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We analyze the effects of imbalancing the populations of two-component trapped fermions, in the BEC limit of the attractive interaction between different fermions. Starting from the gap equation with two fermionic chemical potentials, we…
The variational determination of the two-boson reduced density matrix is described for a one-dimensional system of $N$ (where $N$ ranges from $2$ to $10^4$) harmonically trapped bosons interacting via contact interaction. The ground-state…
We investigate a quasi-one dimensional system of trapped cold bosonic atoms in an optical lattice by using the density matrix renormalization group to study the Bose-Hubbard model at T=0 for experimentally realistic numbers of lattice…
When the binding energy of a two-body system goes to zero the two-body system shows a continuous scaling invariance governed by the large value of the scattering length. In the case of three identical bosons, the three-body system in the…
We compute the pair entanglement between two interacting bosons in a two dimensional (2D)isotropic harmonic trap. The interaction potential is modeled by a 2D regularized pseudo-potential. By analytically decomposing the wave function into…
We study the self-adjoint Hamiltonian that models the quantum dynamics of a one-dimensional (1D) three-body system consisting of a light particle interacting with two heavy ones through a zero-range force. For an attractive interaction we…
We examine the problem of two particles confined in an isotropic harmonic trap, which interact via a finite-ranged Gaussian-shaped potential in two spatial dimensions. We derive an approximative transcendental equation for the energy and…
We demonstrate the possibility of existence of meta-stable N-body Efimov states in trapped Bose systems with large scattering length. We calculate spectra of trapped systems of N=3,4,5,6, and 7 bosons using a stochastic variational method…
We study two-component bosonic systems with strong inter-species and vanishing intra-species interactions. A new class of exact eigenstates is found with energies that are {\it not} sums of the single-particle energies with wave functions…
We investigate a system of bosons in a two-dimensional harmonic trap. In the limit of strong attractive interactions, the bosons make a droplet insensitive to external confinement. For weak interactions, in contrast, the ground state is…
Fragmentation of bosons and pairs in a trapped imbalanced bosonic mixture is investigated analytically using an exactly solvable model, the generic harmonic-interaction model for mixtures. Closed-form expressions for the eigenvalues and…
We investigate the finite-temperature properties of a bosonic Josephson junction composed of N interacting atoms confined by a quasi-one-dimensional asymmetric double-well potential, modeled by the two-site Bose-Hubbard Hamiltonian. We…
We study the ground state of a system of Bose hard-spheres trapped in an isotropic harmonic potential to investigate the effect of the interatomic correlations and the accuracy of the Gross-Pitaevskii equation. We compare a local density…
We analyze interacting one-dimensional bosons in the continuum, subject to a periodic sinusoidal potential of arbitrary depth. Variation of the lattice depth tunes the system from the Bose-Hubbard limit for deep lattices, through the…
Employing a general variational method and perturbation theory, we derived explicit solutions for the description of one-dimensional two species Bose-Einstein condensates confined by a harmonic trap potential in an optical lattice. We…
We analyze the macroscopic dynamics of a Bose gas axially confined in an optical lattice with a superimposed harmonic trap, taking into account weak tunneling effect. Our results show that upon transition to the quasi-two-dimensional (2D)…
Two atoms in an optical lattice may be made to interact strongly at higher partial waves near a Feshbach resonance. These atoms, under appropriate constraints, could be bosonic or fermionic. The universal $l=2$ energy spectrum for such a…
A system of bosons in a two-dimensional harmonic trap in the presence of Rashba-type spin-orbit coupling is investigated. An analytic treatment of the ground state of a single atom in the weak-coupling regime is presented and used as a…
The system of two interacting bosons in a two-dimensional harmonic trap is compared with the system consisting of two noninteracting fermions in the same potential. In particular, we discuss how the properties of the ground state of the…
The theory of Bose-Einstein condensation in a two-dimensional(2D) harmonic trap is developed from 2D Gross-Pitaevskii equation. The 2D interaction strength is obtained from a 2D collision theory. We show the realization of 2D condensation…