Overlaying optical lattices for simulation of complex frustrated antiferromagnets

We present design techniques for special optical lattices that allow quantum simulation of spin frustration in two-dimensional systems. By carefully overlaying optical lattices with different periods and orientations we are able to adjust the ratio between the nearest-neighbor and next-nearest-neighbor interaction strengths in a square spin lattice and realize frustration effects. We show that only laser beams of a single frequency are required and the parameter space reachable in our design is broad enough to study the important phases in the J ₁-J ₂ frustrated Heisenberg model and checkerboard antiferromagnet model. By using the polarization spectroscopy for detection, distinct quantum phases and quantum phase transition points can be characterized straightforwardly. Our design thus offers a suitable setup for simulation of frustrated spin systems.