Interference of Atomic Levels and Superfluid-Mott Insulator Phase Transitions in a Two-Component Bose-Einstein Condensate

The superfluid-Mott insulator phase transition in a Bose-Einstein condensate of neutral atoms with doubly degenerate internal ground states in an optical lattice is theoretically investigated. The optical lattice is created by two counterpropagating linearly polarized laser beams with the angle $\theta$ between the polarization vectors (lin-angle-lin configuration). The phase diagram of the system and the critical values of the parameters are worked out. It is shown that the sign of the detuning plays an important role and that there is a strong suppression of the Mott transition in the case of blue detuning. Varying the laser intensity and/or the angle $\theta$ one can manipulate the Mott insulator to superfluid quantum phase transition as well as prepare the condensate in physically distinguishable “ferromagnetic” and “antiferromagnetic” superfluid states.

Figure 1

Typical dependences of $J/U$ on the dimensionless effective Rabi frequency $q={\Omega }_0^2/4{\omega }_R\Delta$ for red detuning ($\Delta <0$) and corresponding phase diagrams for $n=1$. $\theta =50°$ (a), $64°$ (b), $65.7767°$ (c), and $66.5°$ (d). Horizontal straight lines show the critical values $(2J/U{)}_c=\pm (3-2\sqrt{2})$. Vertical dashed lines on the phase diagrams (right column) indicate the boundary between ferromagnetic ($J>0$) and antiferromagnetic ($J<0$) phase ordering. The regions of the Mott phase are enclosed by the lobes and loops.

Figure 2

The same as in Fig. 1 as functions of $\theta$ ($\Delta <0$). $q=-3.9$ (a), $-4.5$ (b), $-4.80064$ (c), and $-5$ (d).

Figure 3

Phase diagram in the $(\theta ,q)$ plane for $(\mu /U{)}_c=\sqrt{2}-1$ ($\Delta <0$). The boundaries between the superfluid and the Mott ($n=1$) phases are shown by solid (calculation for the two-component BEC) and dotted (approximation, which does not take into account the coupling between the bright and dark states) lines. The dashed line corresponds to $J=0$. It lies always in the Mott phase, separating the regions of the ferromagnetic (SF) and antiferromagnetic (SA) superfluid phases.

Figure 4

The same as in Figs. 1, 2 for blue detuning ($\Delta >0$). $\theta =45°$ (a), $q=6$ (b).

Figure 5

(a) Phase diagram in the $(\theta ,q)$ plane for $(\mu /U{)}_c=\sqrt{2}-1$, $\Delta >0$. The line $J=0$ as well as the two boundaries separating SF and SA superfluid phases from the Mott phase are indistinguishable on the large-scale plot. The Mott phase is located in the extremely narrow region between the superfluid phases. Plot (b), therefore, shows the difference $\delta q_1$ between the two boundaries (solid line) and the difference $\delta q_2$ between the line $J=0$ and the boundary separating the ferromagnetic superfluid phase from the Mott phase (dashed line).