Phase separation in a two-species atomic Bose-Einstein condensate with an interspecies Feshbach resonance

We consider a mixture of two-species atomic Bose-Einstein condensates coupled to a bound molecular state at zero temperature via an interspecies Feshbach resonance. The interspecies Feshbach coupling precludes the possibility of doubly mixed phases while enables not only the pure molecular superfluid but also the pure atomic superfluids to exist as distinct phases. We show that this system is able to support a rich set of phase separations, including that between two distinct mixed atom-molecule phases. We pay particular attention to the effects of the Feschbach coupling and the particle collisions on the miscibility of this multicomponent condensate system.

Figure 1

The phase diagrams in the $\delta \text{−}d$ space where (a) and (b) are produced with $\overline{g}=0$ for (a) and $\overline{g}=1$ for (b), and (c) and (d) correspond, respectively, to (a) and (b) while collisional coefficients are set at ${\overline{\chi }}_{11}=0.2$, ${\overline{\chi }}_{22}=0.3$, ${\overline{\chi }}_{12}=2$, and ${\overline{\chi }}_{3i}=0$. See the text for units. For the sake of clarity, the labels for ASF1 and ASF2, which are located at $\overline{d}=1$ and $-1$, respectively, are omitted.

Figure 2

(Color online) The phase diagrams in the $\delta \text{−}d$ space (the uppermost figure, with total density ${\overline{n}}_t=1$), the chemical potential space [(a) and (b)], and the density space [(c) and (d)] when $\overline{g}=1$, ${\overline{\chi }}_{11}=0.2$, ${\overline{\chi }}_{22}=0.3$, ${\overline{\chi }}_{33}=0.245$, ${\overline{\chi }}_{12}=0.1225$, and ${\overline{\chi }}_{13}={\overline{\chi }}_{23}=0$. Additionally, (a) and (c) are produced with $\overline{\delta }=0.5$ while (b) and (d) are produced with $\overline{\delta }=-0.8$. The gray area in (a) and (b) represents the region where two stable phases can coexist. The red dashed lines inside the gray area are the first-order phase transition lines at which the ground state changes from one phase to the other. See the inset for more details of the region around the first-order line. Consult the text for units and for a detailed explanation of each diagram.

Figure 3

(Color online) The phase diagrams similarly defined as in Fig. 2. The parameters are the same as those in Fig. 2 except that ${\overline{\chi }}_{12}=2$. Additionally, (a) and (c) are produced with $\overline{\delta }=1$ while (b) and (d) are produced with $\overline{\delta }=0.5$. The red dashed lines have the same meanings as that in Fig. 2. Consult the text for units.