Transition to miscibility in a binary Bose-Einstein condensate induced by linear coupling

A one-dimensional mean-field model of a two-component condensate in the parabolic trap is considered, with the components corresponding to different spin states of the same atom. We demonstrate that the linear coupling (interconversion) between them, induced by a resonant electromagnetic wave, can drive the immiscible binary condensate into a miscible state. This transition is predicted in an analytical form by means of a variational approximation (for an infinitely long system), and is confirmed by direct numerical solutions of the symmetric and asymmetric models (the asymmetry accounts for a possible difference in the chemical potential between the components). We define an order parameter of the system as an off-centre shift of the centre of mass of each component. A numerically found dependence of the order parameter on the linear-coupling strength reveals a second-kind phase transition (in an effectively finite system). The phase transition looks very similar in two different regimes, namely, with a fixed number of atoms, or a fixed chemical potential. An additional transition is possible between double- and single-humped density distributions in the weak component of a strongly asymmetric system. We also briefly consider dynamical states, with the two components oscillating relative to each other. In this case, the components periodically separate even if they should be mixed in the static configuration.