Coherent Ultrafast Spin-Light Interactions in One- and Two-Electron Systems

Thanks to the Foldy-Wouthuysen transformation (FWT), the non-relativistic limit at fifth order in powers of 1/m of the one-electron external-electromagnetic-field Dirac equation is performed. It allows us to postulate a general analytical expression of the Hamiltonian related to the direct electron spin-field interaction valid at any order in powers of 1/m. By extending the previous methodology to the case of two interacting electrons and within the framework of the Breit model, we show how an external electric field could modify and control the electron-electron interaction at the third order in 1/m.