Spin dynamics and structure formation in a spin-1 condensate in a magnetic field

7 págs.; 5 figs.; PACS number s : 03.75.Mn, 03.75.Kk, 71.15.MbWe study the dynamics of a trapped spin-1 condensate in a magnetic field. First, we analyze the homogeneous system, for which the dynamics can be understood in terms of orbits in phase space. We analytically solve for the dynamical evolution of the populations of the various Zeeman components of the homogeneous system. This result is then applied via a local-density approximation to trapped quasi-one-dimensional condensates. Our analysis of the trapped system in a magnetic field shows that both the mean-field and Zeeman regimes are simultaneously realized, and we argue that the border between these two regions is where spin domains and phase defects are generated. We propose a method to experimentally tune the position of this border. ©2009 The American Physical SocietyThis work was supported by the UK EPSRC Grant No. EP/E025935.Peer Reviewe

Chiral bound states in the continuum

We present a distinct mechanism for the formation of bound states in the continuum (BICs). In chiral quantum systems there appear zero-energy states in which the wave function has finite amplitude only in one of the subsystems defined by the chiral symmetry. When the system is coupled to leads with a continuum energy band, part of these states remain bound. We derive some algebraic rules for the number of these states depending on the dimensionality and rank of the total Hamiltonian. We examine the transport properties of such systems including the appearance of Fano resonances in some limiting cases. Finally, we discuss experimental setups based on microwave dielectric resonators and atoms in optical lattices where these predictions can be tested.Comment: 9 pages, 8 figures. v2: includes results specific to honeycomb lattice; matches published versio

Many-body studies on atomic quantum systems

This thesis presents a set of studies on atomic systems where quantum effects are particularly relevant. These studies have been developed by applying a variety of tools from many-body physics. First of all, we have studied the prospects for the existence of a superfluid transition in an ultracold gas of fermionic atoms, by generalizing the BCS theory of superconductivity to the case when the two species that pair have different densities and the ground state may spontaneously break one or more symmetries. In a second part, we have studied the dynamics of a Bose-Einstein condensate whose spin degree of freedom is free to evolve inside a quasi-onedimensional optical trap. We have used a mean-field formulation to address both the zero temperature case and the finite temperature one. Finally, we have performed a careful study of the ground state and the line tension of two-dimensional systems of helium-4. First, we have used Monte Carlo techniques, then with a Density Functional built on-purpose. Comments are welcome! KEYWORDS: Cold gases, Pairing, Spinor condensate, Helium, Two dimensionsComment: PhD thesis with 216 pages and 48 figures; uses pdflatex. Some figures have been submitted at low resolution to fit arXiv's memory limitations. The "complete" version can be downloaded from http://www.tesisenxarxa.net/TDX-0426106-152454

Measuring molecular electric dipoles using trapped atomic ions and ultrafast laser pulses

We study a hybrid quantum system composed of an ion and an electric dipole. We show how a trapped ion can be used to measure the small electric field generated by a classical dipole. We discuss the application of this scheme to measure the electric dipole moment of cold polar molecules, whose internal state can be controlled with ultrafast laser pulses, by trapping them in the vicinity of a trapped ion.Comment: 13 pages, 6 figures. Substantially modified version, with 4 new appendices; matches published versio

Collective modes of a trapped ion-dipole system

We study a simple model consisting of an atomic ion and a polar molecule trapped in a single setup, taking into consideration their electrostatic interaction. We determine analytically their collective modes of excitation as a function of their masses, trapping frequencies, distance, and the molecule's electric dipole moment. We then discuss the application of these collective excitations to cool molecules, to entangle molecules and ions, and to realize two-qubit gates between them. We finally present a numerical analysis of the possibility of applying these tools to study magnetically ordered phases of two-dimensional arrays of polar molecules, a setup proposed to quantum-simulate some strongly-correlated models of condensed matter.Comment: v2: 13 pages, 8 figures (from 10 figure files). Matches published version in Appl. Phys. B, special issue "Wolfgang Paul 100

Measuring correlations of cold atom systems using multiple quantum probes

We present a non-destructive method to probe a complex quantum system using multiple impurity atoms as quantum probes. Our protocol provides access to different equilibrium properties of the system by changing its coupling to the probes. In particular, we show that measurements with two probes reveal the system's non-local two-point density correlations, for probe-system contact interactions. We illustrate our findings with analytic and numerical calculations for the Bose-Hubbard model in the weakly and strongly-interacting regimes, under conditions relevant to ongoing experiments in cold atom systems.Comment: 11 pages, 6 figures. v2: enhanced discussion in light of other correlation measurement methods available; matches published versio

Dynamical interferences to probe short-pulse photoassociation of Rb atoms and stabilization of Rb_2 dimers

We analyze the formation of Rb_2 molecules with short photoassociation pulses applied to a cold Rb-85 sample. A pump laser pulse couples a continuum level of the ground electronic state X ^1\Sigma_{g}^+ with bound levels in the 0_{u}^+ (5S+5P_{1/2}) and 0_{u}^+ (5S+5P_{3/2}) vibrational series. The nonadiabatic coupling between the two excited channels induces time-dependent beatings in the populations. We propose to take advantage of these oscillations to design further laser pulses that probe the photoassociation process via photoionization or that optimize the stabilization in deep levels of the ground state.Comment: 4 pages, 5 figures. v2: major changes in introduction, discussion clarified. v3: minor corrections. v4: matches published versio

Phase Stabilization of a Frequency Comb using Multipulse Quantum Interferometry

From the interaction between a frequency comb and an atomic qubit, we derive quantum protocols for the determination of the carrier-envelope offset phase, using the qubit coherence as a reference, and without the need of frequency doubling or an octave spanning comb. Compared with a trivial interference protocol, the multipulse protocol results in a polynomial enhancement of the sensitivity O(N^{-2}) with the number N of laser pulses involved. We present specializations of the protocols using optical or hyperfine qubits, Lambda-schemes and Raman transitions, and introduce methods where the reference is another phase-stable cw-laser or frequency comb

Molecule formation and quantum correlations in optical lattices

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