  We argue that it is possible in principle to reduce the uncertainty of an
atomic magnetometer by double-passing a far-detuned laser field through the
atomic sample as it undergoes Larmor precession. Numerical simulations of the
quantum Fisher information suggest that, despite the lack of explicit
multi-body coupling terms in the system's magnetic Hamiltonian, the parameter
estimation uncertainty in such a physical setup scales better than the
conventional Heisenberg uncertainty limit over a specified but arbitrary range
of particle number N. Using the methods of quantum stochastic calculus and
filtering theory, we demonstrate numerically an explicit parameter estimator
(called a quantum particle filter) whose observed scaling follows that of our
calculated quantum Fisher information. Moreover, the quantum particle filter
quantitatively surpasses the uncertainty limit calculated from the quantum
Cramer-Rao inequality based on a magnetic coupling Hamiltonian with only
single-body operators. We also show that a quantum Kalman filter is
insufficient to obtain super-Heisenberg scaling, and present evidence that such
scaling necessitates going beyond the manifold of Gaussian atomic states.
