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Communications in Theoretical Physics

Stability of Two-Component Bose–Einstein Condensates in Bessel Optical Lattices

Chen Hai-Jun, Li Hao-Cai, Xue Ju-Kui

Published Jun 1, 2008• 1 citation
Publisher

Abstract

The stability of the ground state of two-component Bose–Einstein condensates (BECs) loaded into the central well of an axially symmetric Bessel lattices (BLs) potential with attractive or repulsive atoms interactions is studied using the time-dependent Gross–Pitaevskii equation (GPE). By using the variational method, we find that stable ground state of two-component BECs can exist in BLs. The BLs's depth and the intra-species atom interaction play an important role in the stability of ground state. The collapse of two-component BECs in BLs is also studied and a collapse condition for trapped two-component BECs is obtained. It is shown that the two-component BECs exhibit rich collapse dynamics. That is, the two-component BECs can collapse in the system with both intra- and inter-attractive, or with intra-attractive and inter-repulsive, or with intra-repulsive and inter-attractive atom interactions. Furthermore, the control of the collapse of the two-component BECs in BLs is discussed in detail. The stability diagram of the ground state in parameter space is obtained. The results show that the collapse of two-component BECs can be controlled by temporal modulation of the atom interaction.

DOI
10.1088/0253-6102/49/6/37

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The stability of the ground state of two-component Bose–Einstein condensates (BECs) loaded into the central well of an axially symmetric Bessel lattices (BLs) potential with attractive or repulsive atoms interactions is studied using the time-dependent Gross–Pitaevskii equation (GPE). By using the variational method, we find that stable ground state of two-component BECs can exist in BLs. The BLs's depth and the intra-species atom interaction play an important role in the stability of ground state. The collapse of two-component BECs in BLs is also studied and a collapse condition for trapped two-component BECs is obtained. It is shown that the two-component BECs exhibit rich collapse dynamics. That is, the two-component BECs can collapse in the system with both intra- and inter-attractive, or with intra-attractive and inter-repulsive, or with intra-repulsive and inter-attractive atom interactions. Furthermore, the control of the collapse of the two-component BECs in BLs is discussed in detail. The stability diagram of the ground state in parameter space is obtained. The results show that the collapse of two-component BECs can be controlled by temporal modulation of the atom interaction.
The ground state solutions of two-component Bose-Einstein condensates (BECs) in Bessel optical lattices (BLs) are studied by means of the balance condition between BLs strength and inter-atomic interactions. We consider a quasi-two-dimensional (2D) BECs system，strongly confined in longitudinal direction and weakly trapped in the radial direction in the transverse plane，which obeys 2D Gross-Pitaevskii equation (GPE) derived from its 3D counterpart. Analytically we obtained the atom number distribution，atom number and energy of ground state and give the parameter ranges. Compared to single-component BEC，two-component BECs exhibit a rich variety of ground state structures. These structures depend upon various parameters，in particular the inter-atomic interactions and the BLs strength. Neglecting the inter-component atomic interaction，the corresponding results of single-component situation are given.
Abstract The modulational instability of two-component Bose–Einstein condensates (BECs) under an external parabolic potential is discussed. Based on the trapped two-component Gross–Pitaevskill equations, a time-dependent dispersion relation is obtained analytically by means of the modified lens-type transformation and linear stability analysis. It is shown that a modulational unstable time scale exists for trapped two-component BECs. The modulational properties—which are determined by the wave number, external trapping parameter, intra- and inter-species atomic interactions—are modified significantly. The analytical results are confirmed by direct numerical simulation. Our results provide a criterion for judging the occurrence of instability of the trapped two-component BECs in experiment.
In order to investigate the stability and dynamics properties of a cold atom Bose-Einstein Condensate (BEC) in two-dimensional Bessel optical lattices, the stability condition of the system is analyzed and the corresponding Gross-pitaevskii equation (GPE) is solved in this paper by time-dependent variational method and numerical simulation. Firstly, the Euler-Lagrange equation containing the parameters describing the system stability and the effective potential energy needed by the variational analysis method to analyze the system stability is obtained by using the adjustable exponent Gaussian trial wave function. Secondly, according to the analytical solution of Euler-Lagrange equation and the local minimum value of potential energy, the stability condition of the system is further illuminated. Finally, the influence mechanism of these parameters on the local dynamics is revealed by solving the corresponding GPE with numerical method.
The stability of Bose–Einstein condensates (BECs) loaded into a two-dimensional shallow harmonic potential well is studied. By using the variational method, the ground state properties for interacting BECs in the shallow trap are discussed. It is shown that the possible stable bound state can exist. The depth of the shallow well plays an important role in stabilizing the BECs. The stability of BECs in the shallow trap with the periodic modulating of atom interaction by using the Feshbach resonance is also discussed. The results show that the collapse and diffusion of BECs in a shallow trap can be controlled by the temporal modulation of the scattering length.
Bose–Einstein condensation has been realized as dilute atomic vapors. This achievement has generated immense interest in this field. This article review of recent theoretical research into the properties of trapped dilute-gas Bose–Einstein condensates. Among these properties, stability of Bose–Einstein condensates confined in traps is mainly discussed. Static properties of the ground state are investigated by using the variational method. The analysis is extended to the stability of two-component condensates. Time-development of the condensate is well-described by the Gross–Pitaevskii equation which is known in nonlinear physics as the no nlinear Schrödinger equation. For the case that the inter-atomic potential is effectively attractive, a singularity of the solution emerges in a finite time. This phenomenon which we call collapse explains the upper bound for the number of atoms in such condensates under traps.