Dynamic generation of orbital quasiparticle entanglement in mesoscopic conductors

We propose a scheme for dynamically creating orbitally entangled electron-hole pairs through a time-dependent variation of the electrical potential in a mesoscopic conductor. The time-dependent potential generates a superposition of electron-hole pairs in two different orbital regions of the conductor, a two-particle interferometer in the quantum Hall regime. The orbital entanglement is detected via violation of a Bell inequality, formulated in terms of zero-frequency current noise. Adiabatic cycling of the potential, in both the weak and strong amplitude limits, is considered.

Figure 1

(Color online) Two-particle interferometer in the quantum Hall regime. Transport takes place along a single-edge state (thick black line) in the direction shown by the arrows. The potentials $V_C\left(t\right)$ and $V_D\left(t\right)$ at $C$ and $D$ are adiabatically and periodically modulated in time, creating electron-hole pairs propagating towards reservoirs 1–4. The static point contacts at $A$ and $B$ work as controllable beam splitters.

Figure 2

(Color online) The four different electron-hole pair emission processes at $C$: In the two upper processes, the pair is split and (a) the electron is emitted towards $B$ and the hole towards $A$ or (b) the electron towards $A$ and the hole towards $B$. In the two lower processes, both quasiparticles are emitted (c) towards $A$ or (d) towards $B$. The same processes occur at $D$.