Emergent Orders of Spinor BECs in a Multimode Ring Resonator

Cavity quantum electrodynamics (QED) studies strong light-matter interactions inside an optical cavity, where the electromagnetic fields resonating inside the cavity can exhibit their quantum nature. 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. There has been remarkable advances in cavity QED in the last 30 years, which was recognized by the 2012 Nobel Prize in Physics. The EOSBECMR project will achieve a major leap in the field of both theoretical and experimental cavity QED by realizing and investigating truly emergent quantum phenomena driven by quantum effects. Emergent phenomena - 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. An example of emergent order in nature is the complex fractal patterns of snowflakes. Ultracold atoms in a standing wave resonator have already been used to demonstrate emergent phenomena, but in very specific contexts. Using a traveling wave resonator (see Figure) we will explore much richer quantum phenomena, such as the dynamics of defects, crystal frustration, supersolidity, etc. In particular, the following aspects will be investigated. 1) The project EOSBECMR will exploit cavity-mediated long-range interactions between atoms as a novel approach to quantum magnetism: a novel state of matter where an atomic ensemble orders not via the laws of classical physics (i.e. temperature phase transitions) but rather quantum physics, resulting in macroscopically large quantum entangled states. 2) The specific geometry of our bow-tie cavity allows the creation of multiple independent Bose- Einstein condensates (BEC) all coupled to a single common cavity mode. This opens up the intriguing possibility of creating for the first time a quantum network of entangled BECs which form the basic building block for quantum communication/computation protocols. 3) In its theoretical section, EOSBECMR will investigate dynamical gauge fields and set the stage for simulating complex theories such as quantum chromodynamics and the standard model of elementary particles in cavity QED systems. The final aim will be to have table-top experiments complementary to the giant setups of high energy physics, both to confirm their results and to continue the quest for new physics. This project is an international collaboration between the experimental Cold Atom Group at LP2N (PI A. Bertoldi, D. Naik and P. Bouyer) - expert in matter wave interferometry, cavity QED, ultracold gases, quantum measurements - and the theoretical group of cavity QED Innsbruck (PI F. Mivehvar, H. Ritsch, S. Ostermann) - pioneer of self-ordering and superradiance in optical resonators, and world leader in cavity optomechanics and cavity cooling.

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. In the theory side, this project 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 International Join 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, we 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.