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.
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.
We consider a model of a two-component condensate in one dimension, where the components represent two different spin states of the same atom. We demonstrate that linear interconversion between them, induced by a resonant electromagnetic wave, can make the immiscible binary condensate miscible. This transition is predicted by means of a variational approximation, and is then confirmed by direct numerical solutions of the symmetric and asymmetric models (the asymmetry is accounted for by a chemical-potentil difference between the components). The dependence of the corresponding order parameters on the linear-coupling strengths reveals a typical phase transition of the second kind. However, in dynamic states the species may remain separated, even if they would get mixed in a static configuration.
We investigate the effects of dipole-dipole (DD) interactions on immiscibility-miscibility transitions (IMT's) in two-component Bose-Einstein condensates (BEC's) trapped in the harmonic-oscillator (HO) potential, with the components linearly coupled by a resonant electromagnetic field (accordingly, the components represent two different spin states of the same atom). The problem is studied by means of direct numerical simulations. Different mutual orientations of the dipolar moments in the two components are considered. It is shown that, in the binary BEC formed by dipoles with the same orientation and equal magnitudes, the IMT cannot be induced by the DD interaction alone, being possible only in the presence of the linear coupling between the components, while the miscibility threshold is affected by the DD interactions. However, in the binary condensate with the two dipolar components polarized in opposite directions, the IMT can be induced without any linear coupling. Further, we demonstrate that those miscible and immiscible localized states, formed in the presence of the DD interactions, which are unstable evolve into robust breathers, which tend to keep the original miscibility or immiscibility, respectively. An exception is the case of a very strong DD attraction, when narrow stationary modes are destroyed by the instability. The binary BEC composed of copolarized dipoles with different magnitudes are briefly considered as well.
We study the interactions between two atomic species in a binary Bose-Einstein condensate to revisit the conditions for miscibility, oscillatory dynamics between the species, steady-state solutions, and their stability. By employing a variational approach for a quasi-one-dimensional, two-atomic species condensate, we obtain equations of motion for the parameters of each species: amplitude, width, position, and phase. A further simplification leads to a reduction of the dynamics into a simple classical Newtonian system where components oscillate in an effective potential with a frequency that depends on the harmonic trap strength and the interspecies coupling parameter. We develop explicit conditions for miscibility that can be interpreted as a phase diagram that depends on the harmonic trap's strength and the interspecies coupling parameter. We numerically illustrate the bifurcation scenario whereby nontopological, phase-separated states of increasing complexity emerge out of a symmetric state as the interspecies coupling is increased. The symmetry-breaking dynamical evolution of some of these states is numerically monitored and the associated asymmetric states are also explored.
We investigate application of nonlinearity management (NM, i.e., periodic variation of the strength of the intercomponent repulsion) to the miscibility-immiscibility (MIM) transition across the critical point of a two-component Bose-Einstein condensate, both with and without linear mixing [Rabi coupling (RC)] between the components. To this end, we first identify, by means of a variational approximation and numerical solution, diverse stationary domain-wall (DW) structures supported by the system in the absence of management. The approximate analytical solutions for the DWs are found to be in excellent agreement with their numerical counterparts. An analytical estimate is also produced for the upshift of the MIM transition caused by the pressure of the trapping potential in the case of a confined system. An exact DW solution is produced for the system including the Pöschl-Teller potential, which is stable (unstable) if the potential is repulsive (attractive). Further, we find the spectrum of linear excitations in the spatially uniform mixed state, and thus establish parameter regions where the system is stable or unstable against demixing. In particular, RC upshifts the critical strength of the intercomponent repulsion for the onset of the MIM transition. Eigenfrequencies of excitations on top of DW states are identified from numerical simulations through monitoring the evolution of perturbed states. Weak NM applied at the DW eigenfrequency reveals features of the nonlinear resonance. Stronger NM, under which the system periodically crosses the MIM-transition point, restricts the miscibility.
The effects of atom numbers on the miscibility-immiscibility transition of a harmonically trapped population imbalanced binary Bose-Einstein condensate are investigated. In two-dimensional parameter space expanded by the strength of interspecies interaction and the ratio of atom numbers between two components, we have mapped out the ground-state phase diagrams for the ideal model without intraspecies interactions, and for the $^{23}\mathrm{Na}\text{\ensuremath{-}}^{23}\mathrm{Na}$ mixture and the $^{87}\mathrm{Rb}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ mixture with experimentally accessible intraspecies scattering lengths, respectively. It is found that all the phase diagrams include the miscible, symmetric immiscible, and asymmetric immiscible phases, and there exists a tricritical point where those three different phases merge. Furthermore, the phase boundaries among those three phases show a strong dependence on the atom numbers of two components. These results can be observed in current experiments.
The miscibility of two interacting quantum systems is an important testing ground for the understanding of complex quantum systems. Two-component Bose-Einstein condensates enable the investigation of this scenario in a particularly well controlled setting. In a homogeneous system, the transition between mixed and separated phases is fully characterized by a miscibility parameter based on the ratio of intra- to interspecies interaction strengths. Here we show, however, that this parameter is no longer the optimal one for trapped gases, for which the location of the phase boundary depends critically on atom numbers. We demonstrate how monitoring of damping rates and frequencies of dipole oscillations enables the experimental mapping of the phase diagram by numerical implementation of a fully self-consistent finite-temperature kinetic theory for binary condensates. The change in damping rate is explained in terms of surface oscillation in the immiscible regime, and counterflow instability in the miscible regime, with collisions becoming only important in the long time evolution.