Bloch Oscillations Along a Synthetic Dimension of Atomic Trap States*

Synthetic dimensions provide a powerful approach for simulating condensed matter physics in cold atoms and photonics, whereby a set of discrete degrees of freedom are coupled together and re-interpreted as lattice sites along an extra artificial dimension. We experimentally realise for the first time a very long and controllable synthetic dimension of atomic harmonic trap states. To create this, we couple atomic trap states by dynamically modulating the trapping potential of the atomic cloud with patterned light. By controlling the detuning between the frequency of the driving potential and the trapping frequency, we implement a controllable force in the synthetic dimension. This induces Bloch oscillations in which atoms move periodically up and down tens of atomic trap states. We experimentally observe the key characteristics of this behaviour in the real space dynamics of the cloud, and verify our observations with numerical simulations and semiclassical theory. This experiment provides an intuitive approach for the manipulation and control of highly-excited trap states, and sets the stage for the future exploration of topological physics in higher dimensions.