Phase behavior of coherent tunneling through a quantum dot: A consideration of the off-diagonal elastic coupling

The electron transmission amplitude through a quantum dot is studied by considering all elastic coupling elements, not only the diagonal elements Γjj, but also the off-diagonal elements Γij. The Breit-Winger formula is extended to multiple states under the above consideration. The phase of the transmission amplitude exhibits a gradual increase by π along a resonance peak and an abrupt phase drop by π near the center between two consecutive resonance peaks which call be explained completely in a single-electron picture. When the temperature T = 0 the phase drop is absolutely abrupt; when T≠0 the phase drop is on a energy scale much smaller than both Γjj and kBT. In addition, at the phase-drop-point, some interesting manifestations are predicted.