The properties of interacting ultracold Bose systems were investigated using quantum Monte Carlo simulations. The superfluidity and Bose-Einstein condensation of very dilute two species trapped bosons mixtures as a function of temperature were investigated. Depending on the interactions, the system can be in three different modes: mixed, separated into two blobs, and separated in a shell regime. Anisotropy of superfluidity was observed in the case of two blobs. A transition was also observed in which the superfluidity fraction becomes smaller than the condensate fraction for each regime. We further investigated the properties of one dimensional strongly interacting bosonic systems in periodic potentials. The transition of the superfluid to the Mott insulator phase in the robust and fragile superfluid regimes is shown in detail. We investigated transition from a one-dimensional system to a two-dimensional one of helium-4 in the nanopore. We analyzed the scaling of the helium-4 superfluidity with the product of the temperature and the length of the simulation cell and the agreement of the results with the theoretical predictions. The transition of the helium-4 system from one-dimensional to two-dimensional with an increase in the linear density within the nanopores of radius R = 4 A was observed, which is visible in the behavior of the correlation function and suprafluidity.
The properties of interacting ultracold Bose systems were investigated using quantum Monte Carlo simulations. The superfluidity and Bose-Einstein condensation of very dilute two species trapped bosons mixtures as a function of temperature were investigated. Depending on the interactions, the system can be in three different modes: mixed, separated into two blobs, and separated in a shell regime. Anisotropy of superfluidity was observed in the case of two blobs. A transition was also observed in which the superfluidity fraction becomes smaller than the condensate fraction for each regime. We further investigated the properties of one dimensional strongly interacting bosonic systems in periodic potentials. The transition of the superfluid to the Mott insulator phase in the robust and fragile superfluid regimes is shown in detail. We investigated transition from a one-dimensional system to a two-dimensional one of helium-4 in the nanopore. We analyzed the scaling of the helium-4 superfluidity with the product of the temperature and the length of the simulation cell and the agreement of the results with the theoretical predictions. The transition of the helium-4 system from one-dimensional to two-dimensional with an increase in the linear density within the nanopores of radius R = 4 A was observed, which is visible in the behavior of the correlation function and suprafluidity.
We study thermal properties of a trapped Bose-Bose mixture in a dilute regime using quantum Monte Carlo methods. Our main aim is to investigate the dependence of the superfluid density and the condensate fraction on temperature for the mixed and separated phases. To this end we use the diffusion Monte Carlo method in the zero-temperature limit and the path-integral Monte Carlo method for finite temperatures. The results obtained are compared with solutions of the coupled Gross-Pitaevskii equations for the mixture at zero temperature. We notice the existence of an anisotropic superfluid density in some phase-separated mixtures. Our results also show that the temperature evolution of the superfluid density and condensate fraction is slightly different, showing noteworthy situations where the superfluid fraction is smaller than the condensate fraction.
The most recent advances in the ultracold atoms experimental techniques allowed the production of the ultracold gases mixtures in the laboratory.Motivated by these developments, in this project we study systems involving two ultracold atoms mixtures.In the first part, we consider a Bose-Einstein condensate (BEC) with a vortex lattice weakly interacting with another utracold dilute bosonic gas.We apply the Bose-Hubbard (BH) model to describe the atoms of the minority species trapped in the vortex lattice.As occurs in a static optical lattice, we predict the quantum phase transition between the Mott insulator to superfluid phases, which now can be controlled by changing the intra and inter-species scattering length.Considering the intrinsic lattice dynamics, the Tkachenko modes of the vortex lattice, we derive an extended BH Hamiltonian and analyzed new properties in the phase diagram that arise from a long-range attractive potential and density-dependent hopping.In the second part, we study the properties of a mobile impurity living in two dimensions and interacting with a 2 and 3 BEC cloud.The resulting impurity-bath interaction leads to the formation of a polaron (particle "dressed" by the phonon excitations of the BEC), which is characterized by its spectral function.We determine the energy dispersion, spectral weight, effective mass and lifetime of the polaron.These analysis allowed us to identify a dissipative regime for higher impurity velocities, with an increasing scattering rate of phonons.In addition, we observe a self-localization regime for lower impurity velocities which may be a signature for molecular formation.In spite of qualitatively similar results obtained for the 2 and 3 bath, we had differences related to the self-localization and dissipation limits, that allowed us to conclude that a 2 BEC bath would be a better candidate to observe stable quasi-particle properties.
We present diffusion Monte Carlo (DMC) and path-integral Monte Carlo (PIMC) calculations of a one-dimensional Bose system with realistic interparticle interactions in a periodic external potential. Our main aim is to test the predictions of the Luttinger liquid (LL) theory, in particular with respect to the superfluid-Mott insulator transition at both zero and finite temperatures, in the predicted robust and fragile superfluid regimes. For that purpose, we present our results of the superfluid fraction ${\ensuremath{\rho}}_{s}/{\ensuremath{\rho}}_{0}$, the one-body density matrix, the two-body correlation functions, and the static structure factor. The DMC and PIMC results in the limit of very low temperature for ${\ensuremath{\rho}}_{s}/{\ensuremath{\rho}}_{0}$ agree, but the LL model for scaling ${\ensuremath{\rho}}_{s}/{\ensuremath{\rho}}_{0}$ does not fit the data well. The critical depth of the periodic potential is close to the values obtained for ultracold gases with different models of interaction, but with the same value of the bare LL parameter, demonstrating the universality of LL description. Algebraic decay of correlation functions is observed in the superfluid regime and exponential decay in the Mott-insulator one, as well as in all regimes at finite temperature for distances larger than a characteristic length.
Several microscopic theories point out that Bose-Einstein condensation (BEC), i.e., a macroscopic occupation of the lowest energy single particle state in many-boson systems, may appear also in quantum fluids and solids and that it is at the origin of the phenomenon of superfluidity. Nevertheless, the connection between BEC and superfluidity is still matter of debate, since the experimental evidences indicating a non zero condensate fraction in superfluid helium are only indirect. In the theoretical study of BEC in quantum fluids and solids, perturbative approaches are useless because of the strong correlations between the atoms, arising both from the interatomic potential and from the quantum nature of the system. Microscopic Quantum Monte Carlo simulations provide a reliable description of these systems. In particular, the Path Integral Monte Carlo (PIMC) method is very suitable for this purpose. This method is able to provide exact results for the properties of the quantum system, both at zero and finite temperature, only with the definition of the Hamiltonian and of the symmetry properties of the system, giving an easy picture for superfluidity and BEC in many-boson systems. In this thesis, we apply PIMC methods to the study of several quantum fluids and solids. We describe in detail all the features of PIMC, from the sampling methods to the estimators of the physical properties. We present also the most recent techniques, such as the high-order approximations for the thermal density matrix and the worm algorithm, used in PIMC to provide reliable simulations. We study the liquid phase of condensed 4He, providing unbiased estimations of the one-body density matrix g1(r). We analyze the model for g1(r) used to fit the experimental data, highlighting its merits and its faults. In particular we see that, even if it presents some difficulties in the description of the overall behavior of g1(r), it can provide an accurate estimation of the kinetic energy K and of the condensate fraction n0 of the system. Furthermore, we show that our results for n0 as a function of the pressure are in a good agreement with the most recent experimental results. The study of the solid phase of 4He is the most significant part of this thesis. The recent observation of non classical rotational inertia (NCRI) effects in solid helium has generated big interest in the study of an eventual supersolid phase, characterized at the same time by crystalline order and superfluidity. Nevertheless, until now it has been impossible to give a theoretical model able to describe all the experimental evidences. In this work, we perform PIMC simulations of 4He at high densities, according to different microscopic configurations of the atoms. In commensurate crystals we see that BEC does not appear, our model being able to reproduce the momentum distribution obtained form neutron scattering experiments. In a crystal with vacancies, we have been able to see a transition to a superfluid phase at temperatures in agreement with experimental results if the vacancy concentration is low enough. In amorphous solids, superfluid effects are enhanced but appear at temperatures higher than the experimental estimation for the transition temperature. Finally, we study also metastable disordered configurations in molecular para-hydrogen at low temperature. The aim of this study is to investigate if a Bose liquid other than helium can display superfluidity. Choosing accurately a ¿quantum liquid¿ initial configuration and the dimensions of the simulation box, we have been able to frustrate the formation of the crystal and to calculate the temperature dependence of the superfluid density, showing a transition to a superfluid phase at temperatures close to 1 K.
Ultracold atomic gases may be the ultimate quantum simulator.These isolated systems have the lowest temperatures in the observable universe, and their properties and interactions can be precisely and accurately tuned across a full spectrum of behaviors, from few-body physics to highly-correlated many-body effects.The ability to impose potentials on and tune interactions within ultracold gases to mimic complex systems mean they could become a theorist's playground.One of their great strengths, however, is also one of the largest obstacles to this dream: isolation.This thesis touches on both of these themes.First, methods to characterize phases and quantum critical points, and to construct finite temperature phase diagrams using experimentally accessible observables in the Bose Hubbard model are discussed.Then, the transition from a weakly to a strongly interacting Bose-Fermi mixture in the continuum is analyzed using zero temperature numerical techniques.Real materials can be emulated by ultracold atomic gases loaded into optical lattice potentials.We discuss the characteristics of a single boson species trapped in an optical lattice (described by the Bose Hubbard model) and the hallmarks of the quantum critical region that separates the superfluid and the Mott insulator ground states.We propose a method to map the quantum critical region using the single, experimentally accessible, local quantity R, the ratio of compressibility to local number fluctuations.The procedure to map a phase diagram with R is easily generalized to inhomogeneous systems and generic many-body Hamiltonians.We illustrate it here using quantum Monte Carlo simulations of the 2D Bose Hubbard model.Secondly, we investigate the transition from a degenerate Fermi gas weakly coupled List of Tables Table Page 2.1 Techniques to Probe Atoms in Optical Lattices . . . . . .
The most recent advances in the ultracold atoms experimental techniques allowed the production of the ultracold gases mixtures in the laboratory. Motivated by these developments, in this project we study systems involving two ultracold atoms mixtures. In the first part, we consider a Bose-Einstein condensate (BEC) with a vortex lattice weakly interacting with another utracold dilute bosonic gas. We apply the Bose-Hubbard (BH) model to describe the atoms of the minority species trapped in the vortex lattice. As occurs in a static optical lattice, we predict the quantum phase transition between the Mott insulator to superfluid phases, which now can be controlled by changing the intra and inter-species scattering length. Considering the intrinsic lattice dynamics, the Tkachenko modes of the vortex lattice, we derive an extended BH Hamiltonian and analyzed new properties in the phase diagram that arise from a long-range attractive potential and density-dependent hopping. In the second part, we study the properties of a mobile impurity living in two dimensions and interacting with a 2D and 3D BEC cloud. The resulting impurity-bath interaction leads to the formation of a polaron (particle dressed by the phonon excitations of the BEC), which is characterized by its spectral function. We determine the energy dispersion, spectral weight, effective mass and lifetime of the polaron. These analysis allowed us to identify a dissipative regime for higher impurity velocities, with an increasing scattering rate of phonons. In addition, we observe a self-localization regime for lower impurity velocities which may be a signature for molecular formation. In spite of qualitatively similar results obtained for the 2D and 3D bath, we had differences related to the self-localization and dissipation limits, that allowed us to conclude that a 2D BEC bath would be a better candidate to observe stable quasi-particle properties.