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We use exact diagonalization to study the quantum phases and phasetransitions when a single species of fermionic atoms at Landau level fillingfactor $\nu_f = 1$ in a rotating trap interact through a p-wave Feshbachresonance. We show that under weak pairing interaction, the system undergoes asecond order quantum phase transition from $\nu_{f} = 1$ fermionic integerquantum Hall (FIQH) state at positive detuning, to $\nu_{b} = \frac{1}{4}$bosonic fractional quantum Hall (BFQH) state at negative detuning. However,when the pairing interaction increases, a new phase between them emerges,corresponding to a fraction of fermionic atoms stay in a coherent superpositionof bosonic molecule state and an unbound pair. The phase transition from FIQHphase to the new phase is of second order and that from the new phase to BFQHphase is of first order.

physical review. b./physical review. b

Topological Quantum Phase Transition from Fermionic Integer Quantum Hall  Phase to Bosonic Fractional Quantum Hall Phase through P-Wave Feshbach  Resonance