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Microwave Optomechanics with a Carbon Nanotube Quantum Dot

Stefan Blien

Published Jan 1, 2021• 0 citations
Publisher

Abstract

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.

DOI
10.5283/epub.44437

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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.
Due to their small mass and large mechanical stiffness, free-standing carbon nanotubes turn out to be superb high-frequency mechanical resonators that could find applications in mass and force sensing. With resonance frequencies up to the gigahertz regime, one can envision cooling the mechanical motion of such nanotubes to its quantum mechanical ground state at cryogenic temperatures. This opens the possibility to generate highly nonclassical states of the mechanical motion, similar to those created several years ago with electromagnetic radiation in superconducting microwave resonators. Such states are interesting from a fundamental physics point of view, but potentially also for quantum information and sensing applications. While classical activation of a harmonic oscillator will always produce ``quasiclassical'' coherent states, a necessary ingredient for the production of nonclassical states such as Fock states is a nonlinear element, e.g., superconducting qubits in the case of microwaves. This work predicts that for mechanical oscillations, the spin-orbit coupling of the mechanical motion to a single localized electron spin can do the trick by acting as a nonlinear element for phonons.
The quantum behaviour of mechanical resonators is a new and emerging field driven by recent experiments reaching the quantum ground state. The high frequency, small mass, and large quality-factor of carbon nanotube resonators make them attractive for quantum nanomechanical applications. A common element in experiments achieving the resonator ground state is a second quantum system, such as coherent photons or a superconducting device, coupled to the resonators motion. For nanotubes, however, this is a challenge due to their small size. Here, we couple a carbon nanoelectromechanical (NEMS) device to a superconducting circuit. Suspended carbon nanotubes act as both superconducting junctions and moving elements in a Superconducting Quantum Interference Device (SQUID). We observe a strong modulation of the flux through the SQUID from displacements of the nanotube. Incorporating this SQUID into superconducting resonators and qubits should enable the detection and manipulation of nanotube mechanical quantum states at the single-phonon level.
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.
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.
This thesis investigates experimentally the coupling mechanism of the charge and spin degrees of freedom in double quantum dots to high finesse superconducting microwave cavities. We use carbon nanotubes as a coherent conductor to host our quantum dots.We conceived an experimental setup and developed new fabrication methods in order to achieve control over these devices. With these methods, we scrutinize the resonant coupling of the dot's charge electronic transitions to a microwave cavity. We drive the system out of equilibrium to characterise its dynamics and extract its relevant intrinsic parameters. We examine a possible coupling of single photons to a single electron spin, using non-collinear exchange fields induced from ferromagnetic interfaces as a key ingredient to engineer this coupling. The preliminary results in this circuit architecture are promising for future spin-based QED experiments with single spins.