Quantum structures in Rydberg systems

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The goal of this project is to theoretically characterize the many-body dynamics of a quantum degenerate gas of bosonic atoms, which mutually interact via two competing mechanisms: the forces due to the coupling to a Rydberg state (Rydberg dressing) and the optomechanical long-range forces due to multiple scattering of photons in a high-finesse cavity. Both forces induce ordering, their interplay is to large extent unexplored and its systematic characterization would contribute to shed light onto the quantum physical processes undelying complex structure formation. Our analysis will refer at all stages to existing experimental realizations. The main expected result is the full characterization of the atoms and cavity stationary state as a function of the relative strength of the two competing interactions and the corresponding signatures imprinted in the cavity-emitted light.