From quantum quasiparticles to a classical gas

Peer ReviewedPostprint (published version

Superfluid Vortex Dynamics on Planar Sectors and Cones

We study the dynamics of vortices formed in a superfluid film adsorbed on the curved two-dimensional surface of a cone. To this aim, we observe that a cone can be unrolled to a sector on a plane with periodic boundary conditions on the straight sides. The sector can then be mapped conformally to the whole plane, leading to the relevant stream function. In this way, we show that a superfluid vortex on the cone precesses uniformly at fixed distance from the apex. The stream function also yields directly the interaction energy of two vortices on the cone. We then study the vortex dynamics on unbounded and bounded cones. In suitable limits, we recover the known results for dynamics on cylinders and planar annuli.Comment: 10 pages, 8 figure

Efimov trimers under strong confinement

The dimensionality of a system can fundamentally impact the behaviour of interacting quantum particles. Classic examples range from the fractional quantum Hall effect to high temperature superconductivity. As a general rule, one expects confinement to favour the binding of particles. However, attractively interacting bosons apparently defy this expectation: while three identical bosons in three dimensions can support an infinite tower of Efimov trimers, only two universal trimers exist in the two dimensional case. We reveal how these two limits are connected by investigating the problem of three identical bosons confined by a harmonic potential along one direction. We show that the confinement breaks the discrete Efimov scaling symmetry and destroys the weakest bound trimers. However, the deepest bound Efimov trimer persists under strong confinement and hybridizes with the quasi-two-dimensional trimers, yielding a superposition of trimer configurations that effectively involves tunnelling through a short-range repulsive barrier. Our results suggest a way to use strong confinement to engineer more stable Efimov-like trimers, which have so far proved elusive.Comment: 8 pages, 4 figures. Typos corrected, published versio

Polarons, Dressed Molecules, and Itinerant Ferromagnetism in ultracold Fermi gases

In this review, we discuss the properties of a few impurity atoms immersed in a gas of ultracold fermions, the so-called Fermi polaron problem. On one side, this many-body system is appealing because it can be described almost exactly with simple diagrammatic and/or variational theoretical approaches. On the other, it provides quantitatively reliable insight into the phase diagram of strongly interacting population imbalanced quantum mixtures. In particular, we show that the polaron problem can be applied to study itinerant ferromagnetism, a long standing problem in quantum mechanics.Comment: Review paper; published version, 48 pages and 23 figure

Electrochemical C-H Activations with 3d and 4d Transition Metal Catalysts

The oxidative metal-catalyzed C–H activation of inert bonds is a powerful tool for the functionalization of complex molecules. This platform allowed the broadening of the organic chemists’ toolbox and improved the resource-economy of synthetic routes, avoiding prefunctionalizations of starting materials. Nevertheless, its applications were constrained by the use of stoichiometric oxidants, which limited the sustainability of this approach. In contrast, the use of electricity as environmental-friendly and versatile oxidant enhanced the sustainability of oxidative metal-catalyzed C–H activation and opened the way to the study of novel reactivities and selectivities. Within this thesis, electrochemical cobalt catalyzed and ruthenium catalyzed annulation reactions were initially studied. The electrochemical approach was then broadened to the C–H oxygenation reactions with ruthenium catalysis enabled by electrogenerated hypervalent iodine species and with rhodium catalysis. In addition, C–H arylation and C–H alkylation reaction by earth-abundant manganese as catalyst and electricity as sustainable oxidant was developed.2021-12-2

Quantized superfluid vortex dynamics on cylindrical surfaces and planar annuli

Superfluid vortex dynamics on an infinite cylinder differs significantly from that on a plane. The requirement that a condensate wave function be single valued upon once encircling the cylinder means that such a single vortex cannot remain stationary. Instead, it acquires one of a series of quantized translational velocities around the circumference, the simplest being $\pm \hbar/(2MR)$, with $M$ the mass of the superfluid particles and $R$ the radius of the cylinder. A generalization to a finite cylinder automatically includes these quantum-mechanical effects through the pairing of the single vortex and its image in either the top or bottom end of the surface. The dynamics of a single vortex on this surface provides a hydrodynamic analog of Laughlin pumping. The interaction energy for two vortices on an infinite cylinder is proportional to the classical stream function $\chi({\bf r}_{12})$, and it crosses over from logarithmic to linear when the intervortex separation ${\bf r}_{12}$ becomes larger than the cylinder radius. An Appendix summarizes the connection to an earlier study of Ho and Huang for one or more vortices on an infinite cylinder. A second Appendix reviews the topologically equivalent planar annulus, where such quantized vortex motion has no offset, but Laughlin pumping may be more accessible to experimental observation.Comment: 16 pages, 7 figures; published version, with thoroughly revised Appendice