Kondo Effect and Phase Measurement in Double Quantum Dot in Parallel

We propose a double quantum dot (DQD) in parallel as a tractable model for a mesoscopic ring with an embedded quantum dot (QD), which functions as a QD interferometer. One of the DQDs (QD 1) represents the embedded QD with energy level ϵ1 and Coulomb interaction U, whereas the other (QD 2) acts as a reference arm with an enlarged linewidth due to the tunnel coupling to external leads. The conductance at temperature T = 0 is formulated simply in terms of the retarded and advanced Green's functions of the DQD, which are exactly evaluated using the Bethe ansatz solution for the Kondo effect. Using this model, we address two controversial issues concerning the QD interferometer. The first issue concerns the shape of the conductance peak as a function of ϵ1. We show a crossover from an asymmetric Fano resonance (Fano-Kondo effect) to a symmetric Breit-Wigner resonance (Kondo plateau) in the absence (presence) of U, by decreasing the connection between the QDs through the leads. The second is on the measurement of the transmission phase shift through QD 1 by a "double-slit experiment", which is impossible in the two-terminal geometry because of the Onsager's reciprocity theorem. In a three-terminal geometry, we discuss a possible observation of phase locking at π=2 in the Kondo regime.