Tuning of the Fano Effect through a Quantum Dot in an Aharonov-Bohm Interferometer

Abstract

The Fano effect, which arises from an interference between a localized state and the continuum, reveals a fundamental aspect of quantum mechanics. We have realized a tunable Fano system in a quantum dot (QD) in an Aharonov-Bohm interferometer, which is the first convincing demonstration of this effect in mesoscopic systems. With the aid of the continuum, the localized state inside the QD acquires itinerancy over the system even in the Coulomb blockade. Through tuning of the parameters, which is an advantage of the present system, unique properties of the Fano effect on the phase and coherence of electrons have been revealed. PACS numbers: 73.21.La, 73.23.Hk, 72.15.Qm When a discrete energy level is embedded in a continuum energy state and there is coupling between these two states, a resonant state arises around the discrete level. In 1961, Fano proposed [1] that in such a system a transition from an arbitrary initial state occurs through the two interfering configurations -one directly through the continuum and the other through the resonance level -and that this quantum mechanical interference yields a characteristic asymmetric line shape in the transition probability. This is the Fano effect, a ubiquitous phenomenon observed in a large variety of experiments including neutron scattering [2], atomic photoionization [3], Raman scattering [4], and optical absorption [5]. While a statistically averaged nature of the system containing contributions from numerous sites is observed in these experiments, the Fano effect is essentially a single-impurity problem describing how a localized state embedded in the continuum acquires itinerancy over the system [6]. Therefore, an experiment on a single site would reveal this fundamental process in a more transparent way. While the single-site Fano effect has been reported in the scanning tunneling spectroscopy study of an atom on the surface [7,8] or in transport through a quantum dot (QD) [9], there is little, if any, controllability in either case since the coupling between the discrete level and the continuum is naturally formed.In this Letter, we report the first tunable Fano experiment. We have clarified characteristic transport properties arising from this effect, such as the delocalization of the discrete level and the excitation spectra of the Fano system. External control of the relative phase between a localized state and the continuum indicates that the Fano parameter should be treated as a complex number.To realize a well-defined Fano system, we designed an Aharonov-Bohm (AB) ring with a QD embedded in one of its arms as seen in Fig. 1 (a), similar to those in previous studies [10,11,12,13]. The AB ring is essentially a double-slit interferometer of electrons. In contrast, the QD [14], a small electron droplet isolated from its leads by tunneling barriers, has discrete energy levels arising from the electron confinement and the charging energy that is much larger than the thermal energy k B T (k B is the Boltzmann constant, and T is the temperature). In the Co...

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