  The critical quantum metrology, which exploits the quantum phase transition
for high precision measurement, has gained increasing attention recently. The
critical quantum metrology with the continuous quantum phase transition,
however, is experimentally very challenging since the continuous quantum phase
transition only exists at the thermal dynamical limit. Here, we propose an
adiabatic scheme on a perturbed Ising spin model with the first order quantum
phase transition. By employing the Landau-Zener anticrossing, we can not only
encode the unknown parameter in the ground state but also tune the energy gap
to control the evolution time of the adiabatic passage. We experimentally
implement the adiabatic scheme on the nuclear magnetic resonance and show that
the achieved precision attains the Heisenberg scaling. The advantages of the
scheme-easy implementation, robust against the decay, tunable energy gap-are
critical for practical applications of quantum metrology.
