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Abstract We examine key aspects of the theory of the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) crossover, focusing on the temperature dependence of the chemical potential, μ. We identify an accurate method of determining the change of μ in the cuprate high temperature superconductors from angle-resolved-photoemission data (along the ‘nodal’ direction), and show that μ varies by less than a few percent of the Fermi energy over a range of temperatures from far below to several times above the superconducting transition temperature, T c . This shows, unambiguously, that not only are these materials always on the BCS side of the crossover (which is a phase transition in the d-wave case), but are nowhere near the point of the crossover (where the chemical potential approaches the band bottom).

Superconductivity reported in metals driven away from equilibrium via optical pumping has been proposed to arise from nonlinear coupling between electrons and optically excited phonons. The authors use an exact approach to show that here, disorder, which disfavors superconductivity, emerges even though the system is translationally invariant.

We consider the quench of an atomic impurity via a single Rydberg excitation in a degenerate Fermi gas. The Rydberg interaction with the background gas particles induces an ultralong-range potential that binds particles to form dimers, trimers, tetramers, etc. Such oligomeric molecules were recently observed in atomic Bose-Einstein condensates. Understanding the effects of a correlated background on molecule formation, absent in bosonic baths, is crucial to explain ongoing experiments with Fermi gases. In this work we demonstrate with a functional determinant approach that quantum statistics and fluctuations have clear observable consequences. We show that the occupation of molecular states is predicated on the Fermi statistics, which suppresses molecular formation in an emergent molecular shell structure. At high gas densities this leads to spectral narrowing, which can serve as a probe of the quantum gas thermodynamic properties. Rydberg excitations in Fermi gases go beyond traditional impurity problems, creating an opportunity for studies of mesoscopic interactions in synthetic quantum matter.

The exploration of large-scale many-body phenomena in quantum materials has produced many important experimental discoveries, including novel states of entanglement, topology and quantum order as found for example in quantum spin ices, topological insulators and semimetals, complex magnets, and high- T _c superconductors. Yet, the sheer scale of solid-state systems and the difficulty of exercising exacting control of their quantum mechanical degrees of freedom limit the pace of rational progress in advancing the properties of these and other materials. With extraordinary effort to counteract natural processes of dissipation, precisely engineered ultracold quantum simulators could point the way to exotic new materials. Here, we look instead to the quantum mechanical character of the arrested state formed by a quenched ultracold molecular plasma. This novel class of system arises spontaneously, without a deliberate engineering of interactions, and evolves naturally from state-specified initial conditions, to a long-lived final state of canonical density, in a process that conflicts with classical notions of plasma dissipation and neutral dissociation. We take information from experimental observations to develop a conceptual argument that attempts to explain this state of arrested relaxation in terms of a minimal phenomenological model of randomly interacting dipoles of random energies. This model of the plasma forms a starting point to describe its observed absence of relaxation in terms of many-body localization (MBL). The large number of accessible Rydberg and excitonic states gives rise to an unconventional web of many-body interactions that vastly exceeds the complexity of MBL in a conventional few-level scheme. This experimental platform thus opens an avenue for the coupling of dipoles in disordered environments that will demand the development of new theoretical tools.