Microwave spectroscopy of a carbon nanotube charge qubit

Carbon nanotube quantum dots allow accurate control of electron charge, spin and valley degrees of freedom in a material which is atomically perfect and can be grown isotopically pure. These properties underlie the unique potential of carbon nanotubes for quantum information processing, but developing nanotube charge, spin, or spin-valley qubits requires efficient readout techniques as well as understanding and extending quantum coherence in these devices. Here, we report on microwave spectroscopy of a carbon nanotube charge qubit in which quantum information is encoded in the spatial position of an electron. We combine radio-frequency reflectometry measurements of the quantum capacitance of the device with microwave manipulation to drive transitions between the qubit states. This approach simplifies charge-state readout and allows us to operate the device at an optimal point where the qubit is first-order insensitive to charge noise. From these measurements, we are able to quantify the degree of charge noise experienced by the qubit and obtain an inhomogeneous charge coherence of 5 ns. We use a chopped microwave signal whose duty-cycle period is varied to measure the decay of the qubit states, yielding a charge relaxation time of 48 ns

Charge Pumping in Carbon Nanotubes

We demonstrate charge pumping in semiconducting carbon nanotubes by a traveling potential wave. From the observation of pumping in the nanotube insulating state we deduce that transport occurs by packets of charge being carried along by the wave. By tuning the potential of a side gate, transport of either electron or hole packets can be realized. Prospects for the realization of nanotube based single-electron pumps are discussed

A Quantum Dot in the Kondo Regime Coupled to Superconductors

The Kondo effect and superconductivity are both prime examples of many-body phenomena. Here we report transport measurements on a carbon nanotube quantum dot coupled to superconducting leads that show a delicate interplay between both effects. We demonstrate that the superconductivity of the leads does not destroy the Kondo correlations on the quantum dot when the Kondo temperature, which varies for different single-electron states, exceeds the superconducting gap energy

Atomic force microscope nanolithography of graphene: cuts, pseudo-cuts and tip current measurements

We investigate atomic force microscope nanolithography of single and bilayer graphene. In situ tip current measurements show that cutting of graphene is not current driven. Using a combination of transport measurements and scanning electron microscopy we show that, while indentations accompanied by tip current appear in the graphene lattice for a range of tip voltages, real cuts are characterized by a strong reduction of the tip current above a threshold voltage. The reliability and flexibility of the technique is demonstrated by the fabrication, measurement, modification and re-measurement of graphene nanodevices with resolution down to 15 nm

Multi-wall carbon nanotubes as quantum dots

We have measured the differential conductance dI/dV of individual multi-wall carbon nanotubes (MWNT) of different lengths. A cross-over from wire-like (long tubes) to dot-like (short tubes) behavior is observed. dI/dV is dominated by random conductance fluctuations (UCF) in long MWNT devices (L=2...7 $\mu m$), while Coulomb blockade and energy level quantization are observed in short ones (L=300 nm). The electron levels of short MWNT dots are nearly four-fold degenerate (including spin) and their evolution in magnetic field (Zeeman splitting) agrees with a g-factor of 2. In zero magnetic field the sequential filling of states evolves with spin S according to S=0 -> 1/2 -> 0... In addition, a Kondo enhancement of the conductance is observed when the number of electrons on the tube is odd.Comment: 10 pages, 4 figure

Kondo Effect of Quantum Dots in the Quantum Hall Regime

Quantum dots in the quantum Hall regime can have pairs of single Slater determinant states that are degenerate in energy. We argue that these pairs of many body states may give rise to a Kondo effect which can be mapped into an ordinary Kondo effect in a fictitious magnetic field. We report on several properties of this Kondo effect using scaling and numerical renormalization group analysis. We suggest an experiment to investigate this Kondo effect.Comment: To appear in Phys. Rev. B (5 pages, 4 figures); references added; several changes in tex