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A key hallmark of quantum Hall physics is the existence of topological chiral states at the system boundary. Signatures of these edge states have been experimentally observed in cold atoms by using different approaches, including notably that of ``synthetic dimension'' in which internal states are coupled together and reinterpreted as sites along an artificial spatial dimension. However, previous atomic synthetic dimension implementations have been limited to relatively small system sizes with inflexible boundaries. In this paper, we propose instead how to use a synthetic dimension of atomic trap states to observe chiral edge states in a large quantum Hall system with a tunable edge. We present numerical simulations for relevant experimental parameters, showing how this scheme may be used to probe the properties and robustness of the edge states to defects. Our work opens the way for future experiments in topological physics with synthetic dimensions, while also providing new ways to manipulate and control highly-excited trap states., Comment: 21 Pages, 20 figures

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 artificial spatial dimension. However, atomic experimental realisations have been limited so far by the number of artificial lattice sites that can be feasibly coupled along the synthetic dimension. Here, we experimentally realise for the first time a very long and controllable synthetic dimension of atomic harmonic trap states. To create this, we couple 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.

We report on the realization and characterisation of optical potentials for ultracold atoms using a superluminescent diode. The light emitted by this class of diodes is characterised by high spatial coherence but low temporal coherence. On the one hand, this implies that it follows Gaussian propagation similar to lasers, allowing for high intensities and well-collimated beams. On the other, it significantly reduces those interference effects that lead to severe distortions in imaging. By using a high-resolution optical setup, we produce patterned optical potentials with a digital micromirror device and demonstrate that the quality of the patterns produced by our superluminescent diode is consistently and substantially higher than those produced by our laser. We show that the resulting optical potentials can be used to arrange the atoms in arbitrary structures and manipulate them dynamically. Our results can open new opportunities in the fields of quantum simulations and atomtronics.