A Non Equilibrium Green’s Function Formalism Applied to STM/ESR Experiments: Surface Spins as Quantum Bits


A non equilibrium Green’s Function formalism applied to STM/ESR experiments: Surface spins as quantum bits — •Jose Reina-Galvez1, Nicolas Lorente2, and Christoph Wolf1 — 1Center for Quantum nanoscience, Seoul, South Korea — 2Centro de Fisica de Materiales, San Sebastian, Spain

The demonstration of reproducible single-atom and single-molecule electron spin resonance (ESR) in a STM junction opened new possibilities in the analysis of surface science at the atomic scale. They can be tailored to a desired spin state, manipulated to form structures with designed interactions and as of recent have been used to implement basic quantum logic operations - a control-NOT gate - in a scanning tunneling microscope (STM).

Here, we want to focus on the theory we developed to reproduce some relevant results in the field. Our theoretical framework uses open quantum systems formalism in combination with non- equilibrium Green’s Function technique. The model is a modified Anderson impurity Hamiltonian where a quantum impurity is connected by hopping terms to a polarized STM tip and an isolated surface, both considered as fermionic baths. The time dependent AC voltage used in the experiments introduces a modulation of the tunneling barrier which affects the hopping terms, making possible to drive the quantum impurity and have resonances. The modified Anderson impurity model includes localized electronic states, a Coulomb repulsion term and a Zeeman term. It also allows connections with an arbitrary number of localized spins and the addition of anisotropy terms, enabling the possibility of building any quantum spin.

We will demonstrate how driving the system on resonance modifies the population and the calculated true current through the many-body impurity and how we are able to perform basic quantum logic gate operations on different spin systems.