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We study single-electron tunneling in a two-junction device in the presence of microwave radiation. We introduce a model for numerical simulations that extends the Tien-Gordon theory for photon-assisted tunneling to encompass correlated single-electron tunneling. We predict sharp current jumps which reflect the discrete photon energy h f, and a zero-bias current whose sign changes when an electron is added to the central island of the device. Measurements on split-gate quantum dots show microwave-induced features that are in good agreement with the model. An oscillating potential with frequency f changes the energy F. of an electron state into a set of energies E+nhf with n=0,~1,~2, . . . . These so-called sideband energies can lead to electron tunneling that involves the emission (n&0) and absorption (n)0) of photons. The formation of sidebands has been important for many time-dependent transport studies addressing issues such as photon-assisted tunneling of quasiparticles in superconducting junctions, the tunneling time, and time-dependent resonant tunneling. Recent theoretical work has begun to focus on the effects of an oscillating potential on transport through small capacitance devices where the charging energy regulates the tunnel processes. For instance, Bruder and Schoeller have calculated the photoresponse of a two-level system. However, little theoretical work exists on realistic systems, e.g. , quantum dots with many quantum levels, and no experiments have been reported except at very low frequencies. "In this paper, we present numerical simulations and experiments on photon-assisted tunneling through a quantum dot. We assume a continuous single-particle density of states, i.e. , a metallic system with an equivalent single electron circuit shown in the inset of Fig. 1 . Our model extends theTien-Gordon theory' to include the correlated tunneling of single electrons through a two-junction device. This model predicts discrete photon features, and is in agreement with measurements on split-gate quantum dot devices irradiated by 19-GHz microwaves.We model the microwaves as an oscillating potential V cos(2mft) of the central island relative to the source and drain leads. To allow for an asymmetry in the ac coupling, we model the microwave amplitude by two parameters a; =eV;/h f, i =s,d where V, and Vd are the ac voltage drops across the source and drain junctions. Analogous to the Tien-Gordon description, we write the tunnel rate I; in the presence of microwaves in terms of the rate 1; without microwaves as

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We have measured photon-assisted tunneling through a quantum dot with zero dimensional (0D) states. For photon energies smaller than the separation between 0D states we observe photon sideband resonances of the ground state. When the photon energy exceeds the separation between 0D states we observe photon-induced excited state resonances. We identify the different resonances by studying their dependence on photon frequency and magnetic field. [S0031-9007(97)02424-1] PACS numbers: 73.20. Dx, 73.40.Gk, 73.50.Mx, 73.50.Pz In analogy to spectroscopy on atoms it is interesting to study the interaction between light and electrons confined in quantum dots. However, since it is difficult to realize identical quantum dots the response of an ensemble of quantum dots to light excitation is strongly averaged over sample differences. Despite this averaging, excitation studies on quantum dot arrays by far-infrared light have shown the spectrum of collective modes [1], and inelastic light scattering experiments have probed single particle excitations [2]. The latter technique has also probed excitons in a single quantum dot [3]. We have used microwaves with relatively low frequency to study the discrete electron excitation spectrum in the conduction band of a single quantum dot. In contrast to the light transmission or luminescence measurements of the above spectroscopy techniques, we measure the photoresponse in the dc current.Current can flow through a quantum dot when a discrete energy state is aligned to the Fermi energies of the leads. This current is carried by resonant elastic tunneling of electrons between the leads and the dot. An additional time-varying potential e V cos͑2pft͒ can induce inelastic tunnel events when electrons exchange photons of energy hf with the oscillating field. This inelastic tunneling with discrete energy exchange is known as photonassisted tunneling (PAT). PAT has been studied before in superconductor-insulator-superconductor tunnel junctions [4], in superlattices [5], and in quantum dots [6,7]. The quantum dots in Ref. [6] were rather large and effectively had a continuous density of states. So far, PAT through small quantum dots with discrete states has only been studied theoretically [8,9]. In this paper we show for the first time different types of PAT processes through a quantum dot with well resolved discrete 0D states. We first show that an elastic resonant tunneling peak in the current develops photon sideband resonances when we apply microwaves. We then use PAT as a spectroscopic tool to measure the energy evolution of the first excited state as a function of magnetic field [10].Transport through a quantum dot is dominated by Coulomb blockade effects [11]. The energy to add an extra electron to a quantum dot constitutes the charging energy E c for a single electron, and a finite energy difference D´arising from the confinement. A dot is said to have 0D states if D´is larger than the thermal energy k B T [11]. Assuming sequential tunneling of single electrons, the current can be cal...