Recoil energy ($E_R=p_R^2/(2m)$)

Recoil energy is the kinetic energy gained by an initially stationary atom absorbing a photon of momentum $p_R$. In a standing-wave optical lattice of spacing $d$, the photon wavenumber is $\pi /d$, giving $E_R={\hslash }^2{\pi }^2/(2m{d}^2)$.