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This work implements a variational determination of the elements of two-electron reduced density matrices corresponding to the ground and excited states of N-electron interacting systems based on the dispersion operator technique. The procedure extends the previously reported proposal [Nakata et al., J. Chem. Phys. 125, 244109 (2006)] to two-particle interaction Hamiltonians and N-representability conditions for the two-, three-, and four-particle reduced density matrices in the doubly occupied configuration interaction space. The treatment has been applied to describe electronic spectra using two benchmark exactly solvable pairing models: reduced Bardeen–Cooper–Schrieffer and Richardson–Gaudin–Kitaev Hamiltonians. The dispersion operator combined with N-representability conditions up to the four-particle reduced density matrices provides excellent results., Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas

This work incorporates translational and reflection symmetry reductions to the variational determination of the two-particle reduced density matrix (2-RDM) corresponding to the ground state of N-particle systems, within the doubly occupied configuration interaction (DOCI) space. By exploiting these symmetries within this lower-bound variational methodology it is possible to treat larger systems than those previously studied. The 2-RDM matrix elements are calculated by imposing up to four-particle N-representability constraint conditions using standard semidefinite programing algorithms. The method is applied to the one- and two-dimensional XXZ spin 1/2 model of quantum magnetism. Several observables including the energy and the spin–spin correlation functions are obtained to assess the physical content of the variationally determined 2-RDM. Comparison with quantum-Monte Carlo and matrix product state simulations shows that in most cases only requiring up to three-particle positivity conditions is enough to correctly describe the ground-state properties of these one- and two-dimensional models.

We develop a multimode model that describes the dynamics on a rotating Bose-Einstein condensate confined by a ring-shaped optical lattice with large filling numbers. The parameters of the model are obtained as a function of the rotation frequency using full 3D Gross-Pitaevskii simulations. From such numerical calculations, we extract the velocity field induced at each site and analyze the relation and the differences between the phase of the hopping parameter of our model and the Peierls phase. To this end, a detailed discussion of such phases is presented in geometrical terms which takes into account the position of the junctions for different configurations. For circularly symmetric onsite densities a simple analytical relation between the hopping phase and the angular momentum is found for arbitrary number of sites. Finally, we confront the results of the rotating multimode model dynamics with Gross-Pitaevskii simulations finding a perfect agreement.

We study the propagation of a density perturbation in a weakly interacting boson gas confined on a lattice and in the presence of square dimerized impurities. Such a two-dimensional random-dimer model (2D-DRDM), previously introduced in [Capuzzi et al., Phys. Rev. A 92, 053622 (2015)], is the disorder transition from a single square lattice, where impurities are absent, to a bipartite square lattice, where the number of impurities is maximum and coincides with half the number of lattice sites. We show that disorder correlations can play a crucial role in the dynamics for a broad range of parameters by allowing density fluctuations to propagate in the 2D-DRDM lattice, even in the limit of strong disorder. In such a regime, the propagation speed depends on the percentage of impurities, interpolating between the speed in a single monoperiodic lattice and that in a bipartite one., 9 pages, 7 figures

10 pags., 7 figs., The variational reduced density matrix theory has been recently applied with great success to models within the truncated doubly occupied configuration interaction space, which corresponds to the seniority zero subspace. Conservation of the seniority quantum number restricts the Hamiltonians to be based on the SU(2) algebra. Among them there is a whole family of exactly solvable Richardson-Gaudin pairing Hamiltonians. We benchmark the variational theory against two different exactly solvable models, the Richardson-Gaudin-Kitaev and the reduced BCS Hamiltonians. We obtain exact numerical results for the so-called PQGT N-representability conditions in both cases for systems that go from 10 to 100 particles. However, when random single-particle energies as appropriate for small superconducting grains are considered, the exactness is lost but still a high accuracy is obtained., A.R. and J.D. acknowledge the financial support of the Spanish Ministerio de Economıá y Competitividad and the European regional development fund (FEDER) under Projects No. FIS2015-63770-P. D.R.A. acknowledges financial support of the Consejo Nacional de Investigaciones Cientıfícas y Tećnicas under Grants Nos. PIP 11220130100377CO and 2013- 1401PCB and of the Agencia Nacional de Promocioń Cientıfíca y Tecnológica, Argentina under Grant No. PICT-201-0381. P.C. acknowledges financial support of the Consejo Nacional de Investigaciones Cientıfícas y Tećnicas under Grant. No. PIP 11220150100442CO. D.R.A. and P.C. acknowledge financial support of the Universidad de Buenos Aires under Grant No. 20020150100157BA.

This work deals with the variational determination of the two-particle reduced density matrix (2-RDM) and the energy corresponding to the ground state of N-particle systems within the doubly occupied configuration interaction (DOCI) space. Here, we impose for the first time up to four-particle N-representability constraint conditions in the variational determination of the 2-RDM matrix elements using the standard semidefinite programming algorithms. The energies and 2-RDMs obtained from this treatment and the corresponding computational costs are compared with those arisen from previously reported less restrictive variational methods [D. R. Alcoba et al., J. Chem. Phys. 149, 194105 (2018)] as well as with the exact DOCI values. We apply the different approximations to the one-dimensional XXZ model of quantum magnetism, which has a rich phase diagram with one critical phase and constitutes a stringent test for the method. The numerical results show the usefulness of our treatment to achieve a high degree of accuracy., Facultad de Ciencias Exactas, Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas

We study a special dynamical regime of a Bose-Einstein condensate in a ring-shaped lattice where the populations in each site remain constant during the time evolution. The states in this regime are characterized by equal occupation numbers in alternate wells and nontrivial phases, while the phase differences between neighboring sites evolve in time yielding persistent currents that oscillate around the lattice. We show that the velocity circulation around the ring lattice alternates between two values determined by the number of wells and with a specific time period that is only driven by the on-site interaction energy parameter. In contrast to the self-trapping regime present in optical lattices, the occupation number at each site does not show any oscillation and the particle imbalance does not possess a lower bound for the phenomenon to occur. These findings are predicted with a multimode model and confirmed by full three-dimensional Gross-Pitaevskii simulations using an effective on-site interaction energy parameter. Fil: Nigro, Mauro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina Fil: Capuzzi, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina Fil: Jezek, Dora Marta. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina

We study the dynamics of three-dimensional weakly linked Bose-Einstein condensates using a multimode model with an effective interaction parameter. The system is confined by a ring-shaped four-well trapping potential. By constructing a two-mode Hamiltonian in a reduced highly symmetric phase space, we examine the periodic orbits and calculate their time periods both in the self-trapping and Josephson regimes. The dynamics in the vicinity of the reduced phase space is investigated by means of a Floquet multiplier analysis, finding regions of different linear stability and analyzing their implications on the exact dynamics. The numerical exploration in an extended region of the phase space demonstrates that two-mode tools can also be useful for performing a partition of the space in different regimes. Comparisons with Gross-Pitaevskii simulations confirm these findings and emphasize the importance of properly determining the effective on-site interaction parameter governing the multimode dynamics., 12 pages, 13 figures

11 pags., 6 figs., 5 tabs., 2 apps., Ground-state energies and two-particle reduced density matrices (2-RDMs) corresponding to N-particle systems are computed variationally within the doubly occupied configuration interaction (DOCI) space by constraining the 2-RDM to satisfy a complete set of three-particle N-representability conditions known as three-positivity conditions. These conditions are derived and implemented in the variational calculation of the 2-RDM with standard semidefinite programming algorithms. Ground state energies and 2-RDMs are computed for N2, CO, CN−, and NO+ molecules at both equilibrium and nonequilibrium geometries as well as for pairing models at different repulsive interaction strengths. The results from the full three-positivity conditions are compared with those from the exact DOCI method and with approximated 2-RDM variational ones obtained within two-positivity and two-positivity plus a subset of three-positivity conditions, as recently reported [D. R. Alcoba et al., J. Chem. Phys. 148, 024105 (2018) and A. Rubio-Garc´ıa et al., J. Chem. Theory Comput. 14, 4183 (2018)]. The accuracy of these numerical determinations and their low computational cost demonstrate the usefulness of the three-particle variational constraints within the DOCI framework. Published by AIP Publishing., The authors acknowledge financial support from the Universidad de Buenos Aires (Grant No. 20020150100157BA), the Consejo Nacional de Investigaciones Cientıficas y Tecnicas (Grant Nos. PIP 11220130100377CO, PIP ´ 11220130100311CO, 11220150100442CO, and 2013-1401- PCB), the Agencia Nacional de Promocion Cientfica y Tecnologica, Argentina (Grant No. PICT-201-0381), and the ´ Spanish Ministerio de Economıa y Competitividad and the European regional development fund (FEDER) (No. FIS2015- 63770-P).

We study the dynamics of three-dimensional Bose-Einstein condensates confined by double-well potentials using a two-mode model with an effective on-site interaction energy parameter. The effective on-site interaction energy parameter is evaluated for different numbers of particles ranging from a low experimental value to larger ones approaching the Thomas-Fermi limit, yielding important corrections to the dynamics. We analyze the time periods as functions of the initial imbalance and find a closed integral form that includes all interaction-driven parameters. A simple analytical formula for the self-trapping period is introduced and shown to accurately reproduce the exact values provided by the two-mode model. Systematic numerical simulations of the problem in 3D demonstrate the excellent agreement of the two-mode model for experimental parameters., Comment: 7 pages, 5 figures

This work deals with the spin contamination in N-electron wave functions provided by the excitation-based configuration interaction methods. We propose a procedure to ensure a suitable selection of excited N-electron Slater determinants with respect to a given reference determinant, required in these schemes. The procedure guarantees the construction of N-electron wave functions which are eigenfunctions of the spin-squared operator S 2, avoiding any spin contamination. Our treatment is based on the evaluation of the excitation level of the determinants by means of the expectation value of an excitation operator formulated in terms of spin-free replacement operators. We report numerical determinations of energies and S 2 expectation values, arising from our proposal as well as from traditional configuration interaction methods, in selected open-shell systems, in order to compare the behavior of these procedures and their computational costs., Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas

We study the dynamics of two gray solitons in a Bose-Einstein condensate confined by a toroidal trap with a tight confinement in the radial direction. Gross-Pitaevskii simulations show that solitons can be long living objects passing through many collisional processes. We have observed quite different behaviors depending on the soliton velocity. Very slow solitons, obtained by perturbing the stationary solitonic profile, move with a constant angular velocity until they collide elastically and move in the opposite direction without showing any sign of lowering their energy. In this case the density notches are always well separated and the fronts are sharp and straight. Faster solitons present vortices around the notches, which play a central role during the collisions. We have found that in these processes the solitons lose energy, as the outgoing velocity turns out to be larger than the incoming one. To study the dynamics, we model the gray soliton state with a free parameter that is related to the soliton velocity. We further analyze the energy, soliton velocity and turning points in terms of such a free parameter, finding that the main features are in accordance with the infinite one-dimensional system., Comment: 15 pages, 11 figures. Accepted in PRA

We present a configuration interaction method in which the Hamiltonian of an N-electron system is projected on Slater determinants selected according to the seniority-number criterion along with the traditional excitation-based procedure. This proposed method is especially useful to describe systems which exhibit dynamic (weak) correlation at determined geometric arrangements (where the excitation-based procedure is more suitable) but show static (strong) correlation at other arrangements (where the seniority-number technique is preferred). The hybrid method amends the shortcomings of both individual determinant selection procedures, yielding correct shapes of potential energy curves with results closer to those provided by the full configuration interaction method., Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas

We investigate the origin of a disagreement between the two-mode model and the exact Gross-Pitaevskii dynamics applied to double-well systems. In general this model, even in its improved version, predicts a faster dynamics and underestimates the critical population imbalance separating Josephson and self-trapping regimes. We show that the source of this mismatch in the dynamics lies in the value of the on-site interaction energy parameter. Using simplified Thomas-Fermi densities, we find that the on-site energy parameter exhibits a linear dependence on the population imbalance, which is also confirmed by Gross-Pitaevskii simulations. When introducing this dependence in the two-mode equations of motion, we obtain a reduced interaction energy parameter which depends on the dimensionality of the system. The use of this new parameter significantly heals the disagreement in the dynamics and also produces better estimates of the critical imbalance., 5 pages, 4 figures, accepted in PRA

We present numerical predictions for the shape of the pairing fluctuations in harmonically trapped atomic 6Li with two spin projections, based on the fluiddynamical description of cold fermions with pairing interactions. In previous works it has been shown that when the equilibrium of a symmetric mixture is perturbed, the linearized fluiddynamic equations decouple into two sets, one containing the sound mode of fermion superfluids and the other the pairing mode. The latter corresponds to oscillations of the modulus of the complex gap and is driven by the kinetic energy densities of the particles and of the pairs. Assuming proportionality between the heat flux and the energy gradient, the particle kinetic energy undergoes a diffusive behavior and the diffusion parameter is the key parameter for the relaxation time scale. We examine a possible range of values for this parameter and find that the shape of the pairing oscillation is rather insensitive to the precise value of the transport coefficient. Moreover, the pairing fluctuation is largely confined to the center of the trap, and the energy of the pairing mode is consistent with the magnitude of the equilibrium gap. Fil: Capuzzi, Pablo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina Fil: Hernandez, Ester Susana. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina Fil: Szybisz, Leszek. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica; Argentina

We develop a procedure to modify the correlations of a speckle potential. This procedure, that is suitable for spatial light modulator devices, allows one to increase the localization efficiency of the speckle in a narrow energy region whose position can be easily tuned. This peculiar energy-dependent localization behavior is explored by pulling the potential through a cigar-shaped Bose-Einstein condensate. We show that the percentage of dragged atoms as a function of the pulling velocity depends on the potential correlations below a threshold of the disorder strength. Above this threshold, interference effects are no longer clearly observable during the condensate drag., Comment: 8 pages, 8 figures, final version

We study the dynamics of a harmonically trapped quasi-one-dimensional Bose-Einstein condensate subjected to a moving disorder potential of finite extent. We show that, due to the inhomogeneity of the sample, only a percentage of the atoms is localized at supersonic velocities of a random potential. We find that this percentage can be sensitively increased by introducing suitable correlations in the disorder potential such as those provided by random dimers., Comment: 6 pages, 9 figures

We study the ground-state configurations of few interacting bosons confined in two dimensions by anisotropic harmonic potentials. By means of variational calculations, including correlation effects, we show that the arrangement of bosons strongly depends on the strength of the repulsive interaction and the anisotropy of the confinement. We compute the condensate fraction of the system and found that by increasing the anisotropy of the potential a weaker interaction suffices to destroy the condensate and favors the emergence of a crystal-like structure. © 2011 American Physical Society. Fil: Mese, A.I.. Trakya Üniversitesi; Turquía Fil: Capuzzi, Pablo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina Fil: Aktas, S.. Trakya Üniversitesi; Turquía Fil: Akdeniz, Z.. Pîrî Reis Üniversitesi; Turquía Fil: Okan, S.E.. Trakya Üniversitesi; Turquía

We study, experimentally and theoretically, the controlled transfer of harmonically trapped ultracold gases between different quantum states. In particular we experimentally demonstrate a fast decompression and displacement of both a non-interacting gas and an interacting Bose-Einstein condensate which are initially at equilibrium. The decompression parameters are engineered such that the final state is identical to that obtained after a perfectly adiabatic transformation despite the fact that the fast decompression is performed in the strongly non-adiabatic regime. During the transfer the atomic sample goes through strongly out-of-equilibrium states while the external confinement is modified until the system reaches the desired stationary state. The scheme is theoretically based on the invariants of motion and scaling equations techniques and can be generalized to decompression trajectories including an arbitrary deformation of the trap. It is also directly applicable to arbitrary initial non-equilibrium states., Comment: 36 pages, 14 figures

We study the formation of Faraday waves in an elongated Bose-Einstein condensate in the presence of a one-dimensional optical lattice. The waves are parametrically excited by modulating the radial confinement of the condensate close to a transverse breathing mode of the system. For very shallow optical lattices, phonons with a well-defined wave vector propagate along the condensate, as in the absence of the lattice, and we observe the formation of a Faraday pattern. We find that by increasing the potential depth the local sound velocity decreases, and when it equals the condensate local phase velocity, the condensate develops an incoherent superposition of several modes and the parametric excitation of Faraday waves is suppressed.

We present an investigation of the fast decompression of a three-dimensional (3D) Bose-Einstein condensate (BEC) at finite temperature using an engineered trajectory for the harmonic trapping potential. Taking advantage of the scaling invariance properties of the time-dependent Gross-Pitaevskii equation, we exhibit a solution yielding a final state identical to that obtained through a perfectly adiabatic transformation, in a much shorter time. Experimentally, we perform a large trap decompression and displacement within a time comparable to the final radial trapping period. By simultaneously monitoring the BEC and the non-condensed fraction, we demonstrate that our specific trap trajectory is valid both for a quantum interacting many-body system and a classical ensemble of non-interacting particles., 5 pages, 4 figures

We numerically obtain stationary rings of vortices in pancake-shaped Bose-Einstein condensates confined in a three-dimensional nonrotating trap. For this purpose we use a static axisymmetric trapping potential that can sustain locally stable off-axis vortices. We analyze the maximum number of vortices the system can host as a function of the number of particles. We also show that this system provides a very suitable scenario for predicting vortex dynamics in inhomogeneous media. Specifically, on the one hand, we derive an exact and simple analytical expression for the velocity field in a particular vortex position due to the presence of the other vortices of the array. On the other hand, using the fact that in stationary conditions this field should balance all other contributions to the velocity, we investigate the applicability of approximated expressions for the precession velocity obtained in previous works for condensates with a single vortex. © 2008 The American Physical Society. Fil: Jezek, Dora Marta. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina Fil: Capuzzi, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina Fil: Guilleumas, M.. Universidad de Barcelona; España Fil: Mayol, R.. Universidad de Barcelona; España

We use hydrodynamic equations to study the formation of Faraday waves in a superfluid Fermi gas at zero temperature confined in a strongly elongated cigar-shaped trap. First, we treat the role of the radial density profile in the limit of an infinite cylindrical geometry and analytically evaluate the wavelength of the Faraday pattern. The effect of the axial confinement is fully taken into account in the numerical solution of hydrodynamic equations and shows that the infinite cylinder geometry provides a very good description of the phenomena., Comment: 6 pages, 7 figures. Figures 4 and 6 in high resolution on request

We present a generalization of the fluid-dynamical scheme developed for nuclear physics to the case of two trapped fermion species with pairing interactions. To establish a macroscopic description of the mass and momentum conservation laws, we adopt a generalization of the usual Thomas-Fermi approach that includes the pairing energy. We analyze the equilibrium density and gap profiles for an equal population mixture of harmonically trapped Li6 atoms for different choices of the local equation of state. We examine slight departures from equilibrium within our formulation, finding that density oscillations can propagate as first sound coupled to pairing vibrations, that in a homogeneous fermion system exhibit a Bogoliubov-like quasiparticle spectrum. In this case, the dispersion relation for the coupled modes displays a rich scenario of stable, unstable, and damped regimes. © 2008 The American Physical Society. Fil: Capuzzi, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina Fil: Hernandez, Ester Susana. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina Fil: Szybisz, Leszek. Universidad de Buenos Aires; Argentina. Comisión Nacional de Energía Atómica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina

We evaluate the extraction of angular momentum from quantized vortices in trapped Bose-Einstein condensates. Within a variational approach we show that the energy barrier between the ground state and the state containing an axisymmetric vortex can be crossed in a scattering process by density perturbations. The transfer of angular momentum can be made total for suitably chosen density perturbations carrying about 10% of the ground-state energy, irrespectively of the number of particles in the condensate. A similar pattern is reproduced by the full solution of the Gross-Pitaevskii equation, although interference and diffusion effects are now seen to limit the efficiency of the process. © 2008 The American Physical Society. Fil: Capuzzi, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina Fil: Federici, F.. Centre National de la Recherche Scientifique; Francia Fil: Tosi, M. P.. Centre National de la Recherche Scientifique; Francia

To complement existing knowledge of the density matrix γF (x, y) of independent fermions for N particles in one dimension under harmonic confinement, the corresponding matrix γIB (x, y) for impenetrable bosons is given for N = 2 and 3 (with the N = 4 form available also). For fermions the momentum density is then obtained and illustrated numerically for N = 10. The boson momentum density is studied analytically at high momentum p, the coefficients of the p-4 and p-6 terms being tabulated for N = 2 - 5 inclusive. Their dependence on powers of N is exhibited numerically. Finally, the functional relationship between γIB (x, y) and γF (x, y) is formally set out and illustrated. © 2006 Elsevier B.V. All rights reserved. Fil: Capuzzi, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Scuola Normale Superiore; Italia Fil: Howard, I. A.. Universiteit Antwerp; Bélgica Fil: March, N. H.. Universiteit Antwerp; Bélgica. University of Oxford; Reino Unido Fil: Tosi, M. P.. Scuola Normale Superiore; Italia

We investigate the momentum distribution of interacting electrons confined in a two-dimensional parabolic quantum dot for varying values of the interaction strength and for different number of electrons. We use an optimized Jastrow-type wave function for the ground state in which the Slater determinant part has been calculated using density-functional theory and evaluate the ground-state momentum distribution using the Fermi hypernetted-chain equations. We discuss the effects of interactions on the momentum distribution and reveal the existence of a shell structure in momentum space in analogy with what happens to the spatial density profile. The momentum distribution can thus be used as a further tool to investigate the effects of the interaction in parabolic quantum dots. © 2006 The American Physical Society. Fil: Gattobigio, M.. Institut de Physique de Nice; Italia Fil: Capuzzi, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina

We use hydrodynamic equations to study sound propagation in a superfluid Fermi gas at zero temperature inside a strongly elongated cigar-shaped trap, with main attention to the transition from the BCS to the unitary regime. First, we treat the role of the radial density profile in the limit of a cylindrical geometry and then evaluate numerically the effect of the axial confinement in a configuration in which a hole is present in the gas density at the center of the trap. We find that in a strongly elongated trap the speed of sound in both the BCS and the unitary regime differs by a factor 3/5 from that in a homogeneous three-dimensional superfluid. The predictions of the theory could be tested by measurements of sound-wave propagation in a setup such as that exploited by Andrews [Phys. Rev. Lett. 79, 553 (1997)] for an atomic Bose-Einstein condensate. © 2006 The American Physical Society. Fil: Capuzzi, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina Fil: Vignolo, P.. Consiglio Nazionale delle Ricerche; Italia Fil: Federici, F.. Consiglio Nazionale delle Ricerche; Italia Fil: Tosi, M.P.. Consiglio Nazionale delle Ricerche; Italia

We evaluate the transition from zero-sound to first-sound behaviour with increasing collisionality in the propagation of density waves through an ultracold gaseous mixture of fermionic atoms confined in the normal state inside a cigar-shaped harmonic trap. We study for this purpose the evolution of the one-body distribution functions associated with a density perturbation generated in the central region of the cloud, as obtained by solving numerically the Vlasov-Landau equations. We examine a variety of trap anisotropies and of repulsive or attractive interaction strengths between the components of the mixture, and the speed of propagation of the density disturbance is found to decrease in both cases as the magnitude of the coupling strength is increased. The results are compared with the values of the speed of zero sound and of first sound, as obtained analytically from the limit of vanishing collisionality and from linearized hydrodynamics. The main effects of the quasi-one-dimensional confinement are the stabilization of zero-sound excitations in the attractive regime before collapse and the lowering of the hydrodynamic sound velocity by a factor \sqrt{3/5} relative to three-dimensional behaviour., Comment: 12 pages, 4 figures, contribution to the Cortona BEC special issue

We evaluate the low-lying oscillation modes and the ballistic expansion properties of a harmonically trapped gas of fermionic K40 atoms containing thermal Rb87 impurities as functions of the anisotropy of the trap. Numerical results are obtained by solving the Vlasov-Landau equations for the one-body phase-space distribution functions and are used to test simple scaling Ansatzes. Starting from the gas in a weak impurity-scattering regime inside a spherical trap, the time scales associated to motions in the axial and azimuthal directions enter into competition as the trap is deformed to an elongated cigar-like shape. This competition gives rise to coexistence of collisionless and hydrodynamic behaviors in the low-lying surface modes of the gas as well as to a dependence of the aspect ratio of the expanding cloud on the collision time., 6 pages, 4 figures, accepted for publication in Phys. Rev. A

We present an extensive comparative study of ground-state densities and pair distribution functions for electrons confined in two-dimensional parabolic quantum dots over a broad range of coupling strength and electron number. We first use spin-density-functional theory to determine spin densities that are compared with Diffusion Monte Carlo (DMC) data. This accurate knowledge of one-body properties is then used to construct and test a local approximation for the electron-pair correlations. We find very satisfactory agreement between this local scheme and the available DMC data, and provide a detailed picture of two-body correlations in a coupling-strength regime preceding the formation of Wigner-like electron ordering., Comment: 18 pages, 12 figures, submitted

We present a numerical study of the micro-dynamical roots of dissipation in two colliding mesoscopic clouds of point-like fermions as a function of the scattering length and of temperature approaching full quantum degeneracy. This study, which is motivated by current experiments on ultracold gaseous mixtures of fermionic atoms inside magnetic traps, combines the solution of the coupled Vlasov-Landau equations for the Wigner distribution functions with a locally adaptive importance-sampling technique for handling collisional interactions. The results illustrate the consequences of genuinely quantum collisional phenomena, and in particular the role of Pauli blocking in the transition to hydrodynamic behaviour. We also compare the computed quantum collision rate as a function of temperature in the weak-coupling case with theoretical results assuming that equilibrium distributions determine the quantum collision integral.

We study the collective modes of a confined gaseous cloud of bosons and fermions with mutual attractive interactions at zero temperature. The cloud consists of a Bose-Einstein condensate and a spin-polarized Fermi gas inside a spherical harmonic trap and the coupling between the two species is varied by increasing either the magnitude of the interspecies $s$-wave scattering length or the number of bosons. The mode frequencies are obtained in the collisional regime by solving the equations of generalized hydrodynamics and are compared with the spectra calculated in the collisionless regime within a random-phase approximation. We find that, as the mixture is driven towards the collapse instability, the frequencies of the modes of fermionic origin show a blue shift which can become very significant for large numbers of bosons. Instead the modes of bosonic origin show a softening, which becomes most pronounced in the very proximity of collapse. Explicit illustrations of these trends are given for the monopolar spectra, but similar trends are found for the dipolar and quadrupolar spectra except for the surface $(n=0)$ modes which are essentially unaffected by the interactions.

We present a theoretical study of the dynamical behavior of a gas made of ultracold fermionic atoms, which during their motions can collide with a much smaller number of thermal bosonic impurities. The atoms are confined inside harmonic traps and the interactions between the two species are treated as due to s-wave scattering with a negative scattering length modeling the 40K-87Rb fermion-boson system. We set the fermions into motion by giving a small shift to their trap center and examine two alternative types of initial conditions, referring to (i) a close-to-equilibrium situation in which the two species are at the same temperature (well below the Fermi temperature and well above the Bose-Einstein condensation temperature); and (ii) a far-from-equilibrium case in which the impurities are given a Boltzmann distribution of momenta while the fermions are at very low temperatures. The dynamics of the gas is evaluated by the numerical solution of the Vlasov-Landau equations for the one-body distribution functions, supported by some analytical results on the collisional properties of a fermion gas. We find that the trapped gaseous mixture is close to the collisionless regime for values of the parameters corresponding to current experiments, but can be driven towards a collisional regime even without increasing the strength of the interactions, either by going over to heavier impurity masses or by matching the width of the momentum distribution of the impurities to the Fermi momentum of the fermion gas., Comment: 7 pages, 4 figures, RevTeX 4, accepted in PRA

We study the transition from the collisionless to the hydrodynamic regime in a two-component spin-polarized mixture of 40K atoms by exciting its dipolar oscillation modes inside harmonic traps. The time evolution of the mixture is described by the Vlasov-Landau equations and numerically solved with a fully three-dimensional concurrent code. We observe a master/slave behaviour of the oscillation frequencies depending on the dipolar mode that is excited. Regardless of the initial conditions, the transition to hydrodynamics is found to shift to lower values of the collision rate as temperature decreases., 11 pages, iop style. submitted to the proceedings of the Levico 2003 workshop

We calculate the spectrum of low-lying collective excitations in a mesoscopic cloud formed by a Bose-Einstein condensate and a spin-polarized Fermi gas as a function of the boson-fermion repulsions. The cloud is under isotropic harmonic confinement and its dynamics is treated in the collisional regime by using the equations of generalized hydrodynamics with inclusion of surface effects. For large numbers of bosons we find that, as the cloud moves towards spatial separation (demixing) with increasing boson-fermion coupling, the frequencies of a set of collective modes show a softening followed by a sharp upturn. This behavior permits a clear identification of the quantum phase transition. We propose a physical interpretation for the dynamical transition point in a confined mixture, leading to a simple analytical expression for its location., revtex4, 9 pages, 8 postscript files

We investigate the role of the interparticle-interaction strength in the distribution of two species of atoms inside a condensate. We focus upon the study of systems for which the minima of the trapping potentials for the species are displaced from each other by a distance that is small compared to the size of the total condensate. We show that in a small range of the interparticle-interaction strength the distribution of species undergoes dramatic changes, and exhibits a variety of different features. We demonstrate that this behavior can be easily understood in terms of the Thomas-Fermi approximation. This effect may be useful in experimentally determining the values of the scattering lengths., Comment: 4 pages, 2 figures, revtex4

We develop a three-dimensional analysis of the phase separation of two-species Bose-Einstein condensates in the presence of vorticity within the Thomas-Fermi approximation. We find different segregation features according to whether the more repulsive component is in a vortex or in a vortex-free state. An application of this study is aimed at describing systems formed by two almost immiscible species of rubidium-87 that are commonly used in Bose-Einstein condensation experiments. In particular, in this work we calculate the density profiles of condensates for the same conditions as the states prepared in the experiments performed at JILA [Matthews et al., Phys. Rev. Lett. 83, 2498 (1999)], Comment: 4 pages, 3 figures

Within a mean field plus Random-Phase Approximation formalism, we investigate the collective excitations of a three component Fermi-Bose mixture of K atoms, magnetically trapped and subjected to repulsive s-wave interactions. We analyze both the single-particle excitation and the density oscillation spectra created by external multipolar fields, for varying fermion concentrations. The formalism and the numerical output are consistent with the Generalized Kohn Theorem for the whole multispecies system. The calculations give rise to fragmented density excitation spectra of the fermion sample and illustrate the role of the mutual interaction in the observed deviations of the bosonic spectra with respect to Stringari's rule., 9 pages, 6 eps figures, submitted to Phys.Rev.A

We present a Random-Phase-Approximation formalism for the collective spectrum of two hyperfine species of dilute 40K atoms, magnetically trapped at zero temperature and subjected to a repulsive s-wave interaction between atoms with different spin projections. We examine the density-like and the spin-like oscillation spectra, as well as the transition density profiles created by external multipolar fields. The zero sound spectrum is always fragmented and the density and spin channels become clearly distinguishable if the trapping potentials acting on the species are identical. Although this distinction is lost when these confining fields are different, at selected excitation frequencies the transition densities may display the signature of the channel., 10 pages, 9 figures

slightly above the prediction of Ref. @2#, and the calculation confirms the magnetic properties of these systems. The total magnetic moment of the cluster may then permit its confinement in a magnetic trap. We show that if such an impurity becomes trapped together with the bosonic atoms, its only effect upon the condensate is suppression of a moderate number of bosons from its vecinity; neither the density profile of the condensed particles, nor their low-energy excitations, are significantly disturbed by the foreign agent. We perform a detailed calculation of the motion of the impurity, subjected to the force provided by the condensed density. Assuming various initial conditions, and also some simplifying calculatory assumptions that retain the main physics of the problem, we show that the cluster can undergo oscillations around the trap center. Anyway, its center of mass remains localized, at least during times comparable with the condensate lifetime. This outcome differs from previous findings by Chin and Forbert @4#, who predict expulsion of the molecule from the trap. To the best of our knowledge, the study of Ref. @4# is the only prior estimate of the response of a condensate to doping by a large molecular cluster; the calculation stresses the geometrical aspects of exclusion of bosons in the trap, induced by the presence of an impenetrable sphere, and on those grounds it has been concluded that due to the reaction of the excluded cloud, the impurity would be most likely expelled from the condensate. The result of the present paper is due to the fact that we have explicitly taken into account the attractive interaction well between atoms in the impurity and those in the condensate. This attraction is the source of the effective restoring force. This paper is organized as follows. In Sec. II we present the Thomas-Fermi description of a condensate doped with a small 3 He cluster and in Sec. III, we discuss the stationary solutions of the Gross-Pitaevsky equations and the spectrum of small amplitude oscillations of the trapped atoms interacting with the impurity. In Sec. IV, we examine the dynamics of the drop. The final summary and conclusions are the subject of Sec. V.

We investigate the collective excitations of a single-species Bose gas at T=0 in a harmonic trap where the confinement undergoes some splitting along one spatial direction. We mostly consider onedimensional potentials consisting of two harmonic wells separated a distance 2 z_0, since they essentially contain all the barrier effects that one may visualize in the 3D situation. We find, within a hydrodynamic approximation, that regardless the dimensionality of the system, pairs of levels in the excitation spectrum, corresponding to neighbouring even and odd excitations, merge together as one increases the barrier height up to the current value of the chemical potential. The excitation spectra computed in the hydrodynamical or Thomas-Fermi limit are compared with the results of exactly solving the time-dependent Gross-Pitaevskii equation. We analyze as well the characteristics of the spatial pattern of excitations of threedimensional boson systems according to the amount of splitting of the condensate., RevTeX, 12 pages, 13 ps figures

We present a generalization of fermionic fluiddynamics to the case of two trapped fermion species with a contact interaction. Within a mean field approximation, we derive coupled equations of motion for the particle densities, particle currents, and anomalous pair density. For an inhomogeneous system, the equilibrium situation with vanishing currents is described by a generalized Thomas-Fermi relation that includes the superfluid gap, together with a new nonlocal gap equation that replaces the usual BCS one. These equations are numericaly solved resorting to a local density approximation (LDA). Density and gap profiles are analyzed in terms of the scattering length, revealing that the current frame can exhibit microscopic details of quantum origin that are frequently absent in more macroscopic scenarios.