Bose-Einstein Condensation and strong-correlation behavior of phonons in ion traps

We show that the dynamics of phonons in a set of trapped ions interacting with lasers is described by a Bose-Hubbard model whose parameters can be externally adjusted. We investigate the possibility of observing several quantum many-body phenomena, including (quasi) Bose-Einstein condensation as well as a superfluid-Mott insulator quantum phase transition.Comment: 5 pages, 3 figure

Quantum phases of interacting phonons in ion traps

The vibrations of a chain of trapped ions can be considered, under suitable experimental conditions, as an ensemble of interacting phonons, whose quantum dynamics is governed by a Bose--Hubbard Hamiltonian. In this work we study the quantum phases which appear in this system, and show that thermodynamical properties, such as critical parameters and critical exponents, can be measured in experiments with a limited number of ions. Besides that, interacting phonons in trapped ions offer us the possibility to access regimes which are difficult to study with ultracold bosons in optical lattices, like models with attractive or site--dependent phonon-phonon interactions.Comment: 10 page

Mesoscopic Spin-Boson Models of Trapped Ions

Trapped ions arranged in Coulomb crystals provide us with the elements to study the physics of a single spin coupled to a boson bath. In this work we show that optical forces allow us to realize a variety of spin-boson models, depending on the crystal geometry and the laser configuration. We study in detail the Ohmic case, which can be implemented by illuminating a single ion with a travelling wave. The mesoscopic character of the phonon bath in trapped ions induces new effects like the appearance of quantum revivals in the spin evolution.Comment: 4.4 pages, 5 figure

Collective generation of quantum states of light by entangled atoms

We present a theoretical framework to describe the collective emission of light by entangled atomic states. Our theory applies to the low excitation regime, where most of the atoms are initially in the ground state, and relies on a bosonic description of the atomic excitations. In this way, the problem of light emission by an ensemble of atoms can be solved exactly, including dipole-dipole interactions and multiple light scattering. Explicit expressions for the emitted photonic states are obtained in several situations, such as those of atoms in regular lattices and atomic vapors. We determine the directionality of the photonic beam, the purity of the photonic state, and the renormalization of the emission rates. We also show how to observe collective phenomena with ultracold atoms in optical lattices, and how to use these ideas to generate photonic states that are useful in the context of quantum information.Comment: 15 pages, 10 figure

DMRG and periodic boundary conditions: a quantum information perspective

We introduce a picture to analyze the density matrix renormalization group (DMRG) numerical method from a quantum information perspective. This leads us to introduce some modifications for problems with periodic boundary conditions in which the results are dramatically improved. The picture also explains some features of the method in terms of entanglement and teleportation.Comment: 4 page

Convolutional Goppa Codes

We define Convolutional Goppa Codes over algebraic curves and construct their corresponding dual codes. Examples over the projective line and over elliptic curves are described, obtaining in particular some Maximum-Distance Separable (MDS) convolutional codes.Comment: 8 pages, submitted to IEEE Trans. Inform. Theor

P.O.S. coverage index: Measurement procedure of the relationship between ball and hand

Este trabajo diseña un novedoso procedimiento de medición que relaciona el tamaño de la mano y el tamaño del balón. Se detalla este procedimiento ideado para la determinación del “Índice de Cobertura de la Mano Porras, Oliver, Sosa” (I.C.M.P.O.S.) sobre el balón. A partir de tres medidas obtenidas de la mano dominante de los deportistas con la mano en máxima apertura tomadas sobre un plano, calcularemos sus coordenadas en el espacio, y las aplicaremos sobre la esfera del balón. Posteriormente, a través de una fórmula, y teniendo en cuenta el valor central de la medida de la circunferencia del balón del deporte y de la categoría deportiva correspondiente, podremos conocer el Índice de Cobertura de la mano del deportista sobre el balón, o cantidad del balón que un deportista es capaz de abarcar con su mano completamente abierta respecto a la media esfera del balón de su categoría deportivaThis paper designs a novel measurement procedure that relates the size of the hand and the size of the ball. This procedure was devised in order to determine the "Hand Coverage Index of Porras, Oliver, Sosa" (H.C.I.P.O.S.) on the ball. Using three measurements obtained from the dominant hand of athletes with the hand on its maximum aperture taken on a flat plane, we calculated their coordinates in space, and their applications on the sphere of the ball. Subsequently, through a formula, and taking into account the central value of the measurement of the circumference of the ball and the corresponding sport category, we will be able to know the Hand Coverage Index of the athlete over the ball, or the surface of the ball that an athlete is able to cover with his fully open hand with respect to the the sphere of the ball of his sport categor

Simulating quantum-optical phenomena with cold atoms in optical lattices

We propose a scheme involving cold atoms trapped in optical lattices to observe different phenomena traditionally linked to quantum-optical systems. The basic idea consists of connecting the trapped atomic state to a non-trapped state through a Raman scheme. The coupling between these two types of atoms (trapped and free) turns out to be similar to that describing light-matter interaction within the rotating-wave approximation, the role of matter and photons being played by the trapped and free atoms, respectively. We explain in particular how to observe phenomena arising from the collective spontaneous emission of atomic and harmonic oscillator samples such as superradiance and directional emission. We also show how the same setup can simulate Bose-Hubbard Hamiltonians with extended hopping as well as Ising models with long-range interactions. We believe that this system can be realized with state of the art technology

Single and two photon emission from a semiconductor quantum dot in an optical microcavity

We calculate the single and two photon emission from a cavity containing quantum dot incoherently pumped. Results for correlation functions and the entanglement visibility of linearly polarized photons are presented