Quantum control approach to creating and detecting fractional quantum Hall puddles

We theoretically explore a novel approach to generating few-body analogs of bosonic fractional quantum Hall states [1]. We consider an array of identical few-atom clusters (n = 2, 3, 4), each cluster trapped at the node of an optical lattice. By temporally varying the amplitude and phase of the trapping lasers, one can introduce a rotating deformation at each site. This allows for coherently transferring atoms into highly correlated states. We study target state fidelities and experimental signatures by exactly solving the many-body time dependent Schr\"{o}dinger equation within a truncated basis. In addition to bosonic quantum hall states our method provides a path to create fermionic quantum hall states and other exotic states. [1] SKB, KRAH, and EJM, Phys. Rev. A 78, 061608(R) (2008)