Introduction

Chaos is the phenomenon that the outcome of events can depend very sensitively on the initial conditions of these events. One example is the weather, where the proverbial butterfly beats its wings in Beijing to cause a thunderstorm in New York. Now chaos is limited to the classical world: in quantum mechanics chaos cannot exist. But the world is made out of atoms, which are ruled by quantum mechanics. So where does this go wrong?

Our BEC forms a system where quantum effects are hugely magnified, so that it becomes easy to do experiments where quantum effects show up. We are studying a quantum system that is classically chaotic, the delta-kicked rotor.

This rotor is a ball on the end of a stick, and this can rotate. Gravity is only on during some very short times, the “kick”. The potential due to gravity (when it is on) depends on the cosine of the angle the stick makes with the vertical, as illustrated below.

The quantum mechanical equivalent is generated by putting a quantum particle, such as a neutral atom, in a standing wave of laser light. The laser light is detuned from a resonance in the atoms, so that it is unlikely that the atom is excited, but the atom experiences a potential proportional to the amount of laser light. This is going to be maximum in the anti-nodes of the standing wave, and minimum in the nodes, and thus gives a potential proportional to the cosine of the position. Naturally, the standing wave is only “on” during the “kicks”.

Loschmidt time reversal

One thing that has always confused people is the flow of time: almost every natural (microscopic) law is time-reversible. The only exception so far is a weak effect in beta-decay. On the other hand, it is obvious that the macroscopic world is not time reversable. Again, how do we build an everyday, irreversible world from reversible laws?

What we did is to first establish a bit of chaos, and then to carefully undo that chaos. Classically, this is impossible, as the outcome is extremely sensitive to the initial conditions and the experiment. But according to quantum mechanics, this is possible. We have found good evidence that quantum mechanics is right (again) and that we can undo the chaos.

This results are published in Physical Review E, a preprint can be found at the preprint archive.