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Journal of the Physical Society of Japan

Stability of a Two-Component Bose-Einstein Condensate

Hirofumi Morise, Takeya Tsurumi, Miki Wadati

Published Jun 15, 1999• 7 citations
Publisher

Abstract

The stability of a two-component Bose-Einstein condensate is studied. Using the variational method, we investigate the stable and unstable conditions as functions of the particle numbers and the s-wave scattering lengths. We find that interaction between the different species of atoms (simply, interspecies interaction) has significant effects on the stability of each condensate.

DOI
10.1143/jpsj.68.1871

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The stability of a two-component Bose-Einstein condensate is studied. Using the variational method, we investigate the stable and unstable conditions as functions of the particle numbers and the s-wave scattering lengths. We find that interaction between the different species of atoms (simply, interspecies interaction) has significant effects on the stability of each condensate.
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We examine the effect of the intra- and interspecies scattering lengths on the dynamics of a two-component Bose-Einstein condensate, particularly focusing on the existence and stability of solitonic excitations. For each type of possible soliton pairs, stability ranges are presented in tabulated form. We also compare the numerically established stability of bright-bright, bright-dark, and dark-dark solitons with our analytical prediction and with that of Painlev\'e analysis of the dynamical equation. We demonstrate that tuning the interspecies scattering length away from the predicted value (keeping the intraspecies coupling fixed) breaks the stability of the soliton pairs.
In one-dimensional trapped Bose-Fermi mixture, described by time-dependent one-dimensional nonlinear equations that are derived from a three-dimensional Bose-Fermi system, we study the effect of atom-interactions on stability using a Gaussian Variational approach. We investigate the stable and the unstable conditions as functions of the atoms number and s-wave scattering length. We find that the interaction between the different species of atoms has significant effect on the stability of Bose-Fermi mixture. We also give critical conditions of the atoms number and s-wave scattering length for both special and general cases.
A simple method is presented to analyze the stability of static solitonic excitations of two-component Bose-Einstein condensates described within the Gross-Pitaevskii approximation. First, a quick assessment can be made for the values of interspecies scattering length a12{a}_{12}a12​ allowing existence of static solitons independent of the particle numbers N1{N}_{1}N1​ and N2{N}_{2}N2​. If the true value of a12{a}_{12}a12​ falls into that acceptable interval, then a fine tuning is performed to get the ratio N2∕N1{N}_{2}∕{N}_{1}N2​∕N1​ at which the static solitons may be created. The technique is illustrated for the lithium-rubidium and sodium-rubidium condensates.
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.