Guillermo Cordourier-Maruri

Graphene-enabled low-control quantum gates between static and mobile spins

We show that the features of Klein tunneling make graphene a unique interface for implementing low control quantum gates between static and mobile qubits. A ballistic electron spin is considered as the mobile qubit, while the static qubit is the electronic spin of a quantum dot fixed in a graphene nanoribbon. Scattering is the low control mechanism of the gate, which in other systems is very difficult to exploit because of both backscattering and the momentum dependence of transmission. We find that the unique features of Klein tunneling enable quasideterministic quantum gates between the spin of a ballistic electron and a static spin held in a dot, regardless of the momenta or the shape of the incident electron wave function. The Dirac equation is used to describe the system in the one particle approximation, with the interaction between the static and the mobile spins modeled by a Heisenberg Hamiltonian. Furthermore, we discuss an application of this model to generate entanglement between two well-separated static qubits.

TRANSMISSION PROPERTIES OF THE ONE-DIMENSIONAL ARRAY OF DELTA POTENTIALS

The problem of one-dimensional quantum wire along which a moving particle interacts with a linear array of N delta-function potentials is studied. Using a quantum waveguide approach, the transfer matrix is calculated to obtain the transmission probability of the particle. Results for arbitrary N and for specific regular arrays are presented. Some particular symmetries and invariances of the delta-function potential array for the N = 2 case are analyzed in detail. It is shown that perfect transmission can take place in a variety of situations.

RECURRENCE IN RESONANT TRANSMISSION OF ONE-DIMENSIONAL ARRAY OF DELTA POTENTIALS

In this paper, the resonant transmission of a moving particle which interacts with a one-dimensional array of N δ-function potentials is investigated. A suitable transfer matrix formulation is used to obtain the particle transmission. We give the parameters for perfect tunneling and the transcendental equation for the quasi-bound state energies for N = 2, 3 and 4. Conditions for perfect tunneling and resonant transmission are discussed for arrays with arbitrary N. A model to explain how the tunneling energy filter works in these systems is proposed here.