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Concept# Fermion

Summary

In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin 1/2, spin 3/2, etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks and leptons and all composite particles made of an odd number of these, such as all baryons and many atoms and nuclei. Fermions differ from bosons, which obey Bose–Einstein statistics.
Some fermions are elementary particles (such as electrons), and some are composite particles (such as protons). For example, according to the spin-statistics theorem in relativistic quantum field theory, particles with integer spin are bosons. In contrast, particles with half-integer spin are fermions.
In addition to the spin characteristic, fermions have another specific property: they possess conserved baryon or lepton quantum numbers. Therefore, what is usually referred to as the spin-statistics relation is, in fact, a spin statistics

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L'objectif de ce cours est de familiariser l'étudiant avec les concepts, les méthodes et les conséquences de la physique quantique. En particulier, le moment cinétique, la théorie de perturbation, les systèmes à plusieurs particules, les symétries, et les corrélations quantique seront traité

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There once was a harsh competition between different computer memory technologies, and now we cheer triumph for the Random Access-Memory (RAM) devices, -- cheap, fast, tiny, stable. The competing Magnetic Bubble Memory had faded away as magnetic bubbles are undesirably large and pretty much not robust, manifesting both low data density and high operational costs. However, what we do possess now are nanosize objects of topological nature, magnetic skyrmions, which are protected from continuous field variations and take very little energy cost to be moved. Thus, skyrmions are considered as promising information carriers for future memory devices and ultradense data storage, while skyrmion phases in bulk materials are interesting from fundamental point of view in exploring topological states of matter. In this thesis, I develop and advance several effective theoretical approaches, diverse both in their methods and use, which were of appeal for several skyrmionic experiments in our lab (LQM/EPFL). We were and are primarily interested in the open issues in the applied field of skyrmionics, which may be taken under the umbrella of creation, stabilization and control of magnetic skyrmions under electric fields, mechanical strains, thermal gradients, etc. For the goals achieved and yet to be achieved, the magnetoelectric insulator Cu2OSeO3, which uniquely responses to all the above mentioned fields, is a highly advantageous candidate. Magnetoelectric here means that the spins of a magnetic material are coupled to external electric fields, while insulating properties are very advantageous to preserve both the state and the very existence of skyrmions by eliminating the Joule heating. The novel results in this thesis are calculations for both individual and arrayed skyrmions under electric fields, mechanical strains and uniform pressures, and thermal gradients. Furthermore, several fundamental questions were addressed by developing an extended formalism for calculation skyrmion-pocket phase diagrams, studying the topologically-governed crossover between skyrmions and magnetic bubbles, and discussing the possible role of merons (half-skyrmions) in skyrmion phase formation. The result with the most immediate appeal is probably the theoretical and experimental study of skyrmion lattices in electric fields, with a direct demonstration of writing and erasing of the full skyrmion phase under electric fields of few Volts per micrometer, as compatible with modern microelectronic devices.

Non topological solitons, Q balls can arise in many particle theories with U(1) global symmetries. As was shown by Cohen et al. [2], if the corresponding scalar field couples to massless fermions, large Q-balls are unstable and evaporate, producing a fermion flux proportional to the Q ball's surface. In this work we analyse Q-ball instabilities as a function of Q-ball size and fermion mass. In particular, we construct an exact quantum-mechanical description of the evaporating Q-ball. This new construction provides an alternative method to compute Q-Ball's evaporation rates. We shall also find a new expression for the upper bound on evaporation as a function of the produced fermion mass and study the effects of the size of the Q ball on particle production. We also analyse what happens if external fermion is scattered on a Q ball and demonstrate that it can be converted into antiparticle with a probability of the order of one. This result has important implications for astrophysical applications of dark matter Q balls.

This thesis presents the first cavity quantum electrodynamics experiments performed with a degenerate gas of $^6$Li with strong atom-atom interactions. The first part of this manuscript describes the design and the building of the apparatus that has been especially developed to bring together a high-finesse optical cavity and a strongly interacting Fermi gas. I described how the cavity and all the laser-cooling procedure can be realized in the same vacuum chamber, thus speeding up the production cycle of the degenerate Fermi gas.This new experimental apparatus is the first of its kind combining these two field of quantum physics. Placing a quantum gas of Fermions within an optical resonator gives a important technical advantages, allowing for the fast, all-optical production of a degenerate gas of $^6$Li. We apply an technique that make it possible to modify the longitudinal structure of the cavity trap to cancel its lattice structure. It increases the phase space density after the evaporative cooling leading to a ultracold gas at temperature lower than ten percent of the Fermi temperature. We describe how magnetic field allows us to tune the interatomic interactions, making use of the broad Feshbach resonance of $^6$Li at $832$ G and how we characterize the thermodynamic properties of the ultracold Fermi gas. The direct observation of phase separation for a spin-imbalanced Fermi gas between a fully paired region at the cloud center, surrounded by a spin-polarized shell experimentally proves the apparition of superfluidity at low enough temperature.The first experiment showing the strong coupling between the cavity photons and the strongly interacting Fermi gas is shown in this manuscript. The observation of large avoided-crossings when performing cavity transmission spectroscopy experiment are the experimental smoking gun of the strong light-matter coupling regime. We observe the expected scaling of the light-matter coupling strength with the number of atoms in the gas, proving the coherent coupling of the atoms with the cavity field.The thirs part of this manuscript presents the first cavity quantum electrodynamics experiment where a pairs of atoms couple to the cavity photons, forming a new dressed state: the pair-polariton. This dressed state inherits from its atomic part the characteristics of the many-body physics of the strongly interacting Fermi gas. We confirm experimentally that the properties of the short-range two-body correlation function, know as Tan's contact, can directly be measured optically, on the pair-polariton transmission spectrum. We observe the coherent coupling of the ground state Fermion pairs with the cavity photons and use the pair-polariton to perform single shot, real-time, weakly destructive measurement of the short range two body correlation function. This new measurement of Tan's contact allows to follow in-time the evolution of a single system, contrasting with existing techniques.The last part of this thesis will show experiment carried far in the dispersive regime, where both the cavity resonance and the probe laser frequency are far detuned from the atomic resonance. We will discuss how we can, in this regime, measure the atom number evolution in-time, with a weak destructivity. We show that optical non-linearity emerges and depends on the atom-atom interaction strength. Last we implement a pump not aligned with the cavity axis that allows to create long-range interactions between atoms.