Electro-nanomechanical Quantum Simulator with Four Dots Exhibits Robust Bell Phase at Mesoscopic Scales

The quest to understand strongly correlated systems receives a boost from new research into nanoscale mechanical devices, as David Ullrich, Marta Cagetti, Stefan Forstner, and colleagues at ICFO and Universitat Autònoma de Barcelona demonstrate. They investigate carbon nanotubes engineered to host tiny, electronically defined dots, creating a system where electrons interact with mechanical vibrations, or phonons. This setup, featuring two parallel nanotubes, not only exhibits attraction between electrons mediated by these vibrations, but also supports a remarkably stable “Bell phase” extending across the entire system, even at relatively large scales. This achievement establishes the platform’s potential as a powerful simulator for exploring complex quantum phenomena and advancing our understanding of materials with strong electron interactions.

Suspended carbon nanotubes hosting electrostatically defined quantum dots provide an exceptional platform for exploring quantum mechanics and mechanical resonators, exhibiting strong and tunable electromechanical coupling and mechanical modes that can reach the quantum ground state. Researchers demonstrate the emergence of a Bell phase within this electro-nanomechanical quantum simulator, a phenomenon predicted for coupled quantum systems, and observe a violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality, confirming the presence of entanglement. This achievement represents a significant step towards developing quantum technologies based on electromechanical systems and provides new insights into the foundations of quantum mechanics.

Parallel Nanotube Quantum Dot Simulation Platform

Scientists engineered a quantum simulation platform using two parallel carbon nanotubes, each hosting four quantum dots, to investigate electron-phonon interactions and correlated electron behaviour. Recent advances in deterministic carbon nanotube stamping allowed precise placement of the nanotubes with spatial accuracy exceeding 100nm, crucial for establishing proximity between the parallel structures. The team fabricated these devices and employed gate-voltage control during fabrication and measurement to fine-tune the quantum dots’ properties. To model the complex interactions within the system, researchers applied the Lang-Firsov (LF) transformation, simplifying calculations while retaining key physical insights.

The team investigated the system’s behaviour in the zero-tunnelling regime, where electronic and phononic degrees of freedom are effectively decoupled. Analysis revealed a transition between a “Mott insulating state” and a “Paired state” as the coupling strength increased. When the inter-tube interaction was activated, direct diagonalisation revealed a new ground state configuration emerging, breaking symmetry within each tube and correlating the electronic states of the two nanotubes, representing a highly entangled electronic state. To address computational challenges, scientists employed the single-mode approximation, restricting the analysis to the lowest phonon mode, a technique validated in previous single-CNT studies, allowing for meaningful insights into the system’s behaviour and the emergence of correlated electron phenomena.

Carbon Nanotube Quantum Dot Simulation of Matter

This research focuses on building a quantum simulator using carbon nanotubes as the physical platform to mimic complex condensed matter physics, specifically exploring electron-phonon interactions and potentially realising exotic states like superconductivity. The researchers use carbon nanotubes configured as quantum dots, which act as the qubits of the simulator, and aim to achieve a strong coupling regime, where the electron-phonon interaction is dominant, essential for observing and controlling interesting quantum effects. They employ a combination of quantum mechanical calculations and classical simulations to model and optimise the system, with a long-term goal of engineering conditions within the nanotube simulator that could lead to the emergence of superconductivity, ultimately simulating the behaviour of complex materials and potentially leading to new discoveries in materials science. The researchers have successfully implemented a working platform for simulating quantum systems using carbon nanotubes and achieved a degree of control over the electron-phonon interactions within the nanotube quantum dots.

The system operates in a strong coupling regime, enabling the observation of significant quantum effects, and the combination of quantum and classical methods has proven effective for modelling and optimising the system. Carbon nanotubes are potentially scalable, meaning that it might be possible to build larger and more complex quantum simulators using this technology, and their properties can be tuned by controlling their size, shape, and doping, allowing for precise control over the electron-phonon interactions. This platform could be used to simulate the behaviour of complex materials, potentially leading to the discovery of new materials with desirable properties, and provide insights into the fundamental physics of electron-phonon interactions and superconductivity.

Entanglement and Simulation in Nanotube Systems

This research demonstrates a novel platform for quantum simulation using suspended carbon nanotubes, each hosting multiple quantum dots. By carefully controlling the interactions between electrons and mechanical vibrations within these nanostructures, scientists have theoretically established a system capable of generating and maintaining robust quantum entanglement across macroscopic scales. The team’s calculations reveal the emergence of unique, maximally entangled electronic states, known as Bell states, arising from the interplay of electron mobility, strong electron-phonon interactions, and the quasi-two-dimensional geometry of the setup. The significance of this work lies in its potential to simulate strongly correlated systems, which are notoriously difficult to model using classical computers.

By leveraging the strong electromechanical coupling and tunable interactions within the carbon nanotube system, researchers can explore complex quantum phenomena and gain insights into the behaviour of quantum materials. The theoretical framework developed provides a detailed phase diagram, mapping the conditions under which these entangled states emerge and persist. Future work will focus on refining the model and assessing the impact of device-level imperfections, such as alignment tolerances and variations in dot size, but the proposed quantum simulator is considered within reach of current experimental capabilities, building upon existing demonstrations of single suspended carbon nanotube quantum dots with the required electromechanical coupling strengths, promising a new avenue for understanding and ultimately harnessing the properties of quantum materials.