Impact of long-range interactions on phase transitions in spin-boson models

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The goal of this project is to study the collective behavior of a spin system under the action of collective interactions between all spins, simultaneously acting with long-range interactions between neighbouring spins. In order to carry out this study, we will experimentally implement a Dicke-Ising spin-boson model. Spin states are realized by Zeeman sublevels of the ground state of cold Rubidium atoms. Collective interactions are mediated by positioning the atoms inside an optical cavity. The atoms will be optically pumped transversally to the cavity axis and collectively driven into the Dicke phase transition. At the same time, long-range interactions are generated by coupling one of the spin states to a Rydberg state with detuning (Rydberg dressing). Thus, an effective Ising interaction is realized between the spins, which is long-range on the order of micrometers. We will first study the influence of weak, long-range interactions on the collective dynamics of the atoms, respectively their influence on the Dicke phase diagram. A second step will address the regime, where Ising interactions are comparable and compete with the coupling strength of the Dicke model, and search for new phases and phase transitions. Experimental work will be supported within the research unit "Long-range interacting QUantum SPin systems out of equilibrium: Experiment, Theory and Mathematics (QUSP)" by a collaboration with a theoretical project. This will investigate the Dicke-Ising model theoretically and make predictions on the expected phase diagram and on universal behavior at the phase transition. It will also study dissipative effects based on cavity mirror transmission of photons. The results of this study will lead to tools that can be used within the experiment in order to identify and characterize dynamical phases and phase transitions using photons that are coupled out of the cavity.