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arXiv:0806.2511

How does "Which Way" Detector affect Fano Effect in Mesoscopic Transport --"Phonon-Fano" Or Not

Hai‐Zhou Lu, Zuo-Zi Chen, Rong Lv, Bang‐Fen Zhu

Published Jun 16, 2008• 0 citations

Abstract

We investigate the Fano interference in the presence of a "which way" detector, i.e., a local electron-phonon coupler, in the context of mesoscopic transport. Special attention is paid to study whether the phonon sidebands in the differential conductance spectra exhibit the typical lineshape of the Fano interference. When using a double-dot model we obtain two seemly contradictory results by slightly different approaches: The Markovian approach leads to {\it absolutely no} Fano interference at the phonon sidebands, while the Non-Markovian approach results in {\it finite} Fano interference at the phonon sidebands. On the other hand, by using the usual Aharonov-Bohm (AB)-ring model, i.e., only one dot is embedded into one arm of an AB-ring, only the Non-Markovian results are recovered. We explain these contradictory results and make a comparison between the double-dot model and the usual AB-ring model at length. Moreover, we also point out the essential difference between the manifestation of the "which way" effect in mesoscopic double-slit experiments and its optical counterpart.

DOI: 10.48550/arxiv.0806.2511

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We investigate the Fano interference in the presence of a "which way" detector, i.e., a local electron-phonon coupler, in the context of mesoscopic transport. Special attention is paid to study whether the phonon sidebands in the differential conductance spectra exhibit the typical lineshape of the Fano interference. When using a double-dot model we obtain two seemly contradictory results by slightly different approaches: The Markovian approach leads to {\it absolutely no} Fano interference at the phonon sidebands, while the Non-Markovian approach results in {\it finite} Fano interference at the phonon sidebands. On the other hand, by using the usual Aharonov-Bohm (AB)-ring model, i.e., only one dot is embedded into one arm of an AB-ring, only the Non-Markovian results are recovered. We explain these contradictory results and make a comparison between the double-dot model and the usual AB-ring model at length. Moreover, we also point out the essential difference between the manifestation of the "which way" effect in mesoscopic double-slit experiments and its optical counterpart.

We investigate a non-Hermitian Aharonov-Bohm (AB) ring system with a quantum dot (QD) embedded in each of its two arms. The energy levels of the QDs are complex in order to take into account the physical gain or loss of the ring system during its interacting processes with the environment. When there is magnetic flux threading through the ring, by allocating the flux phase factor into the tunneling amplitudes between the QDs and the leads in different ways, the Hamiltonian of the system can be written into different formalisms. We calculate the transmission through the ring by using these different non-Hermitian Hamiltonians and prove that it is not dependent on the way we treat the phase factor, as in the Hermitian case. In addition, with appropriate parameters, the asymmetric Fano profile will show up in the conductance spectrum just by tuning the physical gain and loss of the system. The Fano effect originates from the interferences of electrons traversing different channels which are broadened or narrowed down due to the interaction between the QDs and the environment. The proof we provide and the transport properties revealed in this paper demonstrate the influences of the environment on an otherwise isolated system and pave the way for the further studies on non-Hermitian AB ring systems.

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.

We have measured transport through mesoscopic Aharonov-Bohm (AB) rings with two different four-terminal configurations. While the amplitude and the phase of the AB oscillations are well explained within the framework of the Landaur-Büttiker formalism, it is found that the probe configuration strongly affects the coherence time of the electrons, i.e., the decoherence is much reduced in the configuration of so-called nonlocal resistance. This result should provide an important clue in clarifying the mechanism of quantum decoherence in solids.

A which–way device is one which is designed to detect which of 2 paths is taken by a quantum particle, whether Schrödinger's cat is dead or alive. One possible such device is represented by an Aharonov–Bohm ring with a quantum dot on one branch. A charged cantilever or spring is brought close to the dot as a detector of the presence of an electron. The conventional view of such a device is that any change in the state of the cantilever implies a change in the electron state which will in turn destroy the interference effects. In this paper we show that it is in fact possible to change the state of the oscillator while preserving the quantum interference phenomenon.

The Aharonov–Bohm (AB) interference oscillations manifested through transmission of an electron in a mesoscopic device with a double-ring in the presence of a magnetic impurity serving as the spin-flipper are studied. The spin-flipper is demonstrated to indeed cause the partial decoherence of the AB interference. Moreover, it is found that the spin-up/down transmission coefficients are asymmetric in the flux reversal while the reflection coefficients as well as that the total transmission coefficient are symmetric.

Coherence in electronic interferometers is typically believed to be restored fully in the limit of small voltages, frequencies and temperatures. However, it is crucial to check this essentially perturbative argument by nonperturbative methods. Here, we use the numerical renormalization group to study ac transport and decoherence in an experimentally realizable model interferometer, a parallel double quantum dot coupled to a phonon mode. The model allows to clearly distinguish renormalization effects from decoherence. We discuss finite frequency transport and confirm the restoration of coherence in the dc limit.