Quantum coherence in solid-state systems has been demonstrated in superconducting circuits [1] and in semiconductor quantum dots [2]. This has paved the way to investigate solid-state systems for quantum information processing with the potential benefit of scalability compared to other systems based on atoms, ions and photons [3]. Coherent coupling of superconducting circuits to microwave photons, circuit quantum electrodynamics (QED) [4], has opened up new research directions [5] and enabled long distance coupling of qubits [6]. Here we demonstrate how the electromagnetic field of a superconducting microwave resonator can be coupled to a semiconductor double quantum dot. The charge stability diagram of the double dot, typically measured by direct current (DC) transport techniques [7], is investigated via dispersive frequency shifts of the coupled resonator. This hybrid all-solid-state approach offers the potential to coherently couple multiple quantum dot and superconducting qubits together on one chip, and offers a method for high resolution spectroscopy of semiconductor quantum structures.Semiconductor quantum dots are highly controllable solid-state quantum systems [8,9]. Charge measurements in the radio frequency (RF) regime have been demonstrated [10][11][12][13] and recently a lumped element RF resonator was used to measure the quantum capacitance of a double dot [14]. A number of schemes have been proposed for the scaling of quantum dot based quantum information processing [15][16][17][18]. In this work we implement a form of circuit QED [4], coupling charge states of a double dot to the field of an on-chip microwave transmission line resonator [15].The sample investigated is shown in Fig. 1a-c along with an electrical circuit schematic (Fig. 1d). The microwave resonator (see Fig. 1a) is realized using a 200 nm thick Aluminum coplanar waveguide on GaAs and is capacitively coupled to an input and output line to probe its transmission spectrum. The double quantum dot (see Fig. 1c), is fabricated at the position of an anti-node of the standing wave field distribution of the resonator. The left and right dots (LD, RD) are arranged in series with respect to the source and drain (S, D) and are realized on an Al x Ga 1−x As heterostructure with the twodimensional electron gas (2DEG) at a depth of about 35 nm below the surface.To enable a strong coupling between the two systems, an additional gate (RG) (Fig. 1c) was implemented, which extends from the resonator to the right quantum dot. This gives a selective capacitive coupling of the resonator to the right quantum dot, confirmed by DC biasing the resonator via an on-chip inductor (Fig. 1a, inset). This results in a strong dipole coupling of the resonator to two charge states in which an electron is on either the left or right quantum dot. In order to accommodate the gate (RG), a design is realized in which the dots are placed at the mesa edge (beyond which the 2DEG is etched away), which is used as part of the confining potential. To complete the formation of ...

We investigate the addition spectrum of a graphene quantum dot in the vicinity of the electronhole crossover as a function of perpendicular magnetic field. Coulomb blockade resonances of the 50 nm wide dot are visible at all gate voltages across the transport gap ranging from hole to electron transport. The magnetic field dependence of more than 50 states displays the unique complex evolution of the diamagnetic spectrum of a graphene dot from the low-field regime to the Landau regime with the n = 0 Landau level situated in the center of the transport gap marking the electron-hole crossover. The average peak spacing in the energy region around the crossover decreases with increasing magnetic field. In the vicinity of the charge neutrality point we observe a well resolved and rich excited state spectrum.PACS numbers: 72.80.Rj, 73.21.La, 75.70.Ak It is an important goal in quantum dot physics to understand the quantum mechanical energy spectra and the corresponding orbital and spin states of these manmade artificial atoms. This knowledge is necessary for designing and operating quantum dots in regimes relevant for particular applications, for example, for the implementation of qubits. It has been shown in various material systems [1,2,3,4] that usually the measured spectra can only be easily understood, and related to theoretical models, in the few-electron (or hole) limit. In recent research on quantum dots made from graphene [5,6,7,8,9], ground and excited states [9] have been observed in the Coulomb blockade regime, but attempts to relate the observations to theoretical spectra remain dissatisfactory so far, mainly because the number and character (electron or hole) of charge carriers in the dots are unknown and fingerprints of the graphenespecific two-dimensional linear dispersion have not been found.Here we characterize the electron-hole crossover in high-quality graphene quantum dots (QD). We present experimental and theoretical results for the evolution of a large number of resonances in a graphene quantum dot near the charge neutrality point in a magnetic field from the low-field regime to the regime of Landau level formation. The addition spectrum displays several intricate features specific to graphene, among them formation of the lowest (n = 0) Landau level at high B-fields. In the following we exploit the magnetic field dependence of the manifold of low energy states to approximately pin down the electron-hole crossover point.The ≈ 50 nm wide and ≈ 80 nm long quantum dot [scanning force microscope (SFM) image, Fig. 1(a)] is connected to source (S) and drain (D) via two 25 nm wide and 10 nm long constrictions, acting as tunneling barriers [ Fig. 1(b)]. The dot and the leads can be tuned by an inplane graphene plunger gate (PG) and the highly doped silicon substrate is used as a back gate (BG). The sample

We investigate ground and excited state transport through small (d≈70  nm) graphene quantum dots. The successive spin filling of orbital states is detected by measuring the difference between ground-state energies as a function of a magnetic field. For a magnetic field in-plane of the quantum dot the Zeeman splitting of spin states is measured. The results are compatible with a g factor of 2, and we detect a spin-filling sequence for a series of states which is reasonable given the strength of exchange interaction effects expected by comparing Coulomb interaction energy and kinetic energy of charge carriers in graphene.

We have realized a hybrid solid-state quantum device in which a single-electron semiconductor double quantum dot is dipole coupled to a superconducting microwave frequency transmission line resonator. The dipolar interaction between the two entities manifests itself via dispersive and dissipative effects observed as frequency shifts and linewidth broadenings of the photonic mode respectively. A Jaynes-Cummings Hamiltonian master equation calculation is used to model the combined system response and allows for determining both the coherence properties of the double quantum dot and its interdot tunnel coupling with high accuracy. The value and uncertainty of the tunnel coupling extracted from the microwave read-out technique are compared to a standard quantum point contact charge detection analysis. The two techniques are found to be consistent with a superior precision for the microwave experiment when tunneling rates approach the resonator eigenfrequency. Decoherence properties of the double dot are further investigated as a function of the number of electrons inside the dots. They are found to be similar in the single-electron and many-electron regimes suggesting that the density of the confinement energy spectrum plays a minor role in the decoherence rate of the system under investigation.

We present microwave frequency measurements of the dynamic admittance of a quantum dot tunnel coupled to a two-dimensional electron gas. The measurements are made via a high-quality 6.75 GHz on-chip resonator capacitively coupled to the dot. The resonator frequency is found to shift both down and up close to conductance resonance of the dot corresponding to a change of sign of the reactance of the system from capacitive to inductive. The observations are consistent with a scattering matrix model. The sign of the reactance depends on the detuning of the dot from conductance resonance and on the magnitude of the tunnel rate to the lead with respect to the resonator frequency. Inductive response is observed on a conductance resonance, when tunnel coupling and temperature are sufficiently small compared to the resonator frequency.

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We present measurements of a hybrid system consisting of a microwave transmission-line resonator and a lateral quantum dot defined on a GaAs heterostructure. The two subsystems are separately characterized and their interaction is studied by monitoring the electrical conductance through the quantum dot. The presence of a strong microwave field in the resonator is found to reduce the resonant conductance through the quantum dot, and is attributed to electron heating and modulation of the dot potential. We use this interaction to demonstrate a measurement of the resonator transmission spectrum using the quantum dot.The interaction of light and matter is one of the most fundamental processes in physics. One way to explore this area is to use artificial atoms such as quantum dots which offer e.g. the possibility to tune the energy spacing of the individual electronic states. Using this possibility the resonant absorption of photons by electrons in a quantum dot has been investigated in transport measurements of photon assisted tunneling 1,2 . Cavity quantum electrodynamics (QED), the study of the coupling of matter to light confined in a cavity 3 , is traditionally studied with atoms but also with solid state systems such as self-assembled quantum dots 4,5 . Furthermore the realization of circuit QED 6 , in which a single microwave photon is trapped in an on-chip cavity and coherently coupled to a quantum two-level system, has led to significant progress in control and coupling of microwave photons and superconducting qubits. The study of the interaction between the electromagnetic field of such a resonator and a semiconductor quantum dot marks an important step toward realizing a hybrid quantum information processor 7 , in which the advantages of different systems, such as a long relaxation time of the individual qubit 8 and interaction between distant qubits 9 , could be exploited in one device.The sample, shown in Fig. 1 (a), consists of a laterally defined quantum dot positioned at an antinode of the electric field of a microwave transmission-line resonator. The dot is realized on an Al x Ga 1−x As heterostructure with a two-dimensional electron gas (2DEG) residing at the heterointerface about 35 nm below the surface. The device is fabricated by three stages of optical lithography followed by local anodic oxidation (LAO) 10 with an atomic force microscope (AFM) to define the quantum dot. In the first of the three lithography steps the mesa for the quantum dot (dark gray parts, labeled M in Fig. 1 (a)) is wet etched. Ohmic contacts (labeled C in Fig. 1 (a)) are then used to contact the 2DEG. Finally, the microwave resonator and its ground plane (labeled R and GND in Fig. 1 (a)) are defined in a lift off process by a) Electronic mail: freytob@phys.ethz.ch FIG. 1. (Color online): (a) Optical micrograph of a microwave resonator (R) with an integrated quantum dot, (GND): ground plane of the resonator, (C): ohmic contact, (M): 2DEG mesa. (b) Magnified view of a coupling capacitor, location on the chip marked with rec...

We report transport experiments on graphene quantum dots. We focus on excited state spectra in the near vicinity of the charge neutrality point and signatures of the electron-hole crossover as a function of a perpendicular magnetic field. Coulomb blockade resonances of a 50 nm wide and 80 nm long dot are visible at all gate voltages across the transport gap ranging from hole to electron transport. The magnetic field dependence of more than 40 states as a function of the back gate voltage can be interpreted in terms of the unique evolution of the diamagnetic spectrum of a graphene dot including the formation of the E = 0 Landau level, situated in the center of the transport gap, and marking the electron-hole crossover.