Quantum information processing (QI) has the potential to revolutionize technology, offering unmatched computing power, security and detection sensitivity.

Qubits, the fundamental units of quantum information hardware, serve as the cornerstone for quantum computers and quantum information processing. However, there remains substantial discussion about which types of qubits are actually best.

Research and development in this field is growing at an astonishing rate to see which system or platform outperforms the other. Platforms as diverse as superconducting Josephson junctions, trapped ions, topological qubits, ultracold neutral atoms, or even vacancies in diamonds, to name a few, form a zoo of possibilities for creating qubits.

So far, only a handful of qubit platforms have been shown to have the potential for quantum computingticking the checklist of gates controlled with high fidelity, easy qubit-qubit coupling, and good isolation from the environment, meaning sufficiently long-lived consistency.

Nanomechanical resonators can be part of the handful of platforms. They are oscillators, like springs and strings (e.g. guitars) that when pushed create harmonic or anharmonic sounds depending on the strength of the drive. But what happens when we cool a nano resonator to a… absolute zero temperature?

The energy levels of the oscillator are quantized and the resonator vibrates with its characteristic zero point movement. The zero-point motion comes from Heisenberg’s uncertainty principle. In other words, a resonator maintains motion even when in its ground state. The realization of a mechanical qubit is possible if the quantized energy levels of a resonator are not equally spaced.

The challenge is to keep the nonlinear effects large enough in the quantum regime, where the zero-point shift of the oscillators is tiny. If this is achieved, the system can be used as a qubit by manipulating it between the two lowest quantum levels without driving it into higher energy states.

For many years there has been much interest in building a qubit system with a mechanical nano resonator. In 2021, Fabio Pistolesi (Univ. Bordeaux-CNRS), Andrew N. Cleland (Univ. Chicago) and Prof. Adrian Bachtold of ICFO established a robust theoretical concept of a mechanical qubit, based on a nanotube resonator coupled to a double quantum dot under an ultrastrong coupling regime.

These theoretical results demonstrated that these nanomechanical resonators could indeed become ideal candidates for qubits. Why? Because they have been shown to have long coherence times, a must for quantum computing.

Taking into account that there was a theoretical framework to work with, the challenge now was to actually create a qubit from a mechanical resonator and find the appropriate conditions and parameters to control the non-linearities in the system.

After several years of endless work on these systems, the challenges of making it experimentally gave it its first very welcome green light. In a recent study published in *Physics of nature*, ICFO researchers Chandan Samanta, Sergio Lucio de Bonis, Christoffer Moller, Roger Tormo-Queralt, W. Yang, Carles Urgell, led by prof. Bordeaux-CNRS achieved the first pre-experimental steps for the future realization of a mechanical qubit by demonstrating a new mechanism for enhancing the anharmonicity of a mechanical oscillator in its quantum regime.

#### The experiment: engineering anharmonicity close to the ground state

The team of researchers fabricated a suspended nanotube device about 1.4 micrometres long, with its ends hooked to the edges of two electrodes. They defined a quantum dot which is a two-level electronic system on the vibrating nanotube by electrostatically creating tunnel junctions at both ends of the suspended nanotube.

Then, by regulating the voltage across the gate electrode, they allowed only one electron to flow through the nanotube at a time. The mechanical motion of the nanotube was then coupled to the single electron in the single electron tunneling regime. This electromechanical coupling created a harmony with the mechanical system.

Next, they reduced the temperature down to mK (milikelvin, near absolute zero) and entered an ultrastrong coupling regime where each additional electron on the nanotube shifted the nanotube’s equilibrium position away from its zero-point amplitude.

With an amplitude of only a factor of 13 of the zero point movement, they were able to notice these non-linear vibrations. The results are surprising because the vibrations present in other resonators, cooled to the quantum ground state, have been shown to be nonlinear only at amplitudes about 106 times greater than its zero-point motion.

This new mechanism exhibits remarkable physics because, contrary to what was expected, anharmonicity increases as the vibrations cool closer to the ground state. This is exactly the opposite of what has been observed in all other mechanical resonators so far.

As first author Chandan Samanta points out, when researchers first started studying nanomechanical resonators, a recurring question was whether it was possible to achieve nonlinearities in the vibrations found in the quantum ground state. Some prominent researchers in the field have argued that this would be a challenging undertaking due to technological limitations, and this view has remained the accepted paradigm until now. In this context, our work represents a significant conceptual advance because we demonstrate that nonlinear vibrations in the quantum regime are indeed achievable. We are confident that the nonlinear effects could have been further enhanced by approaching the quantum ground state, but we were limited by the temperature of our current cryostat. Our work provides a roadmap for achieving nonlinear vibrations in the quantum regime.

Contrary to what has been observed in other mechanical resonators so far, the research team has found a method to increase the anharmonicity of a mechanical oscillator close to its quantum regime. The results of this study set the first milestones for the future development of mechanical qubits or even quantum simulators.

As Adrian Bachtold notes, it is remarkable that we entered an ultra-strong coupling regime and observed strong anharmonicity in the resonator. But the damping rate increases at low temperatures due to the coupling of the resonator to a quantum dot. In future experiments targeting cat states and mechanical qubits, it will be advantageous to couple nanotube vibrations to a double quantum dot, as it allows for strong nonlinearities along with long-lived mechanical states. The damping arising from the electron in the double quantum dot is suppressed exponentially at low temperatures so that it should be possible to achieve a damping rate of 10 Hz measured in nanotubes at low temperatures.

Reference: Nonlinear Nanomechanical Resonators Approaching the Quantum Ground State by C. Samanta, SL De Bonis, CB Mller, R. Tormo-Queralt, W. Yang, C. Urgell, B. Stamenic, B. Thibeault, Y. Jin, DA Czaplewski, F. Pistolesi, and A. Bachtold, June 8, 2023, *Physics of nature*.

DOI: 10.1038/s41567-023-02065-9`

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