RUI: Ultracold Atoms in Ring-Shaped Lattices

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Upheavals of familiar technologies are expected in coming years due to the dramatically enhanced control of atomic, molecular and photonic systems. Among these anticipated revolutions is that in sensor technology, affecting a wide array of devices regularly used to detect and measure everything from electric currents, magnetic and gravitational fields, and light intensities, to name a few examples. The key element driving these developments is quantum entanglement, the strange correlations between observable properties of even widely-separated quantum systems. While entanglement is ubiquitous in quantum systems, it is also extremely delicate, and can be altered or spoiled by interactions of the quantum system with its environment. This delicacy is precisely what makes exquisitely controlled quantum systems the source of potentially revolutionary sensor technology. This project concerns simple sensors formed by entangled ultracold atoms confined in ring-shaped traps. The ring-shape allows for the interference of counter-propagating matter waves, forming a kind of interferometer which has exquisite sensitivity to interactions between the atoms. Additional applications of the results to quantum information processing and to new quantum materials will also be explored. The PI will actively train and involve numerous undergraduate students in physics research at a low cost university, and expand on success under prior grants to leverage this experience to channel students into STEM career paths, including many from under-represented demographics. Specifically, this project will conduct a comprehensive study of phenomena realizable with ultracold atoms trapped in lattices with a global topology that is multiply-connected, such as rings, cylinders or tori. The non-trivial topology naturally introduces periodic and twisted boundary conditions with the inclusion of effective flux via gauge fields or rotation, and reveals coherent and non-local features of quantum states. Within this general context, a broad range of topics will be examined. Models with ring-shaped geometry have played a crucial role in understanding the influences of topology and gauge freedoms in non-relativistic physics. This research will develop and extend those models for viable implementation with cold atoms to probe scenarios often inaccessible when such models were conceived. The phenomena to be so studied will include artificial gauge fields, quantum Hall effect, anyon physics, quantum pumps, Hofstadter model, and Aharonov-Bohm and geometric phase effects. Spin-squeezing, that can bypass uncertainty limits, and nonlinear dynamics will be examined in the novel context of counter-circulating collective modes of atoms sharing the same physical space. Where possible, the phenomena will be examined dynamically with evolution in time and space, noting that time can add or substitute for other degrees of freedom. Treating rings as artificial atoms, counterparts will be established in external degrees of freedom for phenomena usually associated with internal ones.