  We propose a quantum metrology scheme in a cavity QED setup to achieve the
Heisenberg limit. In our scheme, a series of identical two-level atoms randomly
pass through and interact with a dissipative single-mode cavity. Different from
the entanglement based Heisenberg limit metrology scheme, we do not need to
prepare the atomic entangled states before they enter into the cavity. We show
that the initial atomic coherence will induce an effective driving to the
cavity field, whose steady state is an incoherent superposition of orthogonal
states, with the superposition probabilities being dependent on the atom-cavity
coupling strength. By measuring the average photon number of the cavity in the
steady state, we demonstrate that the root-mean-square of the fluctuation of
the atom-cavity coupling strength is proportional to $1/N_c^2$ ($N_c$ is the
effective atom number interacting with the photon in the cavity during its
lifetime). It implies that we have achieved the Heisenberg limit in our quantum
metrology process. We also discuss the experimental feasibility of our
theoretical proposal. Our findings may find potential applications in quantum
metrology technology.
