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Journal of Physics Condensed Matter

Exchange statistics, charge detection and back-action dephasing by a mesoscopic beam collider

Youngnae Lee, Gyong Luck Khym, Kicheon Kang

Published Sep 1, 2008• 2 citations
Publisher

Abstract

We investigate properties of charge detection and detection-induced dephasing of a charge qubit interacting with an electron beam collider composed of a quantum point contact. We predict that the interference of the qubit is fully restored when the two inputs are identically biased so that all the electrons suffer two-electron collision, unlike the case without collision. This phenomenon is related to Fermi statistics and illustrates the peculiar nonlocality of dephasing. We also describe the detection properties of entangled electron pairs. For singlet pairs, the sensitivity of charge detection is enhanced which originates from the bunching behavior of electrons. This demonstrates that control of exchange statistics of particles can help sensitive charge detection.

DOI
10.1088/0953-8984/20/39/395212

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We investigate properties of charge detection and detection-induced dephasing of a charge qubit interacting with an electron beam collider composed of a quantum point contact. We predict that the interference of the qubit is fully restored when the two inputs are identically biased so that all the electrons suffer two-electron collision, unlike the case without collision. This phenomenon is related to Fermi statistics and illustrates the peculiar nonlocality of dephasing. We also describe the detection properties of entangled electron pairs. For singlet pairs, the sensitivity of charge detection is enhanced which originates from the bunching behavior of electrons. This demonstrates that control of exchange statistics of particles can help sensitive charge detection.
We investigate the charge-detection-induced dephasing of a charge qubit interacting with an electronic beam collider composed of a quantum point contact. We report that, while the qubit is dephased by the partitioned beam of uncorrelated electrons, the interference of the qubit is fully restored when the two inputs are identically biased so that all the electrons suffer two-electron collision. This phenomenon is related to Fermi statistics and illustrates the peculiar nonlocality of dephasing. We also describe detection properties for the injection of entangled electron pairs.
Mesoscopic colliders provide an effective platform for probing the mutual statistics of quantum particles. Recent experiments have successfully extracted the mutual statistics of fermions, and more exotic anyons using quantum point contacts (QPCs). Coupling a point-like collider, such as a quantum point contact, to a two-level impurity or qubit can induce statistical transmutation of fermions, causing them to display boson-like bunching tendencies. Here, we extend the analysis to an extended collider. We investigate the scattering of two incoming fermionic and bosonic wave packets in the presence of post-selection on the impurity state, and systematically analyze the possible benchmarks used to characterize bunching and infer the underlying mutual statistics. We show that only a specific benchmark faithfully captures the mutual statistics of the colliding particles, while alternative choices can produce spurious statistical signatures. Hence, the correct benchmark for probing the quantum statistics depends on the intricate details of the mesoscopic collider.
Collision of quantum particles remains an effective way of probing their mutual statistics. Colliders based on quantum point contacts in quantum Hall edge states have been successfully used to probe the statistics of the underlying quantum particles. Notwithstanding the extensive theoretical work focusing on pointlike colliders, when it comes to experiment, the colliders are rarely pointlike objects and can support a resonant level or multiple tunneling points. We present a study of a paradigmatic extended (non-point-like) fermionic collider (and an extension to bosonic colliders). As with particle interferometers, in an extended collider there is an infinite number of trajectories for any single- or multiparticle event. Self-interference of the former can lead to an apparent bunching of fermions when we compare the cross-current correlator with a classical benchmark representing two colliding beams. In view of this apparent bunching behavior of fermions, we identify an experimentally accessible current correlator, which reveals the true mutual statistics of fermions.
We consider the counting statistics of electron transport through a double quantum dot with special emphasis on the dephasing induced by a nearby charge detector. The double dot is embedded in a dissipative enviroment, and the presence of electrons on the double dot is detected with a nearby quantum point contact. Charge transport through the double dot is governed by a non-Markovian generalized master equation. We describe how the cumulants of the current can be obtained for such problems, and investigate the difference between the dephasing mechanisms induced by the quantum point contact and the coupling to the external heat bath. Finally, we consider various open questions of relevance to future research.
We derive an analytical expression for the backaction dephasing rate, which characterizes the disturbance induced by coupling with an environment containing a quantum dot detector (QDD). In this paper, we show in an explicit form that the charge noise induces backaction dephasing. In equilibrium, this backaction dephasing induced by the charge noise can be explained as a relaxation by an inelastic electron-electron scattering in Fermi-liquid theory. Unlike the quantum point contact, the backaction dephasing rate increases or decreases with the bias at low bias and finite-temperature condition. This behavior depends on the QDD energy level with respect to the Fermi energy and the asymmetry of the QDD coupling to the reservoirs. In the high bias voltage regime, the dephasing rate becomes insensitive to the bias because of the saturation of the charge noise.
Quantum point contact (QPC), one of the typical mesoscopic transport devices, has been suggested to be an efficient detector for quantum measurement. In the context of two-state charge qubit, our previous studies showed that the QPC's measurement back-action cannot be described by the conventional Lindblad quantum master equation. In this work, we study the measurement problem of a multistate system, say, an electron in disordered potential, subject to the quantum measurement of the mesoscopic detector QPC. The effect of measurement back-action and the detector's readout current are analyzed, where particular attention is focused on some new features and the underlying physics associated with the measurement-induced delocalization versus the measurement voltages.