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Physical Review Letters

“Stability Signature” in Two-Species Dilute Bose-Einstein Condensates

C. K. Law, Han Pu, N. P. Bigelow, Joseph H. Eberly

Published Oct 27, 1997• 115 citations
Publisher

Abstract

We identify an eigenvalue associated with a dilute two-species Bose-Einstein condensate as the determiner of condensate stability. It plays the same role as the sign of scattering length in a one-species condensate. We predict that there is a range of interspecies interaction strength in which a sodium-rubidium mixture can be stable in a harmonic trap.

DOI
10.1103/physrevlett.79.3105

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We identify an eigenvalue associated with a dilute two-species Bose-Einstein condensate as the determiner of condensate stability. It plays the same role as the sign of scattering length in a one-species condensate. We predict that there is a range of interspecies interaction strength in which a sodium-rubidium mixture can be stable in a harmonic trap.
We study harmonically trapped two-species Bose-Einstein condensates within the Gross-Pitaevskii formalism. By invoking the Thomas-Fermi approximation, we derive an analytical solution for the miscible ground state in a particular region of the system's parameter space. This solution furnishes a simple formula for determining the relative strength of the interspecies interaction from a measurement of the density distribution of only one of the two species. Accompanying numerical simulations confirm its accuracy for sufficiently large numbers of condensed particles. The introduced formula provides a condensate-based scheme that complements the typical experimental methods of evaluating interspecies scattering lengths from collisional measurements on thermal samples.
Abstract We study harmonically trapped two-species Bose–Einstein condensates within the Gross–Pitaevskii formalism. By invoking the Thomas–Fermi approximation, we derive an analytical solution for the miscible ground state in a particular region of the system’s parameter space. This solution furnishes a simple formula that relates the interspecies interaction strength to the second spatial moments of the density distribution of the minority condensate species. Accompanying numerical simulations confirm the accuracy of the solution and the interaction strength formula for sufficiently large numbers of condensed particles. The introduced formula may provide an additional scheme for determining interspecies scattering lengths that complements existing methods, such as those based on collective-excitation spectroscopy of the two-species condensates or on collisional measurements on thermal samples.
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.
We study the interactions between two atomic species in a binary Bose-Einstein condensate to revisit the conditions for miscibility, oscillatory dynamics between the species, steady-state solutions, and their stability. By employing a variational approach for a quasi-one-dimensional, two-atomic species condensate, we obtain equations of motion for the parameters of each species: amplitude, width, position, and phase. A further simplification leads to a reduction of the dynamics into a simple classical Newtonian system where components oscillate in an effective potential with a frequency that depends on the harmonic trap strength and the interspecies coupling parameter. We develop explicit conditions for miscibility that can be interpreted as a phase diagram that depends on the harmonic trap's strength and the interspecies coupling parameter. We numerically illustrate the bifurcation scenario whereby nontopological, phase-separated states of increasing complexity emerge out of a symmetric state as the interspecies coupling is increased. The symmetry-breaking dynamical evolution of some of these states is numerically monitored and the associated asymmetric states are also explored.
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.