Rosario Paredes

An optimized description of a confined interacting Fermi system

We provide an efficient form to express the action of a many-body Hamiltonian of harmonically trapped interacting Fermi particles on wavefunctions built from paired states. The expression is suitable to numerically determine the ground state energy, regardless of the form of the two-body interaction. It takes advantage of the knowledge of the two-particle problem and the inherent properties of the matrix form of the many-body wavefunction. As an example, we evaluate the properties of a system composed of a balanced mixture of two families of fermions confined in a harmonic trap interacting through a short-range exponential potential. Numerical results for N ≤ 10 and N = 35, 56, 84 and 165 particles of each family are reported. In the strong interacting regime corresponding to an infinite s-wave scattering length, our results give an upper bound to the Bertsch parameter for harmonically trapped systems (E/EIFG)2 = 1 + β ≤ 0.376 ± 0.008 with E the total energy and EIFG the energy for the analogous ideal Fermi gas. The influence of the harmonic trap and the interaction potential is exhibited in one and two-body correlation functions.

Intrinsic decoherence in an ultracold Bose gas confined in a double-well potential

We address the intrinsic decoherence of an N-body interacting bosonic quantum fluid confined in a double-well potential in one dimension, and its effect on the transition from coherent oscillations to self-trapping regimes as a function of the interparticle interaction. Performing a full quantum approach to the N-particle system, we study the transition and the observed decoherence through the analysis of the one-particle reduced density matrix. The results are obtained by following the time evolution of such a matrix. For large systems and because of the interparticle interactions, the system reaches stationary states which can be characterized both by the vanishing of the off-diagonal matrix elements, in what one may call the preferred basis, and by the value of its associated von Neumman entropy. The present results could be useful in analysing experimental realizations, such as those by Albiez et al (2005 Phys. Rev. Lett. 95 010402).

BEC-BCS crossover of a trapped Fermi gas without using the local density approximation

We perform a variational quantum Monte Carlo simulation of an interacting Fermi gas confined in a three dimensional harmonic potential. This gas is considered as the precursor system from which a molecular bosonic gas is formed. Based on the results of two-body calculations for trapped atoms, we propose a family of variational many-body wave functions that takes into account the qualitative different nature of the Bardeen-Cooper-Schieffer and Bose-Einstein condensate regimes as a function of the scattering length. Energies, densities, and correlation functions are calculated and compared with previous results for homogeneous gases. Universality tests at the unitarity limit are performed including the verification of the virial relation and the evaluation of the

Quantum simulation of competing orders with fermions in quantum optical lattices

\ensuremath{\beta}

Delocalization to self-trapping transition of a Bose fluid confined in a double-well potential: an analysis via one- and two-body correlation properties

parameter.

Superfluid and supersolid phases in optical lattices in two dimensions

Ultracold Fermi atoms confined in optical lattices coupled to quantized modes of an optical cavity are an ideal scenario to engineer quantum simulators in the strongly interacting regime. The system has both short range and cavity induced long range interactions. We propose such a scheme to study the interplay of density order, antiferromagnetic states, and superfluidity in the Hubbard model in a high finesse optical cavity at T = 0. We demonstrate that those phases can be accessed by properly tuning the linear polarizer of an external pump beam via the cavity back-action effect, while modulating the system doping. This emulates typical escenarios of analog strongly correlated electronic systems.

Phase transitions in ultracold Bose gases confined in optical lattices

We revisit the delocalized to self-trapping transition in an interacting bosonic fluid confined in a double-well potential in the context of full quantum calculations. We first study one- and two-body properties in the energy eigenstates to determine the transition as a function of the energy of the fluid. This occurs provided the interparticle interaction is above a critical or threshold value. Next, we analyse the evolution in time of the same observables in a set of coherent states to show that the N-particle Bose fluid reaches stationary states, whose expectation values turn out to coincide with those in the eigenestates. This stationary or collapsed state alternates with recurrent revivals. Here we show that the time spent in the stationary state increases with the number of particles, relatively to the time during the revivals. This stationarity property is in severe contrast with that of mean-field states since these always appear as coherent oscillations either for delocalized or self-trapped states.

Energetic cooling below the BEC transition: a quantum kinetic description within the Bogoliubov approximation

This work addresses the study of superfluid and supersolid phases of dipolar Fermi molecules lying in a two dimensional space. The prediction of these phases, performed within a mean field analysis, results from proposing a model in which interacting Fermi molecules are confined in a bilayer array of parallel lattices with square symmetry. As a result of the repulsive intralayer and attractive interlayer interactions between dipolar molecules, a checkerboard pattern and a paired superfluid regimes can emerge. The supersolid phase is identified as the spatial coexistence of density ordered and superfluid phases. The model here proposed can be implemented within the current experimental capabilities as a function of the interlayer separation and the application of an external electric field varying the dipolar interaction between molecules.This work addresses the study of superfluid and supersolid phases of dipolar Fermi molecules lying in a two dimensional space. The prediction of these phases, performed within a mean field analysis, results from proposing a model in which interacting Fermi molecules are confined in a bilayer array of parallel lattices with square symmetry. As a result of the repulsive intralayer and attractive interlayer interactions between dipolar molecules, a checkerboard pattern and a paired superfluid regimes can emerge. The supersolid phase is identified as the spatial coexistence of density ordered and superfluid phases. The model here proposed can be implemented within the current experimental capabilities as a function of the interlayer separation and the application of an external electric field varying the dipolar interaction between molecules.

The contact in the BCS–BEC crossover for finite range interacting ultracold Fermi gases

We address the study of quantum Bose fluids confined in optical lattices subject to the influence of a time varying disordered external potential. The aim is to elucidate the interplay among lattice structure, interparticle interactions and the influence of structural disorder on dynamical and stationary ground state properties. The analysis in quasi one-dimension systems is done combining both mean field and Bose–Hubbard schemes to capture the essence of the quantum many body problem. Our predictions include the manifestation of superfluid, Mott and Anderson-like phases. We also present a natural extension of our technique to investigate two-dimensions systems. A general panorama of the current studies in bosonic systems is also given.

Glassy dynamics and Landau-Zener phenomena in trapped quasi-one-dimensional coupled Bose-Einstein condensates

The dynamics of Bose–Einstein condensation in a three-dimensional harmonic trap is studied explicitly including the Bogoliubov approximation for temperatures below the critical one. To model the evolution towards equilibrium at each cooling step, we derive quantum kinetic equations that describe the dynamics of the gas for temperatures above and below the transition temperature. These equations, valid in the Born and Markov approximations, consider the essential role of the chemical potential as the main parameter that signals the transition. The kinetic equation that describes the growth of the condensate below the transition temperature is derived within the Bogoliubov approximation. To illustrate our results we propose an energetic cooling protocol and simulate the whole sequence of the formation of a condensate.