CORDIS - EU research results

Nanotube Mechanical Resonator, Spin, and Superfluidity

Periodic Reporting for period 4 - NaTuRe (Nanotube Mechanical Resonator, Spin, and Superfluidity)

Reporting period: 2021-07-01 to 2022-09-30

Mechanical resonators based on carbon nanotubes are truly exceptional sensors of mass and force. Our work focuses on nuclear magnetic resonance (NMR) and electron spin resonance (ESR) measurements on atoms and molecules using nanotube resonators. Our aim is to perform magnetic-resonance force microscopy in order to image individual nuclear spins. Achieving this objective will be an unprecedented success in magnetic resonance imaging (MRI). Another aim is to measure molecular electron spins in a regime where the magnetic noise of the environment is reduced to an unprecedented level in order to see whether nature can provide molecular electronic spins endowed with long dephasing time, a subject of great interest in quantum technology. Another direction of research is to use nanotube resonators as a completely new experimental approach to investigate helium superfluidity. We probe helium superfluidity adsorbed onto the suspended nanotube. NaTuRe is a highly-interdisciplinary project with possible implications in quantum science, opto-mechanics, nano-science, structural biology, and low-temperature physics.
We developed new methods for the detection of mechanical vibrations down to helium temperature. We report on an ultrasensitive scheme based on a RLC resonator and a low-temperature amplifier to detect nanotube vibrations. This enables us to measure nanotube mechanical resonators with an unpreceded level. We demonstrate 4.3zN/sqrt(Hz) force sensitivity, which is the best force sensitivity achieved thus far with a mechanical resonator. This a major advance towards the detection of individual nuclear spins.

We are developing a new process in order to fabricate a nanotube mechanical resonator bridging a superconducting radio-frequency coplanar wave-guide. This process consists in transferring a nanotube on top of a chip containing the wave-guide. This fabrication process is primordial for the detection of the electron spins of molecules adsorbed on the nanotube.

The vibrations are detected capacitively with a gate electrode. The vibrations modulate the current through the nanotube at a frequency of about 1 MHz by down-mixing. The current is detected with a RLC resonator with a resonance at 1 MHz and a HEMT amplifier installed at the 3.5 K stage of the cryostat. The spectrum is extremely clean. The current sensitivity of about 10fA/sqrt(Hz). This detection scheme is now implemented in all our cryostats.

We use a new fabrication process to grow ultraclean carbon nanotube resonators suspended over shallow trenches. We fabricate 1-2 um long nanotubes contacted electrically to two electrodes and separated from the local gate electrode by about 150 nm. Nanotubes are grown by the `fast heating' chemical vapour deposition method in the last fabrication step. This method consists in rapidly sliding the quartz tube through the oven under a flow of methane. This growth process has two assets compared to the usual growth of nanotube resonators. It allows us to suspend nanotubes over wide trenches. In addition, the electrodes are less prone to melt and change shape.

These advances in detection and fabrication are an important step towards imaging individual nuclear spins. The new fabrication process of nanotube is useful for increasing the gradient of the magnetic field, since it reduces the separation between the current-carrying electrode and the nanotube down to 150 nm. The device layout will also allow us to carry out magnetic resonance force microscopy (MRFM) measurements to image the location of individual nuclear spins adsorbed along the nanotube. We realize the long-standing goal of using electrons to cool a resonator near the quantum regime. We achieve a population number of 4.6 quanta. The resonator is about 20% of the time in the quantum ground state. The cooling method is simple yet powerful. It consists in applying a DC current of electrons through a suspended carbon nanotube.

Carbon Nanotube resonators have shown to be excellent sensing devices for the study of new physical phenomena at the nanoscale (e.g. spin physics, quantum electron transport, surface science, and light-matter interaction). Superfluid helium is known as a great system for the study of phase transitions, in particular for understanding transitions in two and three dimensions. By combining these two systems, it is possible to study various phenomena at the nanoscale, such as adsorption, supersolidity and superfluidity. We were able to build helium superfluid films with a number of atomic layers in a perfectly controlled manner. These helium multilayers adsorbed on a nanotube are of unprecedented quality compared to previous works. Such findings could open a new pathway into the field of topological phase transitions, aiming to carry out novel research of quantum fluids and solids in reduced geometry.

We encountered two major roadblocks in the course of our work on the detection of nuclear spins and electron spins. There is a “heating” roadblock that comes from a large current pulses in a milliKelvin temperature experiment. There is also an “electrostatic” roadblock that is a consequence of the electrostatic force created by the current pulses. For this reason, we decide to focus our last efforts on the study of nanotube electromechanical resonators where the mechanical vibrations are coupled to a double-quantum dot formed along the nanotube. The idea is to replace nuclear spins and electrons spins, as proposed initially in Nature, by the two-level systems formed in double-quantum dots. The coupling is much easier to achieve. We made important progress in the device fabrication, and we carried out the first measurements of such devices showing signatures of double-quantum dots of high quality.

We discovered a mechanism to create strong nonlinearities for vibrations approaching the quantum regime. We achieve this by coupling a mechanical resonator to a two-level system and by operating the system in the ultrastrong coupling regime. Our work will have an important impact on future developments in the field of mechanical systems. It opens a whole new realm of possibilities in quantum science and technology, including the development of mechanical qubits, mechanical ‘Schrödinger cat’ states, and quantum simulators emulating the electron-phonon coupling.

Our work has been published in a large number of papers in high-impact journals and was presented in a large number of scientific conferences.
Progress beyond the state of the art includes (i) the discovery on a mechanism to create strong nonlinearities for vibrations approaching the quantum regime and (ii) the demonstration of cooling mechanical vibrations using electrons close to the quantum ground state.