Entanglement at finite temperatures in the electronic two-particle interferometer

TL;DR

This paper develops a theory for entanglement in fermionic two-particle interferometers at finite temperature, addressing experimental observations of entanglement and its detection amidst thermal effects.

Contribution

It extends previous work by providing a detailed analysis of entanglement generation, characterization, and detection in mesoscopic conductors at finite temperature.

Findings

The emitted two-particle state is entangled despite finite temperature effects.

Reconstructed entanglement from measurements provides a lower bound to the actual entanglement.

Finite temperature does not preclude the detection of entanglement in the system.

Abstract

In this work we discuss a theory for entanglement generation, characterization and detection in fermionic two-particle interferometers at finite temperature. The motivation for our work is provided by the recent experiment by the Heiblum group, Neder et al, Nature 448, 333 (2007), realizing the two particle interferometer proposed by Samuelsson, Sukhorukov, and Buttiker, Phys. Rev. Lett. 92, 026805 (2004). The experiment displayed a clear two-particle Aharonov-Bohm effect, however with an amplitude suppressed due to finite temperature and dephasing. This raised qualitative as well quantitative questions about entanglement production and detection in mesoscopic conductors at finite temperature. As a response to these questions, in our recent work, Samuelsson, Neder, and Buttiker, Phys. Rev. Lett. 102, 106804 (2009) we presented a general theory for finite temperature entanglement in mesoscopic conductors. Applied to the two-particle interferometer we showed that the emitted two-particle state in the experiment was clearly entangled. Moreover, we demonstrated that the entanglement of the reduced two-particle state, reconstructed from measurements of average currents and current cross correlations, constitutes a lower bound to the entanglement of the emitted state. The present work provides an extended and more detailed discussion of these findings.