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Ground-state solutions in a dilute gas interacting via contact and magnetic dipole-dipole forces are investigated. To the best of our knowledge, it is the first example of studies of the Bose-Einstein condensation in a system with realistic long-range interactions. We find that for the magnetic moment of e.g. chromium (6µB) and a typical value of the scattering length all solutions are stable and only differ in size from condensates without long-range interactions. By lowering the value of the scattering length we find a region of unstable solutions. In the neighborhood of this region the ground state wavefunctions show internal structures not seen before in condensates. Finally, we find an analytic estimate for the characteristic length appearing in these solutions.Since the advent of Bose-Einstein condensation in dilute gases of alkalies [1] and hydrogen [2] it has become apparent that the interactions between the condensed atoms govern most of the observed phenomena. In all the experiments so far the interaction can be described by a contact potential which is characterized by the scalar quantity a being the s-wave scattering length. Static properties like the condensate's ground-state density profile, its instability in the case of negative a and the meanfield shift in spectroscopic measurements as well as dynamic properties like collective excitations and propagation of sound have been investigated [3]. Similarly, nonlinear atom optics experiments e.g. four wave mixing [4] are only possible due to the large nonlinearity mediated by the atom-atom interactions. The T =0K situation in almost all experiments can be described very well by the Gross-Pitaevskii equation [5].Any reasonably strong dipole-dipole interaction would largely enrich the variety of phenomena to be observed in dilute gases due to their long range and vectorial character. However, for all of the condensed atomic species the magnetic moment µ was roughly 1 µ B (Bohr magneton) and the respective magnetic dipole-dipole interaction was negligible compared to the contact potential. It has been proposed to induce a strong electric dipoledipole interaction in alkalies by the application of strong DC electric fields [6].Recently it has become possible to trap atoms with higher magnetic moments at high densities. Examples are europium (µ = 7µ B ) [7], which has been trapped magnetically by a buffer-gas loading technique, and chromium (µ = 6µ B ), which has been loaded into a magnetic trap by a buffer-gas technique [8] and by laser cooling [9]. For these species the scattering lengths are not known to date, but, assuming a normal non-resonant behavior, the crossections of the scalar contact potential and the magnetic dipole-dipole interaction are of comparable size.As the dipole-dipole interaction is attractive parallel to a common polarization axis the immediate question arises: can a stable condensate be formed under the influence of a dipole-dipole interaction? What is its effect on anisotropic clouds? What do the ground-state wavefunctions look li...

Phys. Rev. 165, 1579. 12 The quoted ranges include values of A T and A LS from Refs. 8, 10, and 11 and R. A. Arndt, R. H. Hackman, and L. D. Roper, Phys. Rev. C 9, 555 (1974). From the latter reference we include the phase shifts from the 1-500-MeV analysis and two sets of phase shifts obtained from the analysis of the 1-27.6-MeV data.13 Arndt, Hackman, and Roper, Ref. 12. The caption of Fig. 3 is incorrect. The floated curves are the upper one for Fig. 3(a) and the lower ones for Figs. 3(b) and 3(c). The numbers on the vertical scale in Figs. 2(b) and 3(b) should be negative and the values in Fig. 3(b) should be integer multiples of 0.2 [R. A. Arndt, private communication].14

We identify all possible classes of solutions for two-component Bose-Einstein condensates (BECs) within the Thomas-Fermi (TF) approximation, and check these results against numerical simulations of the coupled Gross-Pitaevskii equations (GPEs). We find that they can be divided into two general categories. The first class contains solutions with a region of overlap between the components. The other class consists of non-overlapping wavefunctions, and contains also solutions that do not possess the symmetry of the trap. The chemical potential and average energy can be found for both classes within the TF approximation by solving a set of coupled algebraic equations representing the normalization conditions for each component. A ground state minimizing the energy (within both classes of the states) is found for a given set of parameters characterizing the scattering length and confining potential. In the TF approximation, the ground state always shares the symmetry of the trap. However, a full numerical solution of the coupled GPEs, incorporating the kinetic energy of the BEC atoms, can sometimes select a broken-symmetry state as the ground state of the system. We also investigate effects of finite-range interactions on the structure of the ground state.