Quantum phase transitions of polar molecules in bilayer systems

We investigate the quantum phase transitions of bosonic polar molecules in a two-dimensional double layer system. We show that an interlayer bound state of dipoles (dimers) can be formed when the dipole strength is above a critical value, leading to a zero energy resonance in the interlayer $s$-wave scattering channel. In the positive detuning side of the resonance, the strong {\it repulsive} interlayer pseudo-potential can drive the system into a maximally entangled state, where the wavefunction is a superposition of two states that have all molecules in one of the two layers and none in the other. We critically discuss how the zero-energy resonance, dimer states and the maximally entangled state can be measured in time-of-flight experiments.