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arXiv:quant-ph/0606117 · Physical Review B

Charge detection in a closed-loop Aharonov-Bohm interferometer

Gyong Luck Khym, Kicheon Kang

Published Oct 20, 2006• 17 citations
arXivHTMLPDF

Abstract

We report on a study of complementarity in a two-terminal closed-loop Aharonov-Bohm interferometer. In this interferometer, the simple picture of two-path interference cannot be applied. We introduce a nearby quantum point contact to detect the electron in a quantum dot inserted in the interferometer. We found that charge detection reduces but does not completely suppress the interference even in the limit of perfect detection. We attribute this phenomenon to the unique nature of the closed-loop interferometer. That is, the closed-loop interferometer cannot be simply regarded as a two-path interferometer because of multiple reflections of electrons. As a result, there exist indistinguishable paths of the electron in the interferometer and the interference survives even in the limit of perfect charge detection. This implies that charge detection is not equivalent to path detection in a closed-loop interferometer. We also discuss the phase rigidity of the transmission probability for a two-terminal conductor in the presence of a detector.

DOI
10.1103/physrevb.74.153309

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We report on a study of complementarity in a two-terminal closed-loop Aharonov-Bohm interferometer. In this interferometer, the simple picture of two-path interference cannot be applied. We introduce a nearby quantum point contact to detect the electron in a quantum dot inserted in the interferometer. We found that charge detection reduces but does not completely suppress the interference even in the limit of perfect detection. We attribute this phenomenon to the unique nature of the closed-loop interferometer. That is, the closed-loop interferometer cannot be simply regarded as a two-path interferometer because of multiple reflections of electrons. As a result, there exist indistinguishable paths of the electron in the interferometer and the interference survives even in the limit of perfect charge detection. This implies that charge detection is not equivalent to path detection in a closed-loop interferometer. We also discuss the phase rigidity of the transmission probability for a two-terminal conductor in the presence of a detector.
We study complementarity in a two-terminal closed-loop Aharonov-Bohm interferometer with a quantum dot embedded in an arm of the ring and a nearby charge detector capacitively coupled to the quantum dot. We show that perfect charge detection does riot give full information of the electronic path, so it does not completely suppress the interference. We propose that this property can be verified even in the limit of weak charge detection by investigating the dephasing of the first and the second harmonics of the Aharonov-Bohm oscillation. The first harmonic of the AB oscillation is reduced monotonically as a function of the charge detection strength. In contrast, the second harmonic interference remains unaffected due to the fact that charge detection is not able to detect the electronic path responsible for the second harmonic. Our theory confirms that the particle-like behavior of an electron emerges from the path information itself rather than from the disturbance.
We study dephasing of electrons induced by a which path detector and thus verify Bohr’s complementarity principle for fermions. We utilize a double path interferometer with two slits, with one slit being replaced by a coherent quantum dot (QD). A short one dimensional channel, in the form of a quantum point contact (QPC), in close proximity to the QD, serves as a which path detector. We find that by varying the properties of the QPC detector we affect the visibility of the interference, inducing thus dephasing. We develop a simple model to explain the dephasing due to the nearby detector and find good agreement with the experiment. Bohr’s complementarity principle excludes the possibility of observation of multiple paths interference simultaneously with which path (WP) determination [1]. Wave-like behavior, or interference, is possible only when the different possible paths a particle can take are indistinguishable, even
We demonstrate real-time detection of self-interfering electrons in a double quantum dot embedded in an Aharonov-Bohm interferometer, with visibility approaching unity. We use a quantum point contact as a charge detector to perform time-resolved measurements of single-electron tunneling. With increased bias voltage, the quantum point contact exerts a back-action on the interferometer leading to decoherence. We attribute this to emission of radiation from the quantum point contact, which drives noncoherent electronic transitions in the quantum dots.
Interference results when a quantum particle is free to choose among a few indistinguishable paths. A canonical example of Bohr's complementarity principle [1] is a two-path interferometer with an external detector coupled to one of the paths. Then, interference between the two paths vanishes (i.e. dephasing) if one is able to detect, even in principle, the path taken by the particle. This type of which path (WP) experiment was already executed with photons, cooled atoms, neutrons, solitons, and more recently with electrons in a mesoscopic system [2]. In the latter experiment path determination was provided by inducing a change in the current flowing through the detector. In the present experiment we perform a more intriguing WP determination: only a phase change is being induced in the detector while the current remains unaffected. We show that such detector-interferometer interaction can be understood both, from the WP information obtained by the detector, or alternatively by understanding the disturbance in the interferometer caused by the detector. Moreover, we address the subtle role of detector coherency and point out difficulties in the intuitive interpretation of the experiment.
Motivated by a recent experiment by Buks et al. ( Nature 391 (1998) 871) we consider electron transport through an Aharonov-Bohm interferometer with a quantum dot in one of its arms. The quantum dot is coupled to a quantum system with a finite number of states acting as a which-path detector. The Aharonov-Bohm interference is calculated using a two-particle scattering approach for the joint transitions in detector and quantum dot. Tracing over the detector yields dephasing and a reduction of the interference amplitude. We show that the interference can be restored by a suitable measurement on the detector and propose a mesoscopic quantum eraser based on this principle.
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).