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Realizing quantum Hall states in a fast rotating Bose gas is a long soughtgoal in cold atom research. The effort is very challenging because Bosestatistics fights against quantum Hall correlations. In contrast, Fermistatistics does not cause such conflict. Here, we show that by sweeping theinteger quantum Hall states of a spin-1/2 Fermi gas across the Feshbachresonance from the BCS side to the BEC side at a "projection" rate similar tothat in the "projection" experiment of fermion superfluid, these states can be"fused" into a bosonic quantum Hall states. A projection sweep means the pairassociation is sufficiently fast so that the center of mass of the pair remainsunchanged in the process. We show that the fusion of integer fermion stateswith filling factor $\nu_{\uparrow}=\nu_{\downarrow}=n$ will result in abosonic Laughlin state and Pfaffian state for $n=1$ and 2. The is due to ahidden property of the fermionic integer quantum Hall states -- for anygrouping of opposite spin into pairs, their centers of mass automaticallyassume a bosonic quantum Hall structure.

Fusing Quantum Hall States in Cold Atoms