Optical Generation and Quantitative Characterizations of Electron-hole Entanglement

TL;DR

This paper investigates the optical generation and quantification of electron-hole entanglement using quantum field theory, analyzing experimental results and proposing methods for spatially separating entangled particles.

Contribution

It provides a theoretical framework for understanding electron-hole entanglement in optical systems, especially considering spin-orbit coupling and superposition states.

Findings

Entanglement is characterized as between occupation numbers of single particle states.

Interaction with circularly polarized light creates superpositions of excitonic states.

Band-index states are pure and separable from orbital degrees of freedom.

Abstract

Using a method of characterizing entanglement in the framework of quantum field theory, we investigate the optical generation and quantitative characterizations of quantum entanglement in an electron-hole system, in presence of spin-orbit coupling, and especially make a theoretical analysis of a recent experimental result. Basically, such entanglement should be considered as between occupation numbers of single particle basis states, and is essentially generated by coupling between different single particle basis states in the second quantized Hamiltonian. Interaction with two resonant light modes of different circular polarizations generically leads to a superposition of ground state and two heavy-hole excitonic states. When and only when the state is a superposition of only the two excitonic eigenstates, the entanglement reduces to that between two distinguishable particles, each with two degrees of freedom, namely, band index, as characterized by angular momentum, and orbit, as characterized by position or momentum. The band-index state, obtained by tracing over the orbital degree of freedom, is found to be a pure state, hence the band-index and orbital degrees of freedom are separated in this state. We propose some basic ideas on spatially separating the electron and the hole, so that the entanglement of band-indices, or angular momenta, is between spatially separated electron and hole.