Emergent Phenomena in Atoms Coupled to Dynamic Cavity Fields

The experimental breakthroughs in reaching the quantum (i.e., ultracold) limit of motion in atomic gases have marked the beginning of an era of controllable testing of fundamental models of quantum physics. Ultracold atomic gases provide rich environments for exploring novel single- and many-body phenomena, as well as simulating intractable phenomena and systems. They can be also loaded inside cavities to interact with dynamic electromagnetic cavity fields, where the atom-photon interaction is so strong that the back-action of the atoms on the radiation fields is no longer negligible. This leads to the emergence of exotic composite matter-light states and correlated phenomena with no analog elsewhere. This project aims to theoretically study emergent phenomena in quantum gases strongly coupled to dynamic cavity fields. These emergent phenomena include self-ordering, synthetic dynamic gauge potentials, topological states, etc. Self-ordering the spontaneous appearance of an order out of a disorder under some critical conditions of density, temperature, interaction strength, and/or even disorder itself is an important and widespread emergent phenomenon not only in physics, but also in chemistry, biology and many other fields. On the other hand, gauge potentials (such as electromagnetic potentials) and topological states (states of matter which are insulator in bulk and conductor on edges or surfaces) are among the most fundamental notions of modern physics. The project intends to first investigate truly emergent self-ordering processes in an ultracold multi- level atomic gas dynamically coupled to a multi-mode ring cavity. Thanks to the extra degrees of freedom of atomic internal states and cavity fields, the spatial and internal self-ordering of the atomic gas resembles genuine crystallization and magnetization processes in real materials. This research will significantly advance the study of composite atom-cavity systems and self-ordering in these systems by simultaneously incorporating both atomic internal states and cavity-field polarizations for the first time. The project then plans to study proposed cavity-induced synthetic dynamic magnetic fields for a two- dimensional ultracold atomic gas inside a linear cavity. In particular, it aims to characterize emergent dynamic self-similar bulk energy bands and topological edge states due to the cavity-induced synthetic dynamic magnetic fields, and identify their influences on the self-ordering. Building on results of the second task, the project plans to finally put forward a scheme to simulate quantum electrodynamic (QED) field (or gauge) theory using a cavity QED setup. This study will, therefore, open a new avenue for simulating dynamic quantum field theories in ultracold atomic gases via cavity QED. The proposed systems will be studied using the full quantum theory of light-matter interaction. Various analytical and numerical techniques will then be employed. These methods include, but are no limited to, mean-field theories, real and imaginary time evolutions, free-energy minimization approach, Landau theory of a phase transition, etc. 1

"Emergent Phenomena in Atoms Coupled to Dynamic Cavity Fields" The experimental breakthroughs in reaching the quantum (i.e., ultracold) limit of motion in atomic gases have marked the beginning of an era of controllable testing of fundamental models of quantum physics. Ultracold atomic gases provide rich environments for exploring novel single- and many-body phenomena, as well as simulating intractable phenomena and systems. They can be also loaded inside cavities to interact with dynamic electromagnetic cavity fields, where the atom-photon interaction is so strong that the back-action of the atoms on the radiation fields is no longer negligible. This leads to the emergence of exotic composite matter-light states and correlated phenomena with no analog elsewhere. This project theoretically studied emergent phenomena in quantum gases strongly coupled to dynamic cavity fields. These emergent phenomena include self-ordering, synthetic dynamic gauge potentials, magnetic orders, supersolid states, etc. Self-ordering-the spontaneous appearance of an order out of a disorder under some critical conditions of density, temperature, interaction strength, and/or even disorder itself-is an important and widespread emergent phenomenon not only in physics, but also in chemistry, biology and many other fields. On the other hand, gauge potentials (such as electromagnetic potentials), quantum magnetism, supersolid phases (crystalline states which can flow like a superfluid without a friction) are among the most fundamental notions of modern physics. The research conducted under this Lise-Meitner project has opened new avenues in the many-body cavity-QED field and has attracted a lot of attention from both theory and experiment communities. In particular, along with my collaborators I have developed for the first time the notion of combined density and spin self-ordering in multi-component quantum gases (i.e., ultracold atoms with both internal and motional degrees of freedom), realizing cavity-mediated quantum spin models and emergent magnetic orders. Other important research works under this project include proposals for density-dependent dynamical gauge potentials, driven-dissipative supersolids, and emergent quasicrystalline symmetries in cavity-QED settings. The latter has introduced an interesting notion for the first time where the self-ordering leads to a "quasicrystalline" state with an emergent symmetry across the superradiant phase transition (a YouTube video has been made by the Public Relations Office of the University of Innsbruck on this research work: https://www.youtube.com/watch?v=98SYD4xz7y8). This is in contrast to all previous known examples of superradiant self-ordering in cavity QED, where the self-ordering results in crystalline phases with broken symmetries across the self-ordering transition, therefore opening a new opportunity for realizing exotic states of matter. On the other hand, our proposal on supersolid-based gravimeter has highlighted the potential of cavity QED for quantum-enhanced precise metrology, offering a new perspective for practical cavity-QED applications.