Normal Modes, Multiplicities, and Superfluidity: The Role of the Pauli Principle in Organizational Collective Phenomena

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The Pauli principle, a fundamental tenet of quantum mechanics, states that identical fermions cannot occupy the same quantum state simultaneously. The proof of this simple statement, which has profound implications for the stability of our universe, has remained elusive despite overwhelming experimental evidence supporting it. The Pauli principle underlies the stability of both microscopic and macroscopic matter, controlling phenomena at all length and temperature scales from ultracold Fermi gases to hot neutron stars. In this research, the PI proposes to study the role of the Pauli principle in the creation and stabilization of collective behavior such as superfluidity. Earlier work has suggested that the Pauli principle plays a larger role than expected in the emergence of collective behavior. Understanding such organized behavior is important because it could be used to develop engineered quantum systems for quantum information processing, quantum-enhanced sensors and high temperature superconductors that could revolutionize electrical engineering applications. This project describes a plan to investigate the forces in play during the dynamic transition from complex microscopic motion to simple, collective behavior such as seen in superfluid materials. In particular, the PI plans to study the role of the Pauli principle in the creation and stabilization of organized behavior. Experimentalists have produced controlled systems of ultracold fermions in the laboratory that exhibit universal collective properties. The goal of this project is to study these systems theoretically as collective behavior emerges, to elucidate the driving forces behind this emergence and to propose new ways to produce and control collective behavior in the laboratory. Using a many-body perturbation method that uses group theoretic techniques to obtain analytic normal mode solutions at first order, the PI plans to study the evolution of the character of these normal modes and monitor recently measured properties including excitation frequencies and thermodynamic quantities as system parameters approach the unitary regime which is known to support collective behavior. This work could facilitate our ability to produce and control these systems and enhance their use in technology.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.