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Chinese Physics B

Effects of transverse trapping on the ground state of a cigar-shaped two-component Bose—Einstein condensate

Guo-Dong Cui, Jian-Fang Sun, Bo-Nan Jiang, Jun Qian, Yuzhu Wang

Published Sep 1, 2013• 0 citations
Publisher

Abstract

We derive the coupled nonpolynomial nonlinear Schrödinger equations for a two-component Bose—Einstein condensate in a quasi-one-dimension geometry and investigate the effects of a tightly transverse trapping on the ground state and the miscibility—immiscibility threshold. We find that the density profile of the matter wavepacket is remarkably dependent on the transverse width and the effective one-dimension nonlinear coupling strengths in miscible and immiscible regimes.

DOI
10.1088/1674-1056/22/9/096701

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We derive the coupled nonpolynomial nonlinear Schrödinger equations for a two-component Bose—Einstein condensate in a quasi-one-dimension geometry and investigate the effects of a tightly transverse trapping on the ground state and the miscibility—immiscibility threshold. We find that the density profile of the matter wavepacket is remarkably dependent on the transverse width and the effective one-dimension nonlinear coupling strengths in miscible and immiscible regimes.
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We derive an effective nonpolynomial Schr\"odinger equation (NPSE) for self-repulsive or attractive BEC in the nearly one-dimensional cigar-shaped trap, with the transverse confining frequency periodically modulated along the axial direction. In addition to the usual linear cigar-shaped trap, where the periodic modulation emulates the action of an optical lattice (OL), the model may be also relevant to toroidal traps, where an ordinary OL cannot be created. For either sign of the nonlinearity, extended and localized states are found, in the numerical form [using both the effective NPSE and the full three-dimensional (3D) Gross-Pitaevskii equation] and by means of the variational approximation (VA). The latter is applied to construct ground-state solitons and predict the collapse threshold in the case of self-attraction. It is shown that numerical solutions provided by the one-dimensional NPSE are always very close to full 3D solutions, and the VA yields quite reasonable results too. The transition from delocalized states to gap solitons, in the first finite bandgap of the linear spectrum, is examined in detail, for the repulsive and attractive nonlinearities alike.
We study the miscible-immiscible quantum phase transition in a linearly coupled binary Bose-Hubbard model in one dimension that can describe the low-energy properties of a two-component Bose-Einstein condensate in optical lattices. With the quantum many-body ground state obtained from the density matrix renormalization group algorithm, we calculate the characteristic physical quantities of the phase transition controlled by the linear coupling between the two components. Furthermore we calculate the Binder cumulant to determine the critical point and construct the phase diagram. The strong-coupling expansion shows that in the Mott insulator regime the model Hamiltonian can be mapped to a spin-1/21/21/2 XXZ\mathit{XXZ}XXZ model with a transverse magnetic field.
We characterize the immiscibility-miscibility transition (IMT) of a two-component Bose-Einstein condensate (BEC) with dipole-dipole interactions. In particular, we consider the quasi-two-dimensional geometry, where a strong trapping potential admits only zero-point motion in the trap direction, while the atoms are more free to move in the transverse directions. We employ the Bogoliubov treatment of the two-component system to identify both the well-known long-wavelength IMT in addition to a rotonlike IMT, where the transition occurs at finite-wave number and is reminiscent of the roton softening in the single-component dipolar BEC. Additionally, we verify the existence of the roton IMT in the fully trapped, finite systems by direct numerical simulation of the two-component coupled nonlocal Gross-Pitaevskii equations.
We investigate a harmonically trapped two-component Bose-Einstein condensate within the miscible regime, close to its boundaries, for different ratios of effective intra- and interspecies interactions. We derive analytically a universal equation for the density around the different boundaries in one, two, and three dimensions, for both the coexisting and spatially separated regimes. We also present a general procedure to solve the Thomas-Fermi approximation in all three spatial dimensionalities, reducing the complexity of the Thomas-Fermi problem for the spatially separated case in one and three dimensions to a single numerical inversion. Finally, we analytically determine the frontier between the two different regimes of the system.