Phases of Atom-Molecule Vortex Matter

We study ground state vortex configurations in a rotating atom-molecule Bose-Einstein condensate. It is found that the coherent coupling between the atomic and molecular condensates can render a pairing of atomic and molecular vortices into a composite structure that resembles a carbon dioxide molecule. Structural phase transitions of vortex lattices are also explored through different physical parameters including the rotational frequency of the system.

Figure 1

Vortex lattice configurations for different rotational speeds. Three plots on the left show the density plot of the atomic condensate [blue (or dark gray)] with atomic vortices superposed in green (or light gray) dots. Brighter blue color represents higher density, while dark holes correspond to density dips. Molecular vortices are drawn using red (or gray) crosses. The plots on the right show the local degree of phase matching. The atomic and molecular vortices are drawn in the same manner. The dark region represents matched phase hence reduced coupling energy $E_C$, while the bright region corresponds to high $E_C$.

Figure 2

The degree of phase matching, $D$, as a function of $\Omega$ (top) and coherent coupling constant $\chi$ (bottom). (a) For negative $g_{am}$, discontinuous changes in $D$ are observed corresponding to the discrete phase transition in the structure of vortex lattices with the increase of either $\Omega$ or $\chi$. After phase is frozen, $D$ becomes near $-1$. (b) For the case of positive $g_{am}$, $D$ again changes from 0 to $-1$ with the increase of $\chi$, but continuously without any discrete jumps. With the increase of $\Omega$, no considerable change in $D$ is observed.

Figure 3

(a) Atomic cloud [blue (or dark gray)] is shown with atomic vortices drawn in as green (or light gray) dots while molecular vortices are represented by red (or gray) crosses. Brighter blue color represents higher density, while dark holes correspond to atomic vortices. The magnified inset shows the Archimedean lattice of molecular vortices with a rectangular atomic vortex lattice. (b) Schematic figure of the Archimedean lattice formed by molecular vortices.

Figure 4

Magnified views of vortex configurations for unpaired vortex lattices (a) with $g_{am}<0$, (b) with $g_{am}>0$, and (c) for phase-frozen vortex pairs. Blue (or dark gray) represents the atomic condensate. Brighter color corresponds to higher density while the dark holes represent atomic vortex dips. Molecular vortices are drawn in as red (or gray) dots. $M$, $M^{\prime }$, and $A$ represent two molecular vortices and an atomic vortex that are involved in a phase-frozen vortex pair. The broken symmetry between the positions of $M$ and $M^{\prime }$ with respect to $A$ in (a) explains why there should be a discrete phase transition in transforming from (a) toward (c), while not (b) to (c).