In our experiments we look at the dynamics of atoms in an amplitude modulated standing wave. The effective Hamiltonian for the centre-of-mass motion of the atoms is given by:

q position variable
p momentum variable
e modulation amplitude
w modulation frequency
k driving amplitude of the optical standing wave
 

Therefore the system can be classified as a "Quantum Driven Pendulum" (QDP).

This is the basis of our experimental setup for observing and analyzing the QDP dynamics:

Poincare sections provide an easy way of understanding the dynamics of the QDP:

One can see the islands of regular motion (resonances) in a sea of chaos. These islands of regular motion represent atoms oscillating in an optical potential well.

The following is an experimental picture of the resonances occuring in this system. Up to 70% of all atoms can be loaded into the resonances and can be velocity controlled.

This experiment provides grounds such that a number of interesting directions can be investigated:

1. Dynamic quantum tunneling
2. "Quantum chaos"
3. Decoherence
4. Classical nonlinear Hamiltonian dynamics (recent observation of multiple bifurcations in atom optics)
5. Atomic phase space preparation