Structures, Dynamics, and Thermodynamics of Atomic Boson-Fermion Mixtures

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Atomic mixtures are ubiquitous in our daily life. For example, air is a mixture of nitrogen, oxygen, and other ingredients. Cooling down the air leads to liquefaction, showing a typical example of structural transitions in multi-species mixtures. The microscopic world governed by quantum physics contains mixtures of quantum particles that exhibit many exotic phenomena awaiting our exploration. There are two types of atoms in the universe, bosons and fermions. They differ by their peer-interactions: bosons tends to congregate in the quantum regime while fermions stay away from each other. Questions about the physics of a quantum mixture of both bosons and fermions have fascinated scientists for decades. Helium atoms have offered a platform for exploring quantum mixtures, however, the systems are complicated by the complex atomic interactions and challenging experiments. Nevertheless, recent advances in cooling, trapping, and manipulating atoms have successfully produced boson-fermion quantum mixtures and renewed research interest in such systems. The proposed research will investigate the structures, thermodynamics, and dynamics of the novel atomic boson-fermion mixtures. Explicitly, the research will deliver (1) a full theory of the of quantum boson-fermion mixtures, allowing a detailed analysis of the system in and out of equilibrium, (2) a description of how bosons and fermions push each other to form a homogeneous mixture like air or a separation like oil in water, and (3) an exploration and prediction of the dynamics of quantum boson-fermion mixtures driven across the different structures. Moreover, while the quantum mixtures realized by different experimental research groups are confined in different geometries, the proposed research will extract the universal behavior and elucidate the underlying mechanism. The results will reveal the novel structures and dynamics of quantum boson-fermion mixtures and advance our understanding of the many-body physics behind composite quantum systems. The rapid developments of trapping and manipulating multi-species atomic mixtures have made the investigation of boson-fermion mixtures an important and urgent task, and the research will deliver a timely description of the structures and dynamics of the mixtures. The phase diagrams of atomic mixtures in uniform or harmonic potentials from the framework developed in the research based on quantum field theories will explain the current and future experimental data and guide the investigations of critical phenomena in multi-species quantum systems. The simulations and analysis of the spatial structures of the mixtures will demonstrate the extraction of critical exponents from a phase-separated structure in equilibrium, and the analysis of the quantum dynamics will reveal the influence of the fermions on the vortex formation in the bosonic superfluid. The breakdown of the scaling behavior in boson-fermion mixtures will reflect the first-order structural transition, and a comparison with the conventional analyses across a second-order phase transition will reveal the size of the critical regime. The research will establish collaborations with experimental groups to characterize the structures, thermodynamics, and dynamics of atomic boson-fermion mixtures across structural transitions in different trap geometries. The theoretical framework, simulations, and results will guide and explain experiments of atomic mixtures. To promote the research and advocate public learning, the PI will present public lectures to the local communities that have high populations of under-represented minorities and will recruit minority and women students to participate in the research and increase diversity.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.