Criptografía post-cuántica y códigos correctores de errores

Este proyecto es un estudio sobre un el criptositema de McEliece. Un criptosistema corrector de errores que funciona con los códigos de Goppa. Además, se estudia y analiza una propuesta presentada en el proceso de estandarización de criptografía pos-cuántica del NIST basada en este criptosistema.The main objective of this project is to study the binary Goppa code and the McEliece cryptosystem (1978). Furthermore, there is a proposal based on this cryptosystem in the Post-Quantum Cryptography Standardization Process of the NIST which is analyzed

A magnetic lens for cold atoms controlled by a rf field

We report on a new type of magnetic lens that focuses atomic clouds using a static inhomogeneous magnetic field in combination with a radio-frequency field. The experimental study is performed with a cloud of cold cesium atoms. The rf field adiabatically deforms the magnetic potential of a coil and therefore changes its focusing properties. The focal length can be tuned precisely by changing the rf frequency value. Depending on the rf antenna position relative to the DC magnetic profile, the focal length of the atomic lens can be either decreased or increased by the rf field

Competition between Bose Einstein Condensation and spin dynamics

We study the impact of spin-exchange collisions on the dynamics of Bose-Einstein condensation, by rapidly cooling a chromium multi-component Bose gas. Despite relatively strong spin-dependent interactions, the critical temperature for Bose-Einstein condensation is reached before the spin-degrees of freedom fully thermalize. The increase in density due to Bose-Einstein condensation then triggers spin dynamics, hampering the formation of condensates in spin excited states. Small metastable spinor condensates are nevertheless produced, and manifest strong spin fluctuations.Comment: 5 pages, 4 figure

Optimized production of large Bose Einstein Condensates

We suggest different simple schemes to efficiently load and evaporate a ''dimple'' crossed dipolar trap. The collisional processes between atoms which are trapped in a reservoir load in a non adiabatic way the dimple. The reservoir trap can be provided either by a dark SPOT Magneto Optical Trap, the (aberrated) laser beam itself or by a quadrupolar or quadratic magnetic trap. Optimal parameters for the dimple are derived from thermodynamical equations and from loading time, including possible inelastic and Majorana losses. We suggest to load at relatively high temperature a tight optical trap. Simple evaporative cooling equations, taking into account gravity, the possible occurrence of hydrodynamical regime, Feshbach resonance processes and three body recombination events are given. To have an efficient evaporation the elastic collisional rate (in s$^{-1}$) is found to be on the order of the trapping frequency and lower than one hundred times the temperature in micro-Kelvin. Bose Einstein condensates with more than $10^7$ atoms should be obtained in much less than one second starting from an usual MOT setup.Comment: 14 page

Spontaneous demagnetization of a dipolar spinor Bose gas at ultra-low magnetic field

Quantum degenerate Bose gases with an internal degree of freedom, known as spinor condensates, are natural candidates to study the interplay between magnetism and superfluidity. In the spinor condensates made of alkali atoms studied so far, the spinor properties are set by contact interactions, while magnetization is dynamically frozen, due to small magnetic dipole-dipole interactions. Here, we study the spinor properties of S=3 $^{52}$Cr atoms, in which relatively strong dipole-dipole interactions allow changes in magnetization. We observe a phase transition between a ferromagnetic phase and an unpolarized phase when the magnetic field is quenched to an extremely low value, below which interactions overwhelm the linear Zeeman effect. The BEC magnetization changes due to magnetic dipole-dipole interactions that set the dynamics. Our work opens up the experimental study of quantum magnetism with free magnetization using ultra-cold atoms.Comment: 6 pages, 4 figures, 2 appendice

A method to discriminate between localized and chaotic quantum systems

We derive a criterion that distinguishes whether a generic isolated quantum system initially set out of equilibrium can be considered as localized close to its initial state, or chaotic. Our approach considers the time evolution in the Lanczos basis, which maps the system's dynamics onto that of a particle moving in a one-dimensional lattice where both the energy in the lattice sites and the tunneling from one lattice site to the next are inhomogeneous. We infer a criterion that allows distinguishing localized from chaotic systems. This criterion involves the coupling strengths between Lanczos states and their expectation energy fluctuations. We verify its validity by inspecting three cases, corresponding to Anderson localization as a function of dimension, the out-of-equilibrium dynamics of a many-body dipolar spin system, and integrable systems. We finally show that our approach provides a justification for the Wigner surmise and the eigenstate thermalization hypothesis, which have both been proposed to characterize quantum chaotic systems. Indeed, our criterion for a system to be chaotic implies the level repulsion (also known as spectral rigidity) of eigenenergies, which is characteristic of the Wigner-Dyson distribution; and we also demonstrate that in the chaotic regime, the expectation value of any local observable only weakly varies as a function of eigenstates. Our demonstration allows to define the class of operators to which the eigenstate thermalization applies, as the ones that connect states that are coupled at weak order by the Hamiltonian.Comment: 15 pages, 6 figure

Application of lasers to ultracold atoms and molecules

In this review, we discuss the impact of the development of lasers on ultracold atoms and molecules and their applications. After a brief historical review of laser cooling and Bose-Einstein condensation, we present important applications of ultra cold atoms, including time and frequency metrology, atom interferometry and inertial sensors, atom lasers, simulation of condensed matter systems, production and study of strongly correlated systems, and production of ultracold molecules.Comment: Review paper written in the name of IFRAF to celebrate 50 years of lasers and their applications to cold atom physics; 15 pages, 2 figures; to appear in Comptes Rendus de l'Academie des Sciences, Pari

Cooling of a Bose-Einstein Condensate by spin distillation

We propose and experimentally demonstrate a new cooling mechanism leading to purification of a spinor Bose-Einstein Condensate (BEC). Our scheme starts with a BEC polarized in the lowest energy spin state. Spin excited states are thermally populated by lowering the single particle energy gap set by the magnetic field. Then these spin-excited thermal components are filtered out, which leads to an increase of the BEC fraction. We experimentally demonstrate such cooling for a spin 3 52Cr dipolar BEC. Our scheme should be applicable to Na or Rb, with perspective to reach temperatures below 1 nK.Comment: 4 figure