Abstract
In the study of trapped two-component Bose gases, a widely used dynamical protocol is to start from the ground state of a one-component condensate and then switch half the atoms into another hyperfine state. The slightly different intra-component and inter-component interactions can then lead to highly non-trivial dynamics, especially in the density mismatch between the two components, commonly referred to as ‘spin’ density. We study and classify the possible subsequent dynamics, over a wide variety of parameters spanned by the trap strength and by the inter- to intra-component interaction ratio. A stability analysis suited to the trapped situation provides us with a framework to explain the various types of dynamics in different regimes.
Highlights
Through an analysis of unstable modes, we present a classification of the parameter space into dynamically distinct regions, in relation to the prototypical initial state explained above
This may be regarded as a dynamical ‘phase diagram’
The threshold value at which the dynamics changes sharply corresponds to the second modulation instability line rather than the first, as we demonstrate through a careful choice of parameters in each region of the phase diagram derived from stability analysis
Summary
The relevant time-resolved experiments have been performed in both quasi-1D geometries (highly elongated traps with strong radial trapping) [6] and in a three-dimensional BEC of cylindrical symmetry with the radial variable playing an analogous role as the 1D coordinate [2, 5]. Bosonic systems in elongated traps can be in regimes beyond the applicability of mean field descriptions, e.g. when the particle number is small. In such a case a Lieb–Liniger or Tonks–Girardeau description might be more appropriate. Dynamics in such regimes is beyond the scope of this paper. The scale for trap strengths is itself fixed by imposing g11 = 1 With this convention, small values of λ correspond to a BEC in the Thomas–Fermi limit.
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