Induced transitions between Wannier ladders

Stark-wannier Ladders and Cubic Exponential Sums

Atomic Landau-Zener tunneling and Wannier-Stark ladders in optical potentials.

We calculate the quantum motion of ultracold atoms in an accelerating optical potential, and show how they may be used to observe Landau-Zener tunneling and Wannier-Stark ladders, two fundamental quantum effects in solid state physics. The optical potential is spatially periodic, yielding an energy spectrum of Bloch bands for the atoms. The acceleration provides an inertial force in the moving ...

Bloch oscillations, Zener tunneling, and Wannier-Stark ladders in the time domain.

Local density of states and level width for Wannier-Stark ladders.

The local density of states ρ(x, E) is calculated for a Bloch electron in an electric field. Depending on the system size, we can see one or more sequences of Wannier-Stark ladders in ρ(x, E), with Lorentz type level widths and apparent spatial localization of the states. Our model is a chain of delta function potential barriers plus a staircase-like electric potential, with open boundary condi...

Observation of atomic Wannier-Stark ladders in an accelerating optical potential.

We report observation of Wannier-Stark ladders with ultracold sodium atoms in an accelerating one-dimensional standing wave of light. Atoms are trapped in a far-detuned standing wave that is accelerated for a controlled duration. A small oscillatory component is added to the acceleration, and the fraction of trapped atoms is measured as a function of the oscillation frequency. Resonances are ob...