  We study the energy level crossing behavior in two-dimensional quantum well
with the Rashba and Dresselhaus spin-orbit couplings (SOCs). By mapping the SOC
Hamiltonian onto an anisotropic Rabi model, we obtain the approximate ground
state and its quantum Fisher information (QFI) via performing a unitary
transformation. We find that the energy level crossing can occur in the quantum
well system within the available parameters rather than in cavity and circuit
quantum eletrodynamics systems. Futhermore, the influence of two kinds of SOCs
on the QFI is investigated and an intuitive explanation from the viewpoint of
the stationary perturbation theory is given.
