2 6 A pr 1 99 9 Photon Assisted Tunneling in Quantum Dots

We review experiments on single electron transport through single quantum dots in the presence of a microwave signal. In the case of a small dot with well-resolved discrete energy states, the applied high-frequency signal allows for inelastic tunnel events that involve the exchange of photons with the microwave field. These photon assisted tunneling (PAT) processes give rise to sideband resonances in addition to the main resonance. Photon absorption can also lead to tunneling via excited states instead of tunneling via the ground state of the quantum dot. Transport properties of quantum dots at zero frequency have been extensively studied and by now many aspects are well understood [1]. In some studies finite, but still low frequency signals were applied to a gate electrode nearby the quantum dot. Capacitance spectroscopy on quantum dots has been performed at kHz frequencies [2]. At MHz frequencies, quantum dots can be operated as turnstiles or pumps [3]. These frequencies, f, are low in the sense that the photon energy, hf, is much smaller than the thermal energy, k B T, and thus the discrete photon character cannot be discerned. For sufficiently high frequencies, such that hf ≫ k B T , the interaction of the electromagnetic field with the electrons confined in a quantum dot would be analogous to light spectroscopy studies on atoms. However, different quantum dots are not microscopically equal. The response of an ensemble of quantum dots to light excitation is therefore strongly averaged. Despite this averaging , excitation studies on arrays of quantum dots by far-infrared light (i.e. the THz regime) have revealed the spectrum of collective modes [4], i.e. the sloshing modes of the whole electron puddle in the external potential. Excitations within the electron puddle are difficult to create since, according to the generalized Kohn theorem [4], the dipole field of far-infrared radiation does not couple to the relative coordinates of electrons confined in a parabolic quantum dot. This problem is circumvented by inelastic light scattering experiments which have been able to detect electronic excitations in arrays of quantum dots that can be related to a discrete single-particle spectrum [5]. Recently, this technique has also probed excitons in a single quantum dot [6]. In this review we discuss electron transport experiments