Feshbach-Stabilized Insulator of Bosons in Optical Lattices

Feshbach resonances—namely, resonances between an unbound two-body (atomic) state and a bound (molecular) state, differing in magnetic moment—are a unique tool to tune the interaction properties of ultracold atoms. Here we show that the spin-changing interactions, coherently coupling the atomic and molecular states, can act as a novel mechanism to stabilize an insulating phase—the Feshbach insulator—for bosons in an optical lattice close to a narrow Feshbach resonance. Making use of quantum Monte Carlo simulations and mean-field theory, we show that the Feshbach insulator appears around the resonance, preventing the system from collapsing when the effective atomic scattering length becomes negative. On the atomic side of the resonance, the transition from condensate to Feshbach insulator has a characteristic first-order nature, due to the simultaneous loss of coherence in the atomic and molecular components. These features appear clearly in the ground-state phase diagram of, e.g., ${}^{87}\mathrm{Rb}$ around its 414 G resonance, and they are therefore directly amenable to experimental observation.

Figure 1

Various insulating phases appearing in the lattice atom-molecule coherent mixture. While atomic and molecular Mott insulators (MIs) are stabilized by the repulsive interaction, the Feshbach insulator is stabilized by the atom-molecule coherence (plus a repulsive interaction to avoid collapse); yellow ellipses indicate superposition states between two atoms and a molecule.

Figure 2

(a),(b) Mean-field phase diagram of a symmetric atom-molecule mixture with $t/U=0.06$ and $g/U=0.8$ (a) and with $t/U=0.04$ and $g/U=0.6$ (b) (false colors indicate the compressibility $\kappa$). [Inset of (a)] Phase diagram for $t/U=0.06$ and $g=0$. The following phases appear in the phase diagrams: Feshbach insulator (FI), atomic (BECa), molecular (BECm), and atomic-molecular (BECam) condensates, molecular (MIm) and atomic-molecular (MIam) Mott insulator. Second-order transitions are denoted by solid black lines, first-order transitions by red dashed lines, and tricritical points by white dots. (c),(d) Full width at half maximum of the molecular momentum distribution (FWHMm) versus the conversion $g$ for $\delta /U=-1.2$, $t/U=0.06$ (c), and $t/U=0.04$ (d). Results are from QMC simulations at fixed total density $n=2$ for a system of linear size $L=12$.

Figure 3

(a) Mean-field $T=0$ phase diagram for ${}^{87}\mathrm{Rb}$ close to the 414 G resonance in a cubic optical lattice of depth $V_0=12E_r$. The vertical dashed line marks the crossover from the MIam to the FI region. (Inset) The same phase diagram obtained by artificially setting $g$ to zero. (b) Derivative of the $p\text{−}h$ gap with respect to $g$: the change in sign marks the crossover from MIam to FI.

Figure 4

Peaks in the atomic (a) and molecular (b) distributions for a trapped system ($\omega =2\pi *19\mathrm{Hz}$) with central density $\approx 1.96$ in the BECam phase; the global chemical potential follows the dashed magenta line plot in Fig. 3.