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arXiv:0909.2197 · Physical Review Letters

Coherent Detection of Electron Dephasing

Elia Strambini, Luca Chirolli, Vittorio Giovannetti, Fabio Taddei, Rosario Fazio, Vincenzo Piazza, Fabio Beltram

Published Apr 27, 2010• 11 citations
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Abstract

We show that an Aharonov-Bohm ring with asymmetric electron injection can act as a coherent detector of electron dephasing. The presence of a dephasing source in one of the two arms of a moderately-to-highly asymmetric ring changes the response of the system from total reflection to complete transmission while preserving the coherence of the electrons propagating from the ring, even for strong dephasing. We interpret this phenomenon as an implementation of an interaction-free measurement.

DOI
10.1103/physrevlett.104.170403

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Comment on "Coherent Detection of Electron Dephasing'' [arXiv:0909.2197]

А. В. Никулов

It is shown that the theoretical result according to which electrons can be reflected because of magnetic flux in the Aharonov-Bohm ring contradicts to the fundamental law of momentum conservation and can not conform with the Aharonov-Bohm effect. Therefore a publication of Phys. Rev. Lett. [arXiv:0909.2197] based on this result can not be correct.

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Physical Review B•Dec 1, 2011•4 citations
We show that an Aharonov-Bohm ring with asymmetric electron injection can act as a coherent detector of electron dephasing. The presence of a dephasing source in one of the two arms of a moderately-to-highly asymmetric ring changes the response of the system from total reflection to complete transmission while preserving the coherence of the electrons propagating from the ring, even for strong dephasing. We interpret this phenomenon as an implementation of an interaction-free measurement.
We study a simple model of dephasing of Aharonov-Bohm oscillations in the transmission of an electron across a mesoscopic ring. A magnetic impurity in one of the arms of the ring couples to the electron spin via an exchange interaction. This interaction leads to spin flip scattering and induces dephasing via entanglement. This is akin to the models evoked earlier to explain destruction of interference due to which-path information in double-slit experiments. Total transmission is found to be symmetric under flux reversal but not the spin polarization.
We consider the phase-coherent transport of electrons passing through an Aharonov–Bohm ring while interacting with a tunnel charge in a double quantum dot (representing a charge qubit) which couples symmetrically to both arms of the ring. For Aharonov–Bohm flux Φ AB = h /2 e we find that electrons can only be transmitted when they flip the charge qubit's pseudospin parity an odd number of times. The perfect correlations of the dynamics of the pseudospin and individual electronic transmission and reflection events can be used to entangle the charge qubit with an individual passing electron.
Three different implementations of interaction-free measurements (IFMs) in solid-state nanodevices are discussed. The first one is based on a series of concatenated Mach-Zehnder interferometers, in analogy to optical-IFM setups. The second one consists of a single interferometer and concatenation is achieved in the time domain making use of a quantized electron emitter. The third implementation consists of an asymmetric Aharonov-Bohm ring. For all three cases we show that the presence of a dephasing source acting on one arm of the interferometer can be detected without degrading the coherence of the measured current. Electronic implementations of IFMs in nanoelectronics may play a fundamental role as very accurate and noninvasive measuring schemes for quantum devices.
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 investigate the dephasing rates in quasiballistic Aharonov-Bohm (AB) rings with local- and nonlocal-probe configurations by tuning the transmission through one arm of the ring. The dephasing rates are independent of the probe configuration while the transmissions through the ring paths are equal. In contrast, as AB interferometers are tuned to be strongly asymmetric, the dephasing rate of the local configuration becomes larger than that of the nonlocal configuration. We find that our observations can be qualitatively explained by voltage fluctuations from the measurement circuit, as proposed by G. Seelig, S. Pilgram, A. N. Jordan, and M. B\"uttiker [Phys. Rev. B 68, 161310(R) (2003)].