Structure of binary Bose-Einstein condensates

Abstract

We identify all possible classes of solutions for two-component Bose-Einstein\ncondensates (BECs) within the Thomas-Fermi (TF) approximation, and check these\nresults against numerical simulations of the coupled Gross-Pitaevskii equations\n(GPEs). We find that they can be divided into two general categories. The first\nclass contains solutions with a region of overlap between the components. The\nother class consists of non-overlapping wavefunctions, and contains also\nsolutions that do not possess the symmetry of the trap. The chemical potential\nand average energy can be found for both classes within the TF approximation by\nsolving a set of coupled algebraic equations representing the normalization\nconditions for each component. A ground state minimizing the energy (within\nboth classes of the states) is found for a given set of parameters\ncharacterizing the scattering length and confining potential. In the TF\napproximation, the ground state always shares the symmetry of the trap.\nHowever, a full numerical solution of the coupled GPEs, incorporating the\nkinetic energy of the BEC atoms, can sometimes select a broken-symmetry state\nas the ground state of the system. We also investigate effects of finite-range\ninteractions on the structure of the ground state.\n