Emission of time-bin entangled particles into helical edge states

We propose a single-particle source which emits into the helical edge states of a two-dimensional quantum spin Hall insulator. Without breaking time-reversal symmetry, this source acts like a pair of noiseless single-electron emitters which each inject separately into a chiral edge state. By locally breaking time-reversal symmetry, the source becomes a proper single-particle emitter which exhibits shot noise. Due to its intrinsic helicity, this system can be used to produce time-bin entangled pairs of electrons in a controlled manner. The noise created by the source contains information on the emitted wave packets and is proportional to the concurrence of the emitted state.

Figure 1

Helical single-electron source. A quantum dot is tunnel coupled to helical edge states through a quantum point contact of transmission $D$. A top gate (gray shading) is used to vary the potential $U\left(t\right)$ and thereby shift the discrete levels of the quantum dot. Every time an energy level is shifted above (below) the Fermi energy, an electron (hole) is emitted into the edge states. The current that leaves the source to the right (left) is labeled $I_R$ ($I_L$) and $\varphi$ denotes a magnetic flux that threads the quantum dot.

Figure 2

Current emitted by a helical single-electron source in the presence of an Aharonov-Bohm flux as a function of time (arbitrary scale). The blue (solid) line shows the excess current that flows to the right, and red (dashed) denotes the left-moving current. At each of the four times an energy level crosses the Fermi energy, an electron or hole is emitted in a superposition of right mover and left mover. Parameters: $U_0=-\Delta /8$, $U_1=\Delta /4$, ${\left|d\right|}^2=0.15$, $|d_{\sigma }{|}^2=0.05$, and $\varphi =\pi /6$.

Figure 3

Zero temperature shot noise created by the source as a function of the magnetic flux. At zero flux, equality of the emission times forces the particles into different outputs. For finite flux, the emission times differ and the noise increases until it saturates when the emitted particles have no overlap anymore. The noise is proportional to the concurrence created per cycle. The inset shows the excess noise divided by the zero temperature noise as a function of temperature. Here ${\left|d\right|}^2=0.15$, $|d_{\sigma }{|}^2=0.05$.