We use an atomic ratchet realized by applying short pulses of an optical standing-wave to a Bose–Einstein condensate to study the crossover between classical and quantum dynamics. The signature of the ratchet is the existence of a directed current of atoms, even though there is an absence of a net bias force. Provided that the pulse period is close to one of the resonances of the system, the ratchet behavior can be understood using a classical like theory which depends on a single variable containing many of the experimental parameters. Here we show that this theory is valid in both the true classical limit, when the pulse period is close to zero, as well as regimes when this period is close to other resonances where the usual scaled Planck's constant is nonzero. By smoothly changing the pulse period between these resonances we demonstrate how it is possible to tune the ratchet between quantum and classical types of behavior.
Geometrizing Quantum Dynamics of a Bose-Einstein Condensate