Abstract
In these two lectures, we have presented various methods that have been proposed and implemented to generate dynamics on a gas of neutral atoms equivalent to the well-known magnetism of electron gases. We have classified these methods according to two criteria: i) do we wish to take advantage of the internal structure of the atoms? ii) does the Hamiltonian depend explicitly on time? The first criterion is linked to the fact that, unlike electrons in solids, our atoms possess a series of internal levels that can be coupled together via light beams. This degree of freedom makes it possible to envisage the notion of adiabatic tracking of a "dressed" level, with the Berry phase and geometric gauge field that comes with it. However, this flexibility, specific to atomic gases, is not without its drawbacks: it requires the use of light beams with a frequency close to an atomic resonance, which can lead to photon scattering and atom heating that blur the desired effects. The second criterion is the possibility of temporally modulating the potential acting on the atoms. This modulation can take place at a frequency of the same order as the cyclotron frequency we're trying to achieve: this is what happens when a system is rotated, where the Lorentz magnetic force is simulated by a Coriolis force. We can also choose a modulation frequency much higher than the cyclotron frequency, the gauge field then appearing as a secular term resulting from a well-chosen micromovement. We ended these two lectures with a discussion of spin-orbit coupling; this variant of magnetic coupling can lead to many original phenomena, both on the fundamental level, with the possibility of simulating new phases of matter such as topological insulators, and on the applied level, with strong analogies to spintronic devices.
