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arXiv:0905.1147 · Physical Review A

Tunneling of a few strongly repulsive hard-sphere bosons in an optical lattice with tight external harmonic confinement: A quantum Monte Carlo investigation in continuous space

Asaad R. Sakhel, Jonathan L. DuBois, Roger R. Sakhel

Published Apr 7, 2010• 2 citations
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Abstract

The effect of strongly repulsive interactions on the tunneling amplitude of hard-sphere (HS) bosons confined in a simple cubic optical lattice plus tight external harmonic confinement in continuous space is investigated. The quantum variational Monte Carlo (VMC) and the variational path integral (VPI) Monte Carlo techniques are used at zero temperature. The effects of the lattice spacing on the tunneling amplitude are also considered. The occupancies of the lattice sites as a function of the repulsion between the bosons are further revealed. Our chief result is that for a small number of bosons ($N=8$) the overlap of the wave functions in neighboring wells practically does not change with an increase of the repulsive interactions and changes only minimally for a larger number of particles ($N=40$). The tunneling amplitude rises with a reduction in the lattice spacing. In addition, the occupancy of the center of the trap decreases in favor of a rise in the occupancy of the lattice sites at the edges of the trap with increasing HS repulsion. Further, it was found that the energy per particle at certain optical-lattice barrier heights is insensitive to the number of particles and variations in the HS diameter of the bosons. In order to support our results, we compare the VMC results with corresponding VPI results.

DOI
10.1103/physreva.81.043603

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The effect of strongly repulsive interactions on the tunneling amplitude of hard-sphere (HS) bosons confined in a simple cubic optical lattice plus tight external harmonic confinement in continuous space is investigated. The quantum variational Monte Carlo (VMC) and the variational path integral (VPI) Monte Carlo techniques are used at zero temperature. The effects of the lattice spacing on the tunneling amplitude are also considered. The occupancies of the lattice sites as a function of the repulsion between the bosons are further revealed. Our chief result is that for a small number of bosons (N=8N=8N=8) the overlap of the wave functions in neighboring wells practically does not change with an increase of the repulsive interactions and changes only minimally for a larger number of particles (N=40N=40N=40). The tunneling amplitude rises with a reduction in the lattice spacing. In addition, the occupancy of the center of the trap decreases in favor of a rise in the occupancy of the lattice sites at the edges of the trap with increasing HS repulsion. Further, it was found that the energy per particle at certain optical-lattice barrier heights is insensitive to the number of particles and variations in the HS diameter of the bosons. In order to support our results, we compare the VMC results with corresponding VPI results.
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.
We explore the global and local condensate and superfluid (SF) fractions in a system of a few hard core (HC) bosons (N=8 and N=40) trapped inside a combined harmonic optical cubic lattice (CHOCL) at T=0 K. The condensate fraction (CF) is computed for individual lattice wells by separating the one-body density matrix (OBDM) of the whole system into components at the various lattice sites. Then each lattice-site component is diagonalized to find its eigenvalues. The eigenvalues are obtained by a method presented earlier [Dubois and Glyde, Phys. Rev. A {\bf 63}, 023602 (2001)]. The effects of interference between the condensates in the lattice wells on the CF in one well is also investigated. The SF fraction (SFF) is calculated for N=40 by using the diffusion formula of Pollock and Ceperley [Pollock and Ceperley, Phys. Rev. B {\bf 36}, 8343 (1987)]. Our chief result is an opposing behavior of the global CF and SFF with increasing lattice wave vector kkk. In addition, the CF in a lattice well is enhanced by the interference with its neighbor wells beyond the result when the interference is neglected. The global SF is depleted with a rise of the repulsion between the bosons, yet at very strong interaction superfluidity is still present. The global CF remains almost constant with increasing HC repulsion. A reduction in the lattice dimension, i.e. an increase in the lattice wave vector, increases the local CF in each lattice well, but reduces the corresponding local SFF. At large HC repulsion, a coexisting SF-(vacuum)MI phase is established.
The nonequilibrium dynamics of small boson ensembles in a one-dimensional optical lattice is explored upon a sudden quench of an additional harmonic trap from strong to weak confinement. We find that the competition between the initial localization and the repulsive interaction leads to a resonant response of the system for intermediate quench amplitudes, corresponding to avoided crossings in the many-body eigenspectrum with varying final trap frequency. In particular, we show that these avoided crossings can be utilized to prepare the system in a desired state. The dynamical response is shown to depend on both the interaction strength as well as the number of atoms manifesting the many-body nature of the tunneling dynamics.
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.
The diffusion Monte Carlo method is applied to study the ground-state properties of charged bosons in one dimension confined in a harmonic double-well trap. The particles interact repulsively through a Coulombic 1/ r potential. Numerical results show that the well separation has significant influence on the ground-state properties of the system. When the interaction of the system is weak, ground-state energy decreases with the increasing well separation and has a minimal value. If the well separation increases continually, the ground-state energy increases and approaches to a constant gradually. This effect will be abatable in the strong interacting system. In addition, by calculating the density of the systems for different interaction strengths with various well separations, we find that the density increases abnormally when the well separation is large at the centre of the system.
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.