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arXiv:cond-mat/0703248 · Physical Review A

Condensate depletion in two-species Bose gases: A variational quantum Monte Carlo study

Asaad R. Sakhel, Jonathan L. DuBois, H. R. Glyde

Published Apr 24, 2008• 14 citations
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Abstract

We investigate two-species Bose gases in traps with various interactions using variational quantum Monte Carlo (VMC) techniques at zero temperature. The bosons are represented by hard spheres whose diameter is equivalent to the $s$-wave scattering length in the low-energy and long-wavelength approximation. We explore the role of repulsive and attractive interspecies or intraspecies interactions on the condensate properties of the mixtures, particularly the condensate fraction of each species as compared to the case when each species is in a separate trap of its own. We model the repulsive interactions by a hard-core (HC) potential and the attractive interactions by a shallow model potential. The VMC density profiles and energies are evaluated at various interactions and two mass ratios of the species.

DOI
10.1103/physreva.77.043627

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We investigate two-species Bose gases in traps with various interactions using variational quantum Monte Carlo (VMC) techniques at zero temperature. The bosons are represented by hard spheres whose diameter is equivalent to the sss-wave scattering length in the low-energy and long-wavelength approximation. We explore the role of repulsive and attractive interspecies or intraspecies interactions on the condensate properties of the mixtures, particularly the condensate fraction of each species as compared to the case when each species is in a separate trap of its own. We model the repulsive interactions by a hard-core (HC) potential and the attractive interactions by a shallow model potential. The VMC density profiles and energies are evaluated at various interactions and two mass ratios of the species.
We investigate the properties of an impurity immersed in a dilute Bose gas at zero temperature using quantum Monte Carlo methods. The interactions between bosons are modeled by a hard-sphere potential with scattering length aaa, whereas the interactions between the impurity and the bosons are modeled by a short-range, square-well potential where both the sign and the strength of the scattering length bbb can be varied by adjusting the well depth. We characterize the attractive and the repulsive polaron branch by calculating the binding energy and the effective mass of the impurity. Furthermore, we investigate the structural properties of the bath, such as the impurity-boson contact parameter and the change of the density profile around the impurity. At the unitary limit of the impurity-boson interaction, we find that the effective mass of the impurity remains smaller than twice its bare mass, while the binding energy scales with ${\ensuremath{\hbar}}^{2}{n}^{2/3}/m$, where nnn is the density of the bath and mmm is the common mass of the impurity and the bosons in the bath. The implications for the phase diagram of binary Bose-Bose mixtures at low concentrations are also discussed.
The ground-state properties of a system with a small number of interacting bosons over a wide range of densities are investigated. The system is confined in a two-dimensional isotropic harmonic trap, where the interaction between bosons is treated as a hard-core potential. By using variational Monte Carlo method, we diagonalize the one-body density matrix of the system to obtain the ground-state energy, condensate wavefunction and the condensate fraction. We find that in the dilute limit the depletion of central condensate in the 2D system is larger than in a 3D system for the same interaction strength; however as the density increases, the depletion at the centre of 2D trap will be equal to or even lower than that at the centre of 3D trap, which is in agreement with the anticipated in Thomas–Fermi approximation. In addition, in the 2D system the total condensate depletion is still larger than in a 3D system for the same scattering length.
We evaluate the zero temperature properties and Bose-Einstein condensation (BEC) of hard sphere bosons in a harmonic trap using Quantum Monte Carlo methods. The chief purpose of this work is to go beyond the dilute limit, to test the limits of the Gross-Pitaevskii equation and related mean field approximations and to explore the role of interactions in determining the zero temperature properties of the trapped Bose gas. The density is increased by adjusting both the number of trapped bosons, N , and the s-wave scattering length, a, to study systems from the highly dilute region corresponding to early experiments in trapped BEC [2, 3] up to liquid He densities and beyond. Rather than relying on the perturbative Bogoliubov approximation (which assumes a large condensate fraction) to describe the condensate, we use the one-body density matrix (OBDM) formulation of BEC so that the properties of the condensate for systems with arbitrarily large interactions may be studied. In this formulation of BEC, condensate properties are obtained by diagonalizing the OBDM and obtaining the corresponding single particle “natural orbitals” and their occupation numbers for the system. The condensate wave function and condensate fraction are then obtained from the single particle orbital(s) with macroscopic occupation (N0 >> 1). Within this framework, we calculate the effects of interactions and increased density on the ground state energy, the density profile, the momentum distribution, the condensate fraction and condensate “wave-function” and several other properties.
In this thesis we investigate the properties of impurities immersed in a dilute Bose gas at zero temperature using quantum Monte-Carlo methods. The interactions between bosons are modeled by a hard sphere potential with scattering length a, whereas the interactions between the impurity and the bosons are modeled by a short-range, square-well potential where both the sign and the strength of the scattering length b can be varied by adjusting the well depth. We calculate the binding energy, the effective mass and the pair correlation functions of a impurity along the attractive and the repulsive polaron branch. In particular, at the unitary limit of the impurity-bosons interaction, we find that the binding energy is much larger than the chemical potential of the bath signaling that many bosons dress the impurity thereby lowering its energy and increasing its effective mass. We characterize this state by calculating the bosons-boson pair correlation function and by investigating the dependence of the binding energy on the gas parameter of the bosonic bath. We also investigate the ground-state properties of M impurities in a Bose gas at T=0. In particular, the energy and the phase diagram by using both quantum Monte-Carlo and mean field methods.
Several properties of trapped hard-sphere bosons are evaluated using variational Monte Carlo techniques. A trial wave function composed of a renormalized single-particle Gaussian and a hard-sphere Jastrow function for pair correlations is used to study the sensitivity of condensate and noncondensate properties to the hard-sphere radius and the number of particles. Special attention is given to diagonalizing the one-body density matrix and obtaining the corresponding single-particle natural orbitals and their occupation numbers for the system. The condensate wave function and condensate fraction are then obtained from the single-particle orbital with the highest occupation. The effect of interaction on other quantities such as the ground-state energy, the mean radial displacement, and the momentum distribution is calculated as well. Results are compared with mean-field theory in the dilute limit.
In this thesis we investigate the properties of mixtures of Bose gases in one dimensions at zero temperature using quantum Monte-Carlo methods. First we investigate the limiting case of an impurity interacting with an atomic bath. We characterize the impurity, by calculating its effective mass, binding energy as well as the contact parameter between the impurity and the bath. In particular, we find that the effective mass rapidly increases to very large values when the impurity gets strongly coupled to an otherwise weakly repulsive bath. Then we describe uniform balanced mixtures with repulsive interactions. We investigate the miscibility phase diagram of the two components and find that correlations do not alter the phase diagram predicted by mean-field theories. We investigate the Andreev-Bashkin effect , a non-dissipative drag between the the two components of the gas and find that the drag becomes very large in the strongly interacting regime. In non-homogeneous systems we also investigate the frequency of the spin-dipole mode. Finally we describe mixtures with attractive inter-species interactions, where one can obtain a liquid ground state because of the competition between the inter-species attraction and intra-species repulsion. We characterize the the liquid and we find that the liquid state can be formed if the ratio of coupling strengths between inter-species attractive and intra-species repulsive interactions exceeds a critical value.