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Physical Review Letters

Controlled Dephasing of Electronsviaa Phase Sensitive Detector

David Sprinzak, Eyal Buks, Moty Heiblum, Hadas Shtrikman

Published Jun 19, 2000• 106 citations
Publisher

Abstract

We demonstrate a controlled dephasing experiment via exploiting a unique entangled interferometer-detector system, realized in an electronic mesoscopic structure. We study the dephasing process both from the which path information available in the detector and, alternatively, from the direct effect of the detector on the interferometer. Detection is possible only due to an induced phase change in the detector. Even though this phase change cannot actually be measured, strong dephasing of the interferometer took place. The intricate role of detector's noise and coherency are investigated.

DOI
10.1103/physrevlett.84.5820

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•Jan 1, 1997•6 citations
We demonstrate a controlled dephasing experiment via exploiting a unique entangled interferometer-detector system, realized in an electronic mesoscopic structure. We study the dephasing process both from the which path information available in the detector and, alternatively, from the direct effect of the detector on the interferometer. Detection is possible only due to an induced phase change in the detector. Even though this phase change cannot actually be measured, strong dephasing of the interferometer took place. The intricate role of detector's noise and coherency are investigated.
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.
Controlled dephasing of electrons, via "which path" detection, involves, in general, coupling a coherent system to a current driven noise source. However, here we present a case in which a nearly isolated electron puddle within a quantum dot, at thermal equilibrium and in millikelvin range temperature, fully dephases the interference in a nearby electronic interferometer. Moreover, the complete dephasing is accompanied by an abrupt π phase slip, which is robust and nearly independent of system parameters. Attributing the robustness of the phenomenon to the Friedel sum rule--which relates a system's occupation to its scattering phases--proves the universality of this powerful rule. The experiment allows us to peek into a nearly isolated quantum dot, which cannot be accessed via conductance measurements.
In controlled dephasing a controlled environment causes dephasing of transport through a mesoscopic system. As a result of their interaction the states of the two subsystems are entangled. In this paper we discuss how their entanglement influences dephasing using as an example the ``which path detector,'' where the dephasing of transport through a quantum dot (QD) due to the interaction with a quantum point contact (QPC) is detected by means of an Aharonov-Bohm (AB) interferometer. In particular, we calculate the suppression $\ensuremath{\nu}$ of AB oscillations as a function of the bias eV\mathrm{eV}eV applied to the QPC and the coupling $\ensuremath{\Gamma}$ of the QD to the leads. At low temperatures the entanglement produces a smooth crossover from $\ensuremath{\nu}\ensuremath{\propto}(eV/\ensuremath{\Gamma}{)}^{2},$ when $\mathrm{eV}\ensuremath{\ll}\ensuremath{\Gamma}$ to $\ensuremath{\nu}\ensuremath{\propto}eV/\ensuremath{\Gamma},$ for $\mathrm{eV}\ensuremath{\gg}\ensuremath{\Gamma}.$
Determination of the path taken by a quantum particle leads to a suppression of interference and to a classical behavior. We employ here a quantum "which path" detector to perform accurate path determination in a two-path Mach-Zehnder electron interferometer, leading to full suppression of the interference. Following the dephasing process we recover the interference by measuring the cross correlation between the interferometer and detector currents. Under our measurement conditions every interfering electron is dephased by approximately a single electron in the detector-leading to mutual entanglement of approximately single pairs of electrons.
We study charge detection and controlled dephasing of a mesoscopic system via a quantum dot detector (QDD), where the mesoscopic system and the QDD are capacitively coupled. The QDD is considered to have coherent resonant tunnelling via a single level. It is found that the dephasing rate is proportional to the square of the conductance of the QDD for the Breit-Wigner model, showing that the dephasing is completely different from the shot noise of the detector. The measurement rate, on the other hand, shows a dip near the resonance. Our findings are peculiar especially for a symmetric detector in the following aspect: The dephasing rate is maximum at resonance of the QDD where the detector conductance is insensitive to the charge state of the mesoscopic system. As a result, the efficiency of the detector shows a dip and vanishes at resonance, in contrast to the single-channel symmetric non-resonant detector that has always a maximum efficiency. We find that this difference originates from a very general property of the scattering matrix: The abrupt phase change exists in the scattering amplitudes in the presence of the symmetry, which is insensitive to the detector current but {\em stores} the information of the quantum state of the mesoscopic system.
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