Abstract
We discuss the general features of spontaneous spatial symmetry breaking in trapped two-component alkali-metal--atom Bose-Einstein condensates, and give qualitative guidelines for when it will occur. We further show that the Hartree-Fock equations admit symmetry-broken solutions for as few as two trapped atoms, discussing the particular system of one ${}^{85}\mathrm{Rb}$ atom and one ${}^{87}\mathrm{Rb}$ atom. It is also shown that the critical value of the interspecies scattering length for a mixture of Na and Rb in an isotropic trap depends strongly on the number of atoms in a manner not described by the standard Thomas-Fermi phase separation condition.
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