  We present a theoretical study on the system of laser-driven strongly
interacting Rydberg atoms trapped in a two-dimensional triangular lattice, in
which the dipole-dipole interactions between Rydberg states result in exotic
quantum phases. By using the mean-field theory, we investigate the steady state
solutions and analyze their dynamical stabilities. We find that in the
strong-interaction limit, the dynamics of the system is chaotic and exhibits
random oscillations under appropriate laser detunings. Lyapunov exponent
criterion is introduced to confirm the existence of this chaotic behavior. In
addition, we present a full quantum calculation based on a six-atom model, and
find that the system exhibits some bi-antiferromagnetic properties in every
triangular cell when the one-photon detuning is exactly resonant or
blue-shifted.
