Title: Generation, manipulation and detection of snake state trajectories of a neutral atom in a ring-cavity

Abstract: We propose a set-up to create and detect the atomic counterpart of snake state trajectories which occur at the interface where the magnetic field reverses direction. Such a magnetic field is generated by coupling two counter-propagating modes of a ring cavity to a two-level atom. The spatial distribution and the strength of the induced magnetic field are controlled by the transverse mode profile of the cavity modes and the number of photons in the two modes, respectively. By analysing the atomic motion in such a magnetic field while including the cavity back-action, we find that the atom follows snake state trajectories which can be non-destructively detected and reconstructed from the phase and the intensity of the light field leaking from the cavity. We finally show that the system parameters can be tuned to modify the transport properties of the snake states and even amplify the effect of cavity feedback which can completely alter their topology.