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Carbon nanotubes In DC and microwave superconducting circuits

Ani Nersisyan

Published Jan 1, 2016• 0 citations
Publisher

Abstract

This thesis presents an effort towards integration of superconductor-contacted carbon nanotubes into microwave circuits, as a new tool for building quantum circuits. Carbon nanotubes show a wealth of quantum phenomena demonstrated in transport experiments by different groups in the last two decades. With the development of circuit QED, one can study these phenomena using on-chip microwave circuits. Moreover, in superconductor-contacted nanotubes, Andreev reflection of the particles at the interfaces leads to the formation of Andreev bound states. A pair of such states can potentially serve as a new type of a qubit. Here, fabrication and measurement techniques of superconductor contacted carbon nanotubes and superconductor/normal metal bilayer microwave circuits is developed, and their behaviour is studied. In superconductor-contacted nanotubes the full range of contact transparencies is investigated, showing different transport phenomena such as Coulomb blockade, Kondo effect and Fabry-Pérot interference. In addition, the interplay of these effects with multiple Andreev reflection phenomena and the superconducting proximityinduced non-dissipative current transport through the nanotube is studied. The proximity effect is studied using microwave resonators made of superconductor/ normal metal bilayers. Characteristic parameters of the bilayers, such as the critical temperature and the magnetic penetration depth are reliably extracted from the measurements. Finally, the two experiments are brought together in the first step towards using superconductor-contacted nanotubes in quantum microwave circuits. The successful realization of such circuit is achieved, where the Coulomb blockade in a nanotube quantum dot is probed with a microwave field.

DOI
10.5287/ora-ke1kox7x6

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This thesis presents an effort towards integration of superconductor-contacted carbon nanotubes into microwave circuits, as a new tool for building quantum circuits. Carbon nanotubes show a wealth of quantum phenomena demonstrated in transport experiments by different groups in the last two decades. With the development of circuit QED, one can study these phenomena using on-chip microwave circuits. Moreover, in superconductor-contacted nanotubes, Andreev reflection of the particles at the interfaces leads to the formation of Andreev bound states. A pair of such states can potentially serve as a new type of a qubit. Here, fabrication and measurement techniques of superconductor contacted carbon nanotubes and superconductor/normal metal bilayer microwave circuits is developed, and their behaviour is studied. In superconductor-contacted nanotubes the full range of contact transparencies is investigated, showing different transport phenomena such as Coulomb blockade, Kondo effect and Fabry-Pérot interference. In addition, the interplay of these effects with multiple Andreev reflection phenomena and the superconducting proximityinduced non-dissipative current transport through the nanotube is studied. The proximity effect is studied using microwave resonators made of superconductor/ normal metal bilayers. Characteristic parameters of the bilayers, such as the critical temperature and the magnetic penetration depth are reliably extracted from the measurements. Finally, the two experiments are brought together in the first step towards using superconductor-contacted nanotubes in quantum microwave circuits. The successful realization of such circuit is achieved, where the Coulomb blockade in a nanotube quantum dot is probed with a microwave field.
Circuit quantum electrodynamics has received an increasing amount of attention over the last decade in light of its potential use in quantum information processing. The underlying principle of this architecture is the coherent coupling between microwave photons stored in superconducting resonators and superconducting qubits made from non-linear, non-dissipative electrical circuits. This architecture can be extended to other solid-state systems with transition frequencies in the microwave regime, such as nuclear and electron spins or Andreev bound states. These hybrid devices would allow the coherent exchange of information between such systems and superconducting qubits mediated by a microwave resonator. This could lead to advances in quantum information processing and new insights in the physics governing these interacting systems. In this dissertation experimental work with different types of hybrid quantum circuits is presented. A first experiment investigates the coherent coupling of microwave photons with a spin ensemble in a correlated and uncorrelated state. The coupling strength and magnetic resonance is studied as a function of temperature and magnetic field direction. A pronounced temperature dependent anisotropy of the magnetic resonance is observed, which can be attributed to the onset of antiferromagnetic correlations in the spin ensemble when cooled below T=4 K. A simple one-dimensional model gives a good description of this anisotropy. A next experiment studies the transport characteristics of carbon nanotubes electrically accessed with normal and superconducting contacts. These devices were characterised using both DC and RF reflectometry techniques. The carbon nanotube devices with superconducting contacts exhibit transport characteristics of Josephson junctions with critical currents of up to Ic~18 nA, as well as multiple Andreev reflections. These semiconductor-superconductor hybrid Josephson junctions are then used to realise a carbon-nanotube-based superconducting qubit with voltage tunable transition frequency using a local electrostatic gate. Strong coupling (g~100 MHz) to a coplanar waveguide resonator is demonstrated via a resonator frequency shift dependent on applied gate voltage. Qubit parameters are extracted from spectroscopy and correspond well to the DC measurements of the carbon nanotube Josephson junctions. Qubit relaxation and coherence times in the range 10-100 ns are observed. The hybrid devices investigated in this work present potential building blocks for more extensive hybrid architectures for quantum information processing.
Hybrid circuit QED involves the study of coherent quantum physics in solid-state systems via their interactions with superconducting microwave circuits. Here we present a crucial step in the implementation of a hybrid superconducting qubit that employs a carbon nanotube as a Josephson junction. We realize the junction by contacting a carbon nanotube with a superconducting Pd/Al bilayer, and implement voltage tunability of the quantum circuit's frequency using a local electrostatic gate. We demonstrate a strong dispersive coupling to a coplanar waveguide resonator by investigating the gate-tunable resonator frequency. We extract qubit parameters from spectroscopy using dispersive readout and find qubit relaxation and coherence times in the range of 101010--200ns200\phantom{\rule{0.2em}{0ex}}\mathrm{ns}200ns.
Hybrid circuit quantum electrodynamics (QED) involves the study of coherent quantum physics in solid state systems via their interactions with superconducting microwave circuits.Here we present a crucial step in the implementation of a hybrid superconducting qubit that employs a carbon nanotube as a Josephson junction.We realise the junction by contacting a carbon nanotube with a superconducting Pd/Al bi-layer, and implement voltage tunability of the quantum circuit's frequency using a local electrostatic gate.We demonstrate a strong dispersive coupling to a coplanar waveguide resonator by investigating the gate-tunable resonator frequency.We extract qubit parameters from spectroscopy using dispersive readout and find qubit relaxation and coherence times in the range of 10 -200 ns.
This thesis deals with the implementation and demonstration of an optomechanical system that is composed of a superconducting microwave resonator and a suspended carbon nanotube (CNT). This is of particular interest, as CNTS - being macromolecules - have outstanding electronic and mechanical properties. Single electron effects combined with large mechanical resonance frequencies, quality factors, and zero-point motion amplitudes make possible promising applications in the field of quantum information processing or fundamental research, e.g. the synthesis of arbitrary quantum states. Besides the assembly of a high frequency measurement setup for cryogenic temperatures in the millikelvin range, introductory chapters discuss electronic and mechanical characteristics of carbon nanotubes. Here, two different fabrication techniques are described, the overgrowth and the fork transfer process. The physics of superconducting microwave resonators in coplanar waveguide geometry is introduced. Their high frequency behaviour at low temperatures is described by a transition from Mattis-Bardeen to two-level system theory. This serves as a means to investigate the high frequency material properties of a molybdenum/rhenium alloy, which is particularly suitable for the overgrowth process. Device design adjustments and considerations are described that were necessary for the integration of CNTs into hybrid geometries using the fork transfer process. Through this, the (previously demonstrated) electronic coupling of a carbon nanotube to a microwave resonator could be successfully experimentally demonstrated. There, the transmission of the resonator is sensitive to single electron tunneling processes in the CNT. The central point of this thesis is the introduction to the field of dispersive optomechanics. Here, the interaction of a vibrating carbon nanotube and a microwave field is investigated. A mechanism based on the quantum capacitance enhances this otherwise negligible coupling by orders of magnitude. Through an optomechanically induced transparency experiment, this coupling was experimentally quantified. A comparison to the beforehand deduced theory shows a very good agreement. In conclusion, subsequent prospective experiments towards optomechanical cooling and motion manipulation are explained and preliminary experimental data are discussed.
Coupling carbon nanotube devices to microwave circuits offers a significant increase in bandwidth (BW) and signal-to-noise ratio. These facilitate fast non-invasive readouts important for quantum information processing, shot noise and correlation measurements. However, creation of a device that unites a low-disorder nanotube with a low-loss microwave resonator has so far remained a challenge, due to fabrication incompatibility of one with the other. Employing a mechanical transfer method, we successfully couple a nanotube to a gigahertz superconducting matching circuit and thereby retain pristine transport characteristics such as the control over formation of, and coupling strengths between, the quantum dots. Resonance response to changes in conductance and susceptance further enables quantitative parameter extraction. The achieved near matching is a step forward promising high-BW noise correlation measurements on high impedance devices such as quantum dot circuits. Radio-frequency circuits offer fast low-noise detection of signals in carbon nanotubes, but incompatibilities in fabrication degrade the performance of the hybrid device. Here, the authors use a deterministic mechanical transfer to couple pristine nanotubes to a gigahertz superconducting matching circuit.
We present our recent experiments where we demonstrate a hybrid architecture consisting of a quantum dot circuit coupled to a single mode of the electromagnetic ¯eld. We use single wall carbon nanotube based circuits inserted in superconducting microwave cavities. By probing the nanotube dot using a dispersive readout in the Coulomb blockade and the Kondo regime, we determine an electron-photon coupling strength which should enable circuit QED experiments with more complex quantum dot circuits. We extend our architecture to two quantum dot circuits in a microwave cavity. These circuits are separated by 200 times their own size, but share the same anti-node of the cavity ¯eld. We demonstrate their interaction mediated by the cavity photons.