From non-equilibrium Green's functions to Floquet quantum master equations: an application to all-electrical Electron Spin Resonance

We present a theoretical framework to evaluate the conditions and outcome of experiments directed to controlling quantum systems using electrical means. In particular, recent experiments have shown important progress in the excitation of single-atom spin resonances using a scanning tunneling microscope. Although general, we show that the theory presented here can be applied to understand the ingredients, parameters and results of such experiments. The theory is based on non-equilibrium Green’s functions that allow us to treat realistic bias drops and electron flow through an atomic system connected to two electrodes. The full quantum response of the system is obtained by doing perturbation theory in the hopping terms between the atomic system and the electrodes. Applying an electrical field changes the tunneling conditions of electrons. We suggest this mechanism to explain the process of driving an atomic spin with a time-dependent electrical field. The tunneling barrier is modulated by the time-dependent field and this leads to a timedependent hopping matrix element between the quantum system and the electrodes. An electron that enters the impurity or atomic site is coupled to the rest of the spin of the system via a magnetic exchange interaction. This is equivalent to a Kondo Hamiltonian that takes into account the exchange coupling between electrons and spins in the atomic system. We apply this theory to two cases. The simplest case is just a single atomic orbital subjected to a time-dependent electric field, and the second case consist of a single atomic orbital coupled to a second spin-1/2 under the same type of driving as before. The first case already reproduces the main experimental features Ti atoms on MgO/Ag (100) while the second one directly addresses the experiments on two Ti atoms. These calculations permit us to explore the effect of different parameters in the driving of the spins as well as to reproduce experimental fingerprints.