Interactions and Charge Fractionalization in an Electronic Hong-Ou-Mandel Interferometer

We consider an electronic analog of the Hong-Ou-Mandel (HOM) interferometer, where two single electrons travel along opposite chiral edge states and collide at a quantum point contact. Studying the current noise, we show that because of interactions between copropagating edge states, the degree of indistinguishability between the two electron wave packets is dramatically reduced, leading to reduced contrast for the HOM signal. This decoherence phenomenon strongly depends on the energy resolution of the packets. Insofar as interactions cause charge fractionalization, we show that charge and neutral modes interfere with each other, leading to satellite dips or peaks in the current noise. Our calculations explain recent experimental results [, $\mathrm{et}\mathrm{al}\mathrm{.}$, Science 339, 1054 (2013)] where an electronic HOM signal with reduced contrast was observed.

Figure 1

The setups: two opposite edge states, each made out of two interacting copropagating channels, meet at a QPC. An electronic wave packet is injected on both incoming outer channels. (Main) Setup 1: backscattering occurs for outer channels. (Left inset) Setup 2: backscattering occurs for inner channels. (Right inset) Electron density as a function of position for an energy resolved packet imaged after propagating on a $5\mu \mathrm{m}$ length, revealing the presence of two modes composed each of two $\oplus /\ominus$ excitations.

Figure 2

(a)–(c) Modulus of $S_{\mathrm{HOM}}$ in units of $e^2\mathcal{R}T$ as a function of the time delay $\delta T$, for setups 1 and 2. (a) Packets wide in energy ($\gamma =1$, ${\epsilon }_0=175\mathrm{m}\mathrm{K}$ is the injection energy). (b) Energy-resolved packets ($\gamma =8$) give a lower contrast. Results for setup 1 reveal a triple dip structure, while for setup 2 we obtain a peak-dip-peak structure, with vanishingly small peaks in the case of energy-resolved packets. (c) Electron-hole interference: an electron has been injected on the right moving arm and a hole on the left moving one. (d) Modulus of $S_{\mathrm{HOM}}(0)$ and $2S_{\mathrm{HBT}}$ in units of $e^2\mathcal{R}T$ as a function of $\mathrm{\Gamma }$, for ${\epsilon }_0=0.7\mathrm{K}$. In all plots, $u=0.5$ and $\mathrm{\Theta }=0.1\mathrm{K}$.