The nonlinear response of a quantum dot in a time-dependent field

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Abstract
We calculate the rectification coefficient and the second-harmonic generation coefficient for a quantum dot biased with an ac field. The coefficients are calculated as functions of the gate voltage (i.e. the positions of the resonant levels) and the frequency of the applied field. The rectification coefficient has a peaked dependence on the gate voltage with one central (negative) and two side (positive) peaks around the voltage at which the corresponding energy level for interacting electrons is equal to the collector electrode chemical potential. The peak heights are related to the average number of electrons in the dot - a feature which is a direct consequence of the electron interactions. The second-harmonic generation coefficient has similar behaviour for low frequencies ( at zero frequency). The frequency dependence of the rectification coefficient has features resulting from the photon-assisted tunnelling through the dot. The resonant-like enhancement of the rectification coefficient cannot be attributed to the photon-assisted transitions between different resonant levels in the dot.