  We use exact diagonalization to study the quantum phases and phase
transitions when a single species of fermionic atoms at Landau level filling
factor $\nu_f = 1$ in a rotating trap interact through a p-wave Feshbach
resonance. We show that under weak pairing interaction, the system undergoes a
second order quantum phase transition from $\nu_{f} = 1$ fermionic integer
quantum 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 superposition
of bosonic molecule state and an unbound pair. The phase transition from FIQH
phase to the new phase is of second order and that from the new phase to BFQH
phase is of first order.
