Engineering strong anharmonicity in nanotube mechanical resonators

Quantum information processing (QIP) has the potential to revolutionize technology with its unparalleled computational capabilities, enhanced security, and superior detection sensitivities. The quest to find the best types of qubits, the fundamental units of quantum information, is still ongoing, and various platforms are being explored in research and development.

Among the multitude of possibilities, such as superconducting Josephson junctions, trapped ions, topological qubits, ultra-cold neutral atoms, and diamond vacancies, nano-mechanical resonators have emerged as a promising candidate. These resonators, akin to springs or guitar strings, exhibit harmonic or anharmonic vibrations depending on the driving force. However, what happens when a nano resonator is cooled to absolute zero temperature?

At absolute zero, the energy levels of the oscillator become quantized, and the resonator vibrates with its characteristic zero-point motion. This motion arises due to the Heisenberg uncertainty principle, which implies that even in the ground state, a resonator retains a certain level of motion. To realize a mechanical qubit, it is necessary for the quantized energy levels of the resonator to be unevenly spaced.

The key challenge lies in maintaining sufficiently large nonlinear effects in the quantum regime, where the zero-point displacement of the oscillator is minuscule. If this can be achieved, the system can be manipulated between the two lowest quantum levels without exciting higher energy states, thus functioning as a qubit.

For many years, researchers have been interested in realizing a mechanical qubit using nano resonators. In 2021, a solid theoretical concept for a mechanical qubit was established by Fabio Pistolesi, Andrew N. Cleland, and Prof. Adrian Bachtold, laying the foundation for the use of nanomechanical resonators as ideal qubit candidates. These resonators have demonstrated long coherence times, a crucial requirement for quantum computing.

With a theoretical framework in place, the next challenge was to experimentally create a qubit from a mechanical resonator and determine the appropriate conditions and parameters for controlling the system’s nonlinearities.

After years of dedicated work, the initial steps towards realizing a mechanical qubit have recently been achieved. In a study published in Nature Physics, researchers from ICFO, led by Prof. Adrian Bachtold, in collaboration with scientists from other institutions, demonstrated a novel mechanism to enhance the anharmonicity of a mechanical oscillator in its quantum regime. This significant breakthrough paves the way for the future realization of a mechanical qubit.

In conclusion, the field of quantum information processing is rapidly advancing, and the search for optimal qubit platforms continues. Nano-mechanical resonators have shown great promise as qubit candidates due to their long coherence times. Recent experimental progress brings us closer to harnessing the full potential of mechanical qubits, laying the groundwork for future advancements in quantum computing and information processing.

A platform for an array of 36 mechanical resonator devices. Credit: ICFO

The experiment: Engineering anharmonicity close to the ground state

The team of researchers successfully created a suspended nanotube device, measuring approximately 1.4 micrometers in length, with its ends attached to two electrodes. By manipulating the voltage on the gate electrode, they controlled the flow of individual electrons onto the nanotube, creating a quantum dot—a two-level electronic system—on the vibrating nanotube. This allowed for the coupling of mechanical motion and the single electron in what is known as the single electron tunneling regime. The electromechanical coupling induced anharmonicity in the mechanical system.

To investigate the system further, the researchers cooled it to millikelvin temperatures, approaching absolute zero. In this ultra-strong coupling regime, each additional electron on the nanotube caused a shift in the nanotube’s equilibrium position away from its zero-point amplitude. Remarkably, the researchers observed nonlinear vibrations at an amplitude only 13 times greater than the zero-point motion. This is a significant achievement compared to other resonators, which typically require amplitudes approximately 106 times larger than the zero-point motion to exhibit nonlinearity when cooled to the quantum ground state.

The findings are particularly intriguing because, contrary to expectations, the anharmonicity increased as the vibrations approached the ground state. This contrasts with observations in other mechanical resonators to date. Chandan Samanta, the first author of the study, emphasized the significance of this work, noting that achieving nonlinear vibrations in the quantum ground state was once considered challenging due to technological limitations. This study represents a substantial conceptual advancement, proving that nonlinear vibrations in the quantum regime are indeed achievable.

While the team believes that the nonlinear effects could have been further enhanced by reaching closer to the quantum ground state, their progress was limited by the temperature constraints of their current cryostat. Nonetheless, their work provides valuable insights for achieving nonlinear vibrations in the quantum regime, laying the foundation for the development of mechanical qubits and quantum simulators.

Adrian Bachtold, one of the researchers involved in the study, highlighted the remarkable nature of the findings. Although entering the ultra-strong coupling regime and observing significant anharmonicity in the resonator were noteworthy accomplishments, he acknowledged that the damping rate increased at low temperatures due to the coupling of the resonator to a single quantum dot.

For future experiments aiming to explore cat states and mechanical qubits, Bachtold suggested coupling nanotube vibrations to a double-quantum dot. This configuration offers strong nonlinearities and the potential for long-lived mechanical states. Furthermore, the damping caused by the electron in the double-quantum dot is exponentially suppressed at low temperatures, which should enable achieving a damping rate as low as 10 Hz, similar to measurements in nanotubes at low temperature.

Source: ICFO

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