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Leggett-Garg test of a vibrating carbon nanotube

Periodic Reporting for period 1 - LeGaNa (Leggett-Garg test of a vibrating carbon nanotube)

Reporting period: 2016-03-01 to 2018-02-28

Despite the undeniable success of quantum mechanics, the boundary between quantum and classical mechanics remains unclear. This problem is encapsulated in one of the most famous thought experiments in science, the Schrödinger’s Cat scenario: since quantum superposition is necessary to describe the atomic scale, must it also apply to everyday objects? This is a question that has now moved beyond thought experiments. Theoretical work by Leggett and Garg provided a script for experiments to determine whether an object is at all times in one of its distinct states or whether quantum superposition prevails. This script has been used to demonstrate unambiguous superposition of microscopic objects whose quantum nature was already well-established, such as photons and electrons. Making use of a vibrating carbon nanotube with ~10^5 atoms, the question is: does superposition apply also to mesoscopic objects? Extending quantum control to increasingly macroscopic systems will not only help to answer crucial questions in the foundations of quantum theory, but will also enable quantum superposition and entanglement to be harnessed for new applications. The overall objective is to demonstrate quantum behaviour beyond the most microscopic system on a vibrating carbon nanotube.
The project aimed at coupling a quantum bit (qubit) encoded in a carbon nanotube to its mechanical motion to demonstrate quantum states of motion via Leggett-Garg inequalities. I have succeeded at demonstrating a qubit in a carbon nanotube and at studying its mechanical properties. After careful characterization of the qubit and the mechanics in carbon nanotubes, I concluded that a Leggett-Garg test was impeded by short qubit lifetimes. This conclusion has lead to work on: I) extending these lifetimes in carbon nanotubes by isotopic purification, II) an alternative type of qubit, a transmon qubit, which can also be coupled to the carbon nanotube motion, III) 3D microwave cavities that can couple to the motion of thin membranes. I have written one paper (Phys. Rev. Lett.) related to the carbon nanotube qubit properties, a second paper (published in Phys. Rev. Applied) describing the reflectometry techniques developed for sensitive qubit readout, a third paper (Phys. Rev. Lett. and selected Editor’s Suggestion) about nanotube mechanics and a further paper (submitted to Phys. Rev. X) about a protocol for quantum interference in a carbon nanotube resonator.
I pioneered carbon nanotube circuit optomechanics at low temperature, coupling a suspended nanotube to a radio-frequency circuit for sensitive motion detection. In this way, I explored a new regime of cavity optomechanics in which the frequency of the cavity and the mechanical resonator are degenerate. This work represents a significant contribution to readout of mechanical motion and has been highlighted by a top journal: Phys. Rev. Lett. Improvements on this work have allowed us to detect, via the radio-frequency cavity, the self-oscillations in the carbon nanotube due to electronic transport. This manuscript is on progress now. Further improvements will enable measurement of mechanical motion at the quantum limit near the phonon ground state.

As the fast-paced electronic miniaturization proceeds towards the nanoscale, quantum effects start to play a major role. Understanding how these effects arise and how to enhance or control them on demand, is crucial for existing electronic industries and for the development of innovative technologies, and thus of both scientific and economic value for Europe. The research that forms the core of this project tackles this challenge by exploring the boundary between the macro and the micro scales. In addition, quantum controlled mechanical states would allow quantum-enhanced sensors, as well as microwave-to-optical transducers for quantum information. As the project is highly interdisciplinary, it has encouraged new collaboration networks between outstanding institutions of different European countries. This possibility of building strong competitive European networks is crucial for developing quantum control in the emerging fields of nanotechnology and nanoelectronics, which appear as key pillars in the future world economy.
Resonant Optomechanics with a Vibrating Carbon Nanotube