Multichannel architecture for electronic quantum Hall interferometry

We propose an architecture for implementing electronic interferometry in quantum Hall bars. It exploits scattering among parallel edge channels. In contrast to previous developments, this one employs a simply connected mesa admitting serial concatenation of building elements closer to optical analogs. Implementations of Mach–Zehnder and Hambury–Brown–Twiss interferometers are discussed together with structures yet unexplored in quantum electronics.

Figure 1

(Color online) Mach–Zehnder interferometer implementation. The shaded areas represent top gates that define regions of filling factor $\nu =1$. In the rest of the sample, instead, we assume $\nu =2$. Due to the presence of a strong magnetic field $B$ orthogonal to the bar surface, electrons injected from source contact 1a propagate from left to right following two possible paths. Electrons are finally collected at drain contacts 2a and 2b, where currents are measured. The red lines represent the edge channels effectively taking part to the MZ interferometer. ${\mathrm{BS}}_1$ and ${\mathrm{BS}}_2$ are beam splitters, while the gate MG is used to vary the shape and length of the outer edge $o$ channel. Notice that an experimental implementation of the setup does not require to employ air-bridge elements. Inset: sketch of the optical counterpart of the MZ interferometer.

Figure 2

(Color online) Implementation of the Hanbury–Brown–Twiss interferometer.

Figure 3

(Color online) Interaction-free interferometer. The optical implementation is shown in the lower part of the graph. It consists in a series of $n$ concatenated MZ interferometers characterized by a phase difference $\varphi =\pi ∕n$ among the two internal paths (Ref. 16). One of the two emerging paths from each of the MZ impinges into an external absorber (the green box in the picture), which can be either totally reflecting $(\eta =1)$ or totally absorbing $(\eta =0)$. Incoming photons deterministically end up either in the upper or the lower exit port depending on $\eta$. The electronic implementation of this device for $n=3$ is found in the upper part of the picture. Here, the “absorber” is simulated by the grounded contacts $1c$, $2c$, and $3c$. The absorption $(\eta =0)$ case is simulated by switching on extra top gates (patterned areas in the figure), which put in contact the inner edge with $1c$, $2c$, and $3c$ while leaving unaffected the path of the outer edge states, as in Fig. 2.

Figure 4

(Color online) Example of two MZ interferometers concatenated. The two large shaded areas are characterized, respectively, by AB fluxes ${\Phi }_1$ and ${\Phi }_2$ and path-length differences $\Delta L_{1,2}$. The patterned area represents an auxiliary top gate, which can be inserted to bypass the second BS, converting the whole setup to a the single MZ interferometer of Fig. 1.

Figure 5

(Color online) Conductance $G_a=⟨I_a⟩∕V$ as a function of magnetic field $B$ for different values of voltage $V$, with $D_1=0.8$, $D_2=0.9$, $R_{3u}=0.4$, $T_{3u}=0.6$, and $\Delta L_1∕\Delta L_2-1={10}^{-4}$. Here, the phases associated with the beam splitters have been chosen to give ${\delta }_{1,2}=-\pi$ (consistent with a symmetric scattering matrix). Red (blue) curve is relative to a small (large) voltage, while the black curve is the completely incoherent case (i.e., $D_{1,2}=0$).