An electronic quantum eraser

Abstract

2 IntroductionComplementarity, the incomplete nature of a quantum measurement -a core concept in quantum mechanics -stems from the choice of the measurement apparatus 1 . The notion of complementarity is closely related to Heisenberg's uncertainty principle, but the exact relation between the two remains a source of debate [2][3][4][5][6][7][8] . For example, knowledge of a particle's position in a double slit interference experiment will quench its wave-like nature and, vice versa, observing the wave property via interference implies lack of knowledge of the particle's path. A canonical system for exploring complementarity is the quantum eraser (QE), predominantly studied thus far in photonic systems [9][10][11][12][13][14] . A QE is an interference experiment consisting of two stages. First, one of the interfering paths is coupled to a 'which path' (WP) detectordemonstrating loss of interference due to acquisition of WP information. Second, the WP information is being 'erased' by projecting the detector's wavefunction on a particular basis; this renders the WP information inaccessible, thus allowing reconstruction of the interference pattern.In this work, we present a first implementation of a QE in an electronic system. Our system consists of two identical electronic Mach-Zehnder interferometers (MZIs) 15 entangled via Coulomb interactions. Such novel setup has already attracted a considerable theoretical attention [16][17][18] . With one MZI serving as a path detector and the other as the system interferometer, the visibility of the Aharonov-Bohm oscillation in the System can be controlled by the Detector. We demonstrate how a continuous change of the measurement basis, followed by post selection (via cross correlation of current fluctuations), allows a smooth transition between keeping and erasing the WP information. Theory Mach-Zehnder interferometerAn electronic MZI is formed by manipulating quasi one dimensional, chiral edge channels, which are formed in the integer quantum Hall effect regime 15 . Such a realization allows directing the path of electrons at will -leading to high visibility interference pattern. Potential barriers, formed by quantum point contacts (QPCs), take the role of optical beam splitters, transmitting and reflecting impinging electrons with amplitudes i t and i r , respectively, with 1 2 2Two such coupled MZIs are shown in Fig. 1, where the coupling is mediated by the lower path of the System and the upper path of the Detector, referred to as interacting paths (shaded area in Fig. 1a). Starting with the System, an electron injected from Source S1 arrives at SQPC1 and is put into a superposition of being reflected into the interacting path and transmitted into the noninteracting path, namely: Here, e h = Φ 0 is the magnetic flux quantum, A the area enclosed by the two paths, and B the magnetic field. The visibility of the interfering pattern at D2 is defined asThroughout our experiments, all the QPCs were tuned to have equal transmission and reflection amplitudes, Entangling tw...

Robust electron pairing in the integer quantum hall effect regime

“…4d). Note that very large Fano factors, defined here as e F ¼ e à =e, were found when the visibility was very high, which is attributed to phase noise due to charge fluctuations 26,27 , as, when visibility is high, a small variation in the phase might lead to large variation of the transmission.…”

Dephasing by a Zero-Temperature Detector and the Friedel Sum Rule

“…Our main findings are the following. (i) Thermal fluctuations of the occupancy of the localized state lead to dephasing through statistical averaging over shifted interference patterns [22]. (ii) In the limit of zero temperature, the passage of an electron through the upper arm of the MZI modifies the many-body state of the detector.…”

Crossover between strong and weak measurement in interacting many-body systems

“…A many-body theory of variable strength quantum measurement is called for. In many cases, the interaction strength can be controlled experimentally [10,32].…”