LATIN‐AMERICAN SCHOOL OF PHYSICS XXXVIII ELAF: Quantum Information and Quantum Cold Matter
994(2008); http://dx.doi.org/10.1063/1.2907759View Description Hide Description
In this course, we deal with various important topics in Quantum Information Theory such as the basic tools as gates and circuits, decoherence free subspaces, quantum copying machines and quantum processors and the physical implementation of such ideas with trapped ions.
994(2008); http://dx.doi.org/10.1063/1.2907760View Description Hide Description
This course aims to introduce the student to random matrix models for decoherence and fidelity decay. They present a very powerful alternate approach, that emphasizes the disordered character of many environments and uncontrollable perturbations/couplings. The inherent integrability of such models makes analytic studies possible. We limit our considerations to linear response treatment, as high fidelity and small decoherence are the backbone of quantum information processes. For fidelity decay, where experimental results are available, a comparison with experiments shows excellent agreement with random matrix theory predictions.
994(2008); http://dx.doi.org/10.1063/1.2907761View Description Hide Description
This text corresponds to part of the course presented at the ELAF XXXVIII. It is composed of work previously done along the years. The level of this introduction follows the last year of undergraduate and first year of graduate courses. We apologize to the experts on this field, but the idea here is to provide the basic principles and tools for students just getting involved with this topic. For those interested in a deeper reading on the subject, we strongly recommend the review article published by Courteille, Bagnato and Yukalov  from which part of this text was extracted. The lecture is divided in three parts: an introduction, the basic concepts of Bose‐Einstein Condensation and information about making and probing BECs.
994(2008); http://dx.doi.org/10.1063/1.2907762View Description Hide Description
I review free and trapped Bose‐Einstein condensates (BECs) [1, 2, 3, 4, 5]. In an isotropic harmonic potential the single‐particle ground state introduces a new intrinsic scale of length [the ground‐state size ] and energy [the ground‐state energy ]. When the trap rotates [6, 7, 8], there is a critical angular velocity for the appearance of one or a few quantized vortices. For more rapid rotation [9, 10, 11, 12, 13] the condensate contains a vortex array. The resulting centrifugal forces expand the condensate radially and shrink it axially; thus the condensate becomes effectively two‐dimensional. If the external rotation speed approaches the frequency of the radial harmonic confining potential, the condensate enters the “lowest‐Landau‐level” regime, and a simple description again becomes possible [14, 15]. Eventually, the system is predicted to make a quantum phase transition to a highly correlated state analogous to the fractional quantum Hall states of electrons in a strong magnetic field [16, 17, 18, 19, 20].
994(2008); http://dx.doi.org/10.1063/1.2907757View Description Hide Description
Unification of the Bardeen, Cooper and Schrieffer (BCS) and the Bose‐Einstein condensation (BEC) theories is surveyed in terms of a generalized BEC (GBEC) finite‐temperature statistical formalism. A vital distinction is that Cooper pairs (CPs) are true bosons that may suffer a BEC since they obey BE statistics, in contrast with BCS pairs that are “hard‐core bosons” at best. A second crucial ingredient is the explicit presence of hole‐pairs (2h) alongside the usual electron‐pairs (2e). A third critical element (particularly in 2D where ordinary BEC does not occur) is the linear dispersion relation of CPs in leading order in the center‐of‐mass momentum (CMM) power‐series expansion of the CP energy. The GBEC theory reduces in limiting cases to all five continuum (as opposed to “spin”) statistical theories of superconductivity, from BCS on one extreme to the BEC theory on the other, as well as to the BCS‐Bose “crossover” picture and the 1989 Friedberg‐Lee BEC theory. It accounts for 2e‐ and 2h‐CPs in arbitrary proportions while BCS theory can be deduced from the GBEC theory but allows only equal (50%‐50%) BE condensed‐mixtures of both kinds of CPs. As it yields the precise BCS gap equation for all temperatures as well as the precise BCS zero‐temperature condensation energy for all couplings, it suggests that the BCS condensate is a BE condensate of a ternary mixture of kinematically independent unpaired electrons coexisting with equally proportioned weakly‐bound zero‐CMM 2e‐ and 2h‐CPs. Without abandoning the electron‐phonon mechanism in moderately weak coupling, and fortuituously insensitive to the BF interactions, the GBEC theory suffices to reproduce the unusually high values of (in units of the Fermi temperature ) of 0.01–0.05 empirically found in the so‐called “exotic” superconductors of the Uemura plot, including cuprates, in contrast to the low values of roughly reproduced by BCS theory for conventional (mostly elemental) superconductors.