Detection of Quantum Interference without an Interference Pattern

Quantum interference is typically detected through the dependence of the interference signal on certain parameters (path length, Aharonov-Bohm flux, etc.), which can be varied in a controlled manner. The destruction of interference by a which-path measurement is a paradigmatic manifestation of quantum effects. Here we report on a novel measurement protocol that realizes two objectives: (i) certifying that a measured signal is the result of interference avoiding the need to vary parameters of the underlying interferometer, and (ii) certifying that the interference signal at hand is of quantum nature. In particular, it yields a null outcome in the case of classical interference. Our protocol comprises measurements of cross-correlations between the readings of which-path weakly coupled detectors positioned at the respective interferometer’s arms and the current in one of the interferometer’s drains. We discuss its implementation with an experimentally available platform: an electronic Mach-Zehnder interferometer (MZI) coupled electrostatically to “detectors” (quantum point contacts).

Figure 1

A detection setup. An MZI electrostatically coupled to two QPCs $C$ and $D$ serving as which-path detectors. The transmission through QPC $C(D)$ is slightly modified (with a strength proportional to $\lambda$) upon the detection of a charge fluctuation in the respective MZI’s arm, within a segment $\ell$. The currents are measured in the drains $D1$, $D3$, and $D5$. Sector II of the MZI is threaded with a magnetic flux $\mathrm{\Phi }$.

Figure 2

The WWS value, $⟨{\mathcal{I}}_{D1}{⟩}_{\mathrm{WWS}}^{\mathrm{MB}}$ as function of the phase difference between the two arms, $\chi$, with transmission amplitudes $t_A=\sqrt{0.55}$ and $t_B=\sqrt{0.5}$, for several values of $eV/k_{B}T$. The WWS value oscillates around zero when varying $\chi$. In the two limiting cases, $eV/k_{B}T\gg 1$ and $eV/k_{B}T\ll 1$, the WWS value is proportional to $⟨{\mathcal{I}}_{D1}{⟩}_{\mathrm{WWS}}^{\mathrm{SP}}$ [Eq. (7)], albeit with different proportionality coefficients. The latter reflect the temperature dependence of the two- and three-point correlation functions [see Eq. (S20) in the Supplemental Material [36] ].