The Rashba Effect Within the Coherent Scattering Formalism with Applications to Electron Quantum Optics

Abstract

The influence of spin–orbit coupling in electron quantum optics experiments is investigated within the framework of the Landauer–Buttiker coherent scattering formalism. We begin with a brief review of our electron quantum optics toolbox: an electron intensity interferometer (Hanbury Brown and Twiss-type experiment), an electron collision analyzer (Hong–Ou–Mandel-type experiment), and a proposed Bell state analyzer. These experiments are performed or proposed in two-dimensional electron gas systems and, therefore, may be influenced by the Rashba spin–orbit coupling. To quantify this effect, we define the creation/annihilation operators for the stationary states of the Rashba spin–orbit coupling Hamiltonian and use them to derive the current operator within the Landauer–Buttiker formalism. The current is expressed as it is in the standard spin-independent case, but with the spin label replaced by a new label that we call the spin–orbit coupling label. The spin–orbit coupling effects can then be represented in a scattering matrix that relates the spin–orbit coupling stationary states in different leads. We apply this new formalism to the case of a four-port beamsplitter, and it is shown to mix states with different spin–orbit coupling labels in a manner that depends on the angle between the leads. A noise measurement after the collision of spin-polarized electrons at an electron beamsplitter provides a new experimental means to measure the Rashba parameter α. It is also shown that the degree of electron bunching in an entangled-electron collision experiment is reduced by the spin–orbit coupling according the beamsplitter lead angle.