Electrostatics of quantum dots in high magnetic fields and single far-infrared photon detection

Electron transport through a single electron transistor (SET) is studied with and without illumination of far-infrared (FIR) radiation in high magnetic fields. The SET consists of a $\mathrm{GaAs}/{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum dot (QD). The transport characteristics obtained without the FIR illumination is well analyzed in terms of capacitance matrix by assuming that the QD in strong magnetic fields is split into isolated conductive regions. When a FIR photon is absorbed by a QD upon cyclotron resonance, an excited electron-hole pair induces a charge polarization within the QD, which switches on or off the SET conductance. The absorption of single-FIR photons is thus detected as individual conductance switches of the SET. Experimental results show that the lifetime of the excited state of a QD (with the internal polarization) is longer than the instrumental time constant, 1 ms, in a magnetic field range of $B=3.4\mathrm{}-4.2\mathrm{T},$ in which the lowest orbital Landau levels are completely occupied while the higher Landau level with a small number of electrons is slightly occupied. The wavelength of the FIR-photon detection, being determined by the magnetic field applied to the QD, ranges from 0.2 mm to 0.17 mm.