Phase measurements in quantum dots

Recent measurements of the phase of the transmission amplitude through a quantum dot (QD) revealed interesting and unexpected physics. In particular, the phase evolution across a sequence of Coulomb Blockade (CB) peaks is demonstrated to have a peculiar structure, characterized by an increase of pi across each peak, followed by an abrupt phase lapse of pi in each CB valley. A simple theory accounting for the origin of such phase lapses as well as for their small scale is discussed, though a satisfactory explanation of the presence of a phase lapse in each CB valley is still lacking. As the temperature of the system is reduced, the Kondo effect develops in CB valleys with non-zero QD spin (Kondo valleys). The measured phase evolution in this regime is characterized by a plateau at pi in the valley, and a total increment of the phase close to 2pi across the CB peak-Kondo valley-CB peak structure. This result contrast quantitatively with the theoretical prediction for the phase evolution based on the Anderson model, i.e. a plateau at pi/2 in the Kondo valley and a total increment of pi.