Two-Particle Aharonov-Bohm Effect and Entanglement in the Electronic Hanbury Brown–Twiss Setup

We analyze a Hanbury Brown–Twiss geometry in which particles are injected from two independent sources into a mesoscopic conductor in the quantum Hall regime. All partial waves end in different reservoirs without generating any single-particle interference; in particular, there is no single-particle Aharonov-Bohm effect. However, exchange effects lead to two-particle Aharonov-Bohm oscillations in the zero-frequency current cross correlations. We demonstrate that this is related to two-particle orbital entanglement, detected via violation of a Bell inequality. The transport is along edge states and only adiabatic quantum point contacts and normal reservoirs are employed.

Figure 1

Left: Two-source, four-detector optical Hanbury Brown–Twiss geometry. Two beams incident from $2$ and $3$ are split at the mirrors $C$ and $D$ and impinge on the mirrors $A$ and $B$ to reach detectors along the directions $5$ to $8$. Right: The two scattering processes (i) and (ii) contributing to the phase dependence of the correlators (see text).

Figure 2

Two-source, four-detector electrical Hanbury Brown–Twiss geometry: a rectangular Hall bar with inner and outer edges (thin dashed lines) and four quantum point contacts (grey shaded area). Contacts $2$ and $3$ are sources of electrons (a voltage $eV$ is applied against all other contacts which are at ground). Electrons follow edge states (thick black lines) in the direction indicated by the arrows and pick up phases ${\varphi }_1$ to ${\varphi }_4$. An Aharanov-Bohm flux $\Phi$ penetrates the center of the sample (shaded area) but has no influence on the single particle properties. However, the current correlations are essentially dependent on the phases ${\varphi }_i$ and the Aharonov-Bohm flux. We note that not all contacts have to be realized experimentally to investigate all physical phenomena discussed.