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arXiv:2511.02613

Emergent Bell Phase in an Electro-Nanomechanical Quantum Simulator

David Ullrich, Marta Cagetti, Stefan Forstner, Adrian Bachtold, Anna Sanpera

quant-phcond-mat.mes-hallSubmitted Nov 4, 2025• Announced Nov 5, 2025
v1 · Nov 4, 2025v2 · Jun 10, 2026
arXivHTMLPDF

Abstract

Suspended carbon nanotubes hosting electrostatically defined quantum dots allow for exceptionally strong and tunable electromechanical coupling as well as mechanical modes that can reach the quantum ground state of motion simply by cryogenic cooling. This makes them a unique platform for quantum simulation of electron-phonon coupling. Here, we propose an experimentally realisable setup with two such carbon nanotubes in parallel, each hosting four quantum dots. Our system not only exhibits phonon-mediated electron-electron attraction, but also supports a robust, maximally entangled Bell phase at mesoscopic scales shared across the subsystems. These features highlight its potential as a simulator of strongly correlated quantum systems.

Journal reference
SciPost Phys. 21, 043 (2026)
DOI
10.21468/SciPostPhys.21.2.043
Comments
7 pages, 4 figures

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Suspended carbon nanotubes hosting electrostatically defined quantum dots allow for exceptionally strong and tunable electromechanical coupling as well as mechanical modes that can reach the quantum ground state of motion simply by cryogenic cooling. This makes them a unique platform for quantum simulation of electron-phonon coupling. Here, we propose an experimentally realisable setup with two such carbon nanotubes in parallel, each hosting four quantum dots. Our system not only exhibits phonon-mediated electron-electron attraction, but also supports a robust, maximally entangled Bell phase at mesoscopic scales shared across the subsystems. These features highlight its potential as a simulator of strongly correlated quantum systems.
Quantum simulations can provide new insights into the physics of strongly correlated electronic systems. A well-studied system, but still open in many regards, is the Hubbard-Holstein Hamiltonian, where electronic repulsion is in competition with attraction generated by the electron-phonon coupling. In this context, we study the behavior of four quantum dots in a suspended carbon nanotube and coupled to its flexural degrees of freedom. The system is described by a Hamiltonian of the Hubbard-Holstein class, where electrons on different sites interact with the same phonon. We find that the system presents a transition from the Mott insulating state to a polaronic state, with the appearance of pairing correlations and the breaking of the translational symmetry. These findings will motivate further theoretical and experimental efforts to employ nanoelectromechanical systems to simulate strongly correlated systems with electron-phonon interactions.
The quantum behaviour of mechanical resonators is a new and emerging field driven by recent experiments reaching the quantum ground state. The high frequency, small mass, and large quality-factor of carbon nanotube resonators make them attractive for quantum nanomechanical applications. A common element in experiments achieving the resonator ground state is a second quantum system, such as coherent photons or a superconducting device, coupled to the resonators motion. For nanotubes, however, this is a challenge due to their small size. Here, we couple a carbon nanoelectromechanical (NEMS) device to a superconducting circuit. Suspended carbon nanotubes act as both superconducting junctions and moving elements in a Superconducting Quantum Interference Device (SQUID). We observe a strong modulation of the flux through the SQUID from displacements of the nanotube. Incorporating this SQUID into superconducting resonators and qubits should enable the detection and manipulation of nanotube mechanical quantum states at the single-phonon level.
We describe an approach to electrically control the strong interaction between a single electron spin and the vibrational motion of a suspended carbon nanotube resonator. The strength of the deflection-induced spin-phonon coupling is dependent on the wavefunction of the electron confined in a lateral carbon nanotube quantum dot. An electrical field along the nanotube shifts the effective center of the quantum dot, leading to the corresponding modification of the spin-phonon strength. Numerical simulations with experimentally reachable parameters show that high fidelity quantum state transfer between mechanical and spin qubits driven by electrical pulses is feasible. Our results form the basis for the fully electrical control of the coherent interconvertion between light and spin qubits and for manufacturing electrically driven quantum information processing systems.
Abstract Quantum dots placed along a vibrating nanotube provide a quantum simulation platform that can directly address the electron-phonon interaction. This offers promising prospects for the search of new quantum materials and the study of strong correlation effects. As this platform is naturally operated by coupling the dots to an electronic reservoir, state preparation is straightforwardly achieved by driving into the steady state. Here we show that for intermediate electron-phonon coupling strength, the system with spin-polarized quantum dots undergoes a Peierls transition into an insulating regime which exhibits charge-density wave order in the steady state as a consequence of the competition between electronic Coulomb repulsive interactions and phonon-induced attractive interactions. The transport phenomena can be directly observed as fingerprints of electronic correlations. We also present powerful methods to numerically capture the physics of such an open electron-phonon system at large numbers of phonons. Our work paves the way to study and detect correlated electron-phonon physics in the nanotube quantum simulator with current experimentally accessible techniques.
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Mechanical oscillators have been demonstrated with very high quality factors over a wide range of frequencies.They also couple to a wide variety of fields and forces, making them ideal as sensors.The realization of a mechanically based quantum bit could therefore provide an important new platform for quantum computation and sensing.Here, we show that by coupling one of the flexural modes of a suspended carbon nanotube to the charge states of a double quantum dot defined in the nanotube, it is possible to induce sufficient anharmonicity in the mechanical oscillator so that the coupled system can be used as a mechanical quantum bit.However, these results can only be achieved when the device enters the ultrastrong coupling regime.We discuss the conditions for the anharmonicity to appear, and we show that the Hamiltonian can be mapped onto an anharmonic oscillator, allowing us to work out the energy level structure and find how decoherence from the quantum dot and the mechanical oscillator is inherited by the qubit.Remarkably, the dephasing due to the quantum dot is expected to be reduced by several orders of magnitude in the coupled system.We outline qubit control, readout protocols, the realization of a CNOT gate by coupling two qubits to a microwave cavity, and finally how the qubit can be used as a static-force quantum sensor.