Nambu-Goldstone modes in immiscible two-component Bose-Einstein condensates are studied theoretically. In a uniform system, a flat domain wall is stabilized and then the translational invariance normal to the wall is spontaneously broken in addition to the breaking of two U(1) symmetries in the presence of two complex order parameters. We clarify the properties of the low-energy excitations and identify that there exist two Nambu-Goldstone modes: an in-phase phonon with a linear dispersion and a ripplon with a fractional dispersion. The signature of the characteristic dispersion can be verified in segregated condensates in a harmonic potential.
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
85Rb atom and one
87Rb 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.
We perform a mean-field study of the binary Bose-Einstein condensate mixtures as a function of the mutual repulsive interaction strength. In the phase segregated regime, we find that there are two distinct phases: the weakly segregated phase characterized by a ``penetration depth'' and the strongly segregated phase characterized by a healing length. In the weakly segregated phase the symmetry of the shape of each condensate will not take that of the trap because of the finite surface tension, but its total density profile still does. In the strongly segregated phase even the total density profile takes a different symmetry from that of the trap because of the mutual exclusion of the condensates. The lower critical condensate-atom number to observe the complete phase segregation is discussed. A comparison to recent experimental data suggests that the weakly segregated phase has been observed.