electromagnetic radiation - Force on two level system in standing wave electric field

Given external radiation, produced from an electric field travelling from the left and an electric field travelling from the right, producing a standing wave

$$E_0e^{i(kx - \omega t)} + E_0e^{-i(kx - \omega t)},$$ the Stark energy shift of a two level system under the influence of this electric field is $$\Delta E(x) = \hbar \Delta \omega_0 (x) = \frac{\hbar \Omega^{2}(x)}{4 \delta} = \hbar \bigg( \frac{\vec{d} \cdot \vec{E}_0}{ \hbar} \bigg)^2/ 4 \delta,$$ where $\Omega$ is the Rabi frequency and $\delta$ is the detuning $\omega_0 - \omega$.

How does it follow that the force on the particle depends on the gradient of the electric field at the position of the particle?