According to Bohr's complementarity principle 1 , a particle possesses wave-like properties only when the different paths the particle may take are indistinguishable. In a canonical example of a two-path interferometer with a which-path detector, observation of interference and obtaining which-path information are mutually exclusive 2,3 . Such duality has been demonstrated in optics with a pair of correlated photons 4 and in solid-state devices with phasecoherent electrons 5 . In the latter case, which-path information was provided by a charge detector embedded near one path of a two-path electron interferometer 5 .Note that suppression of interference can always be understood either as obtaining path information or as unavoidable back action by the detector 3 . The present study reports on dephasing of an Aharonov-Bohm (AB) ring interferometer 6 via a coupled charge detector adjacent to the ring. In contrast to the two-path interferometer, charge detection in the ring does not always provide path information. Indeed, we found that the interference was suppressed only when path information could be acquired, even if only in principle. This demonstrates that dephasing does not always take place by coupling the 'environment' to the interfering particle: path information of the particle must be available too. Moreover, this is valid regardlessof the strength of environment-interferometer coupling, which refutes the general notion of the effect of strong interaction with the environment 7 . In other words, it verifies that an acquisition of which-path information is more fundamental than the back-action in understanding quantum mechanical complementarity. Recently, a series of electronic 'which-path' experiments have been performed in mesoscopic solid-state devices. 5 The devices, fabricated in the plane of a highmobility two-dimensional electron gas (2DEG), were based on a double-path interferometer, consisting of an open Aharonov-Bohm (AB) ring, with a source and a drain of electrons weakly coupled to the open ring 5 . In one path of the interferometer a coherent quantum dot (QD) was embedded 5-6,8 , being electrostatically coupled to a quantum-point-contact (QPC) charge detector (in the immediate proximity to the QD).An electron trapped in the QD modified the conductance of the nearby QPC and thus allowed charge detection by the QPC 5,[9][10][11] . Being an open geometry, with multiple grounded drains (bases) along the paths of the electron, assured that only two paths interfered while the backscattered electrons were drained out by the grounded bases.Thus, the detection of a charge inside the QD (by the QPC) provided path information,

We have studied the Fano effect in a few-electron quantum dot side-coupled to a quantum wire. The conductance of the wire, which shows an ordinal staircase-like quantization without the dot, is modified through the interference (the Fano effect) and the charging effects.These effects are utilized to verify the exhaustion of electrons in the dot. The "addition energy spectrum" of the dot shows a shell structure, indicating that the electron confinement potential is fairly circular. A rapid sign inversion of the Fano parameter on the first conductance plateau with the change of the wire gate voltage has been observed, and explained by introducing a finite width of dot-wire coupling.

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We investigate various aspects of the Kondo singlet in a quantum dot (QD) electrostatically coupled to a mesoscopic detector. The two subsystems are represented by an entangled state between the Kondo singlet and the charge-dependent detector state. We show that the phase-coherence of the Kondo singlet is destroyed in a way that is sensitive to the charge-state information restored both in the magnitude and in the phase of the scattering coefficients of the detector. We also introduce the notion of the 'conditional evolution' of the Kondo singlet under projective measurement on the detector. Our study reveals that the state of the composite system is disentangled upon this measurement. The Kondo singlet evolves into a particular state with a fixed number of electrons in the quantum dot. Its relaxation time is shown to be sensitive only to the QD-charge dependence of the transmission probability in the detector, which implies that the phase information is erased in this conditional evolution process. We discuss implications of our observations in view of the possible experimental realization.