Behavior of Electronic Interferometers in the Nonlinear Regime

We investigate theoretically the behavior of the current oscillations in an electronic Mach-Zehnder interferometer (MZI) as a function of its source bias. Recently, the MZI visibility data showed an unexplained lobe pattern with a peculiar phase rigidity. Moreover, the effect did not depend on the MZI path length difference. We argue that these effects may be a new many-body manifestation of particle-wave duality in quantum mechanics. When biasing the interferometer sources so much that multiple electrons are on each arm at any instant in time, quantum shot noise (a particle phenomena) must affect the interference pattern of the electrons that create it. A solution to the interaction Hamiltonian presented here shows that the interference visibility has a lobe pattern with applied bias that has a period proportional to the average path length and independent of the path length difference, together with a phase rigidity.

Figure 1

Schematic of the MZI geometry, with generally asymmetric two paths.

Figure 2

The amplitude and phase shift of the interference oscillations in the chemical potential of the MZI drain, as a function of $⟨N⟩=\overline{L}\Delta \mu /h{v}_g$ in the noninteracting model [gray (red) curves] and in presence of the interaction [Eq. (13), black curves], for $⟨\Delta N⟩/⟨N⟩=\Delta L/\overline{L}=0.2$. The lines between the calculated points are a guide to the eye. Note that we plotted here the total current visibility, which is more suitable for analyzing the lobes then the differential visibility [9].

Figure 3

The pairs of the single-particle eigenvalues of the phase operators $w_1$ and $w_2$ of the two paths [dark gray (blue) and light gray (green) lines], as a function of $⟨N⟩$, for $⟨\Delta N⟩/⟨N⟩=0.2$. Black lines mark the zero visibility in Fig. 2. Note that at every such zero, there is a pair of eigenvalues whose sum is $\pi /2$.