Vortex Phase Diagram in Rotating Two-Component Bose-Einstein Condensates

We investigate the structure of vortex states in rotating two-component Bose-Einstein condensates with equal intracomponent but varying intercomponent-coupling constants. A phase diagram in the intercomponent-coupling versus rotation-frequency plane reveals rich equilibrium structures of vortex states. As the ratio of intercomponent to intracomponent couplings increases, the interlocked vortex lattices undergo phase transitions from triangular to square, to double-core lattices, and eventually develop interwoven “serpentine” vortex sheets with each component made up of chains of singly quantized vortices.

Figure 1

$\overline{\Omega }\mathrm{\text{−}}\delta$ phase diagram of the vortex states in rotating two-component BECs. The classification of the structure is made by the following symbols: △, triangular lattice; ◇, square lattice; $\otimes$, stripe or double-core vortex lattice; ○, vortex sheet. Because of the continuous change from triangular to square, their boundary is shown by using both △ and ◇. The plots at $\overline{\Omega }=1$ show the results of Ref. 11. The shaded region shows the analytically obtained region of vortex sheets; the solid curve represents $b={\Lambda }_p$ and the dashed curve $2b=R_{\mathrm{T}\mathrm{F}}$ (see text).

Figure 2

Two-dimensional density profile of the condensates with $C=2000$ and $\delta =0.7$ for (a) $\overline{\Omega }=0.6$ and (b) $\overline{\Omega }=0.75$. (c) Cross section of (b) along the $y=0$ line. The total density ${\rho }_T=|{\Psi }_1{|}^2+|{\Psi }_2{|}^2$ and the Thomas-Fermi density profile are also shown.

Figure 3

The density profiles of the condensates ${\Psi }_1$ and ${\Psi }_2$ for $\overline{\Omega }=0.7$ and $\delta =1$. The profiles (a) and (b) are obtained by the numerical simulation starting from different trial wave functions. The energy deference between these states is $\Delta E\sim {10}^{-5}$.

Figure 4

(a) The density profiles of the condensates for $\overline{\Omega }=0.75$ and $\delta =1.1$. The vortex sheets are made up of chains of singly quantized vortices whose positions are marked by ×. (b) The density profile of ${\Psi }_1$ and ${\Psi }_2$ in the radial component, and the corresponding velocity profile. The velocity of solid-body rotation is shown by the dotted line. (c) Schematic illustration of the model of the vortex sheet state.