Gauge potentials in ultracold quantum gases

When atoms are trapped and cooled to temperatures only one millionth of a degree above absolute zero, their behaviour becomes dominated by their wave-like quantum nature. How they behave depends on their intrinsic spin. Bosons, having integer spin, tend to occupy the same quantum state and behave coherently. Fermions, having half-integer spin, are forbidden from occupying the same state and behave very differently. This proposal plans to investigate the effects of light propagating through an extremely cold gas. The light will have some peculiar properties. It can for instance propagate very slowly through the cloud of atoms. In vacuum the speed of light is 300 000 km/s, but when the light propagates through a cold gas the situation can be strikingly different. If the frequency of the light is carefully chosen, then the velocity of the light pulse can be as slow as a walking pace. The light can also have an orbital angular momentum associated with a propensity to induce rotation. This means that the incoming light will have a phase profile which resembles a helical spiral. The combination of light with orbital angular momentum propagating through a quantum gas has some remarkable consequences. It turns out that the interaction between such light beams and the atoms is of the form of a vector potential which in turn opens up a whole new playground for the cold atoms. A vector potential is typically encountered when describing the interaction between charged particles, such as electrons, and magnetic fields. In our case the atoms are neutral and does not feel the presence of a magnetic field like electrons would do. But since the interaction between the atoms and the light is of the same mathematical form as the vector potential for charged particles, we can introduce an effective magnetic field in our neutral cloud of atoms. This has some profound consequences in allowing us to explore fundamental systems with charged particles and magnetic fields, but using neutral atoms. It makes it much easier to control parameters, such as the density, or even interaction strengths between the atoms, compared to standard solid state charged particle systems . Another remarkable consequence of the effective vector potential is a direct analogy between ultracold quantum gases and gauge theories encountered typically in high energy physics. This will give us a new tool and allows us to study phenomena known from a wide range of different fields, but now with all the advantages the cold atoms are giving.