental data of C. F. Bharucha et al. [Phys. Rev. A 55, R857 (1997)] obtained for cold sodium atoms in an accelerated optical lattice.
The Schrodinger equation for the interaction of a decaying two-level atom with an external oscillating field is separated via a series of matrix transformations into a time independent and a time dependent part; the former yields the radiofrequency Stark shift for decaying states, the latter is normally negligible for atomic beam resonance experiments. In the limit of stable states, or for the case of two levels of equal lifetime, the shift reduces to that of the Bloch-Siegert effect. Exact analytical expressions for the state amplitudes are obtained for the case when the time dependent matrix can be neglected; the resulting transition probabilities are investigated as functions of frequency, time, and interaction strength and are compared with the rotating field theory and the exact numerical solutions.
We report an experimental study of the Wannier-Stark fan and the fractional Wannier-Stark ladder using laser-cooled sodium atoms in an accelerating one-dimensional standing wave of light. We prepare the atoms in the lowest motional band of the optical lattice and then impose a constant acceleration. A weak oscillatory component is added to the acceleration in order to resonantly drive interband transitions, and the number of atoms that remain in the lowest band is measured as a function of the probe frequency. The spectrum is characterized by a ladder of resonances spaced by the atomic Bloch oscillation frequency ${\ensuremath{\omega}}_{B}.$ When an additional, strong ac component at frequency $\ensuremath{\Omega}$ is added, a fractional ladder is observed with a spacing related to the electric matching ratio $\ensuremath{\Omega}/{\ensuremath{\omega}}_{B}.$