Tunable nonlinear electromechanics at the zero-point motion scale
Christoffer B. Møller, Roger Tormo-Queralt, Elsa Vázquez-Rodríguez, Victor Román-Rodríguez, Marta Cagetti, Eneko Mateos-Madinabeitia, Janine C. Franz, Stefan Forstner, Sergio L. De Bonis, Luca Ornago, Maria El Abbassi, Seoho Jung, Andrew N. Cleland, David A. Czaplewski, Fabio Pistolesi, Adrian Bachtold
quant-phcond-mat.mes-hallSubmitted Jul 23, 2026• Announced Jul 27, 2026
Nonlinearity at the scale of zero-point motion opens new possibilities for the control and readout of nanomechanical systems, but achieving this remains a formidable challenge. Here we demonstrate that ultrastrong coupling (USC) between a nanotube mechanical oscillator and a double-quantum-dot electronic two-level system enables a mechanical Kerr (Duffing) nonlinearity at the zero-point motion scale. In the dispersive regime, this large coupling yields a mechanical anharmonicity of $α= 1.4\%$ - three orders of magnitude larger than in previous work - while preserving the predominantly mechanical nature of the lowest energy states. We further demonstrate a purely quadratic cavity-based continuous readout of the mechanical motion. This continuous nonlinear optomechanical readout is enforced by a double-quantum dot symmetry, which can be broken by gate tuning to introduce a large linear transduction. These results establish a tunable USC platform that enables strong mechanical anharmonicity and nonlinear continuous readout at the zero-point motion scale.
Nonlinearity at the scale of zero-point motion opens new possibilities for the control and readout of nanomechanical systems, but achieving this remains a formidable challenge. Here we demonstrate that ultrastrong coupling (USC) between a nanotube mechanical oscillator and a double-quantum-dot electronic two-level system enables a mechanical Kerr (Duffing) nonlinearity at the zero-point motion scale. In the dispersive regime, this large coupling yields a mechanical anharmonicity of α=1.4% - three orders of magnitude larger than in previous work - while preserving the predominantly mechanical nature of the lowest energy states. We further demonstrate a purely quadratic cavity-based continuous readout of the mechanical motion. This continuous nonlinear optomechanical readout is enforced by a double-quantum dot symmetry, which can be broken by gate tuning to introduce a large linear transduction. These results establish a tunable USC platform that enables strong mechanical anharmonicity and nonlinear continuous readout at the zero-point motion scale.
Abstract It is an open question whether mechanical resonators can be made nonlinear with vibrations approaching the quantum ground state. This requires the engineering of a mechanical nonlinearity far beyond what has been realized so far. Here we discover a mechanism to boost the Duffing nonlinearity by coupling the vibrations of a nanotube resonator to single-electron tunnelling and by operating the system in the ultrastrong-coupling regime. We find that thermal vibrations become highly nonlinear when lowering the temperature. The average vibration amplitude at the lowest temperature is 13 times the zero-point motion, with approximately 42% of the thermal energy stored in the anharmonic part of the potential. Our work may enable the realization of mechanical Schrödinger cat states, mechanical qubits and quantum simulators emulating the electron–phonon coupling.
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.
Nonlinearity is a key resource in both classical and quantum signal processing. Nonlinear nanomechanical elements have found applications ranging from sensing to computing, while networks of nonlinear resonators, as well as nonlinearly coupled networks of linear resonators, constitute promising platforms for simulating complex dynamics. Here, we experimentally demonstrate an approach to realizing strong mechanical nonlinearity in nanomechanical resonators, fully controlled through optical laser drives. The mechanism exploits the nonlinearity of the radiation-pressure interaction in a cavity optomechanical system, which gives rise to a nonlinear optical spring effect. The resulting Duffing nonlinearity is conveniently tunable in strength via pump laser power, while its sign is controlled by laser detuning. Moreover, we demonstrate that the nonlinear optical spring mediates effective interactions between mechanical modes coupled to a common cavity, inducing tunable nonlinear interactions between them that impact spectral response and dynamics. These results establish cavity optomechanics as a versatile and in-situ reconfigurable platform for engineering nonlinear dynamics in resonators and networks.
Silicon nanomechanical resonators display ultra-long lifetimes at cryogenic temperatures and microwave frequencies. Achieving quantum control of single-phonons in these devices has so far relied on nonlinearities enabled by coupling to ancillary qubits. In this work, we propose using atomic forces to realize a silicon nanomechanical qubit without coupling to an ancillary qubit. The proposed qubit operates at 60 MHz with a single-phonon level anharmonicity of 5 MHz. We present a circuit quantum acoustodynamics architecture where electromechanical resonators enable dispersive state readout and multi-qubit operations. The combination of strong anharmonicity, ultrahigh mechanical quality factors, and small footprints achievable in this platform could enable quantum-nonlinear phononics for quantum information processing and transduction.
Mechanical resonators ultrastrongly coupled to quantum two-level systems provide a promising route towards mechanical qubits by introducing significant anharmonicity to the mechanical modes, particularly in the slow-oscillator regime. Although the resulting hybrid system is well described by the quantum Rabi model, a consistent treatment of dissipation remains challenging across the broad parameter space routinely probed in current nanotube electromechanical devices. Here, we investigate dissipation in the open quantum Rabi model using a Born-Markov framework based on the slowly varying bath spectrum approximation, yielding a Lindblad master equation applicable far beyond conventional descriptions while recovering them in their respective limits. Using this framework, we analyze experimentally accessible observables across this parameter space. As the secular approximation breaks down, phonon blockade progressively washes out. Our approach remains valid in this regime, enabling a quantitative description of the continuous evolution of phonon blockade with coupling strength and dissipation. At finite temperature, we find a suppression of the temperature-induced increase of coherence decay rate for weak anharmonicity. Under driving, our approach remains applicable to substantially stronger perturbations than conventional dressed-state master equations and shows that an apparently classical observable can coexist with Wigner negativity. We further capture the weakly anharmonic regime arising from finite detuning in the double-quantum dot. These results establish a unified description of dissipation from weakly anharmonic operating regimes to the strongly anharmonic mechanical-qubit regime and provide experimentally relevant predictions for ultrastrong electromechanical systems.
The coupling of nanomechanical resonators to controllable quantum systems represents a growing and promising area of research. Recent advances in this field have brought to astonishing results, such as the initialization of a mechanical resonator into its quantum ground state and even the preparation of non-classical coherent states of motion. These achievements open up appealing scenarios to quantum information technologies and to the exploration of the quantum-classical boundary. From an application perspective, such quantum-mechanical hybrid systems provide a versatile and attractive tool for a variety of precision measurements, like ultra-sensitive detection of force, mass, and displacement. \n \nQuantum control over a mechanical resonator, or, conversely, the prospect of using resonator's motion for probing quantum states, both involve some tight requirements. First of all, the interaction between the mechanics and its quantum partner has to be large on the scale of the decoherence rates of the coupled systems. In most cases, the coupling mechanism has to be activated by engineering the resonator with electrodes, magnets, or mirrors, or by using tailored laser fields. For this reason, the search for a strong coupling typically competes with the requirement of overcoming decoherence effects. In addition, for quantum effects to be observable, strong coupling has to be accompanied by the preparation of zero entropy initial states, for instance by cooling the resonator into its ground state of motion. \n \nThe motivation pursued by this thesis is to contribute to the inspiring field of hybrid systems by walking through each of the aforementioned directions. We in fact demonstrate a promising system in which optically active quantum dots, embedded in fully self-assembled core-shell nanowires, are coupled to the nanowire motion. Mechanical vibrations of the nanowire modulate the quantum dot emission energy over a broad range exceeding 14 meV, by means of deformation potential coupling. In our system, therefore, both the coupling mechanism and the quantum states themselves are intrinsic to the resonator's structure. Besides revealing unusually strong, such a built-in opto-mechanical interaction produces a hybrid system whose inherent coherence is unspoiled by any functionalization or external field and whose fabrication is simpler than top-down techniques. \n \nWe further demonstrate the use of a quantum point contact as a displacement transducer to measure and control the low-temperature thermal motion of a nearby micromechanical cantilever. We show that by including the QPC in a suitable feedback loop, we are able to cool the cantilever's fundamental mechanical mode down to the level of the measurement noise, achieving a squashing of the QPC noise at high gain. Due to its off-board design, our system is particularly versatile and suitable to force-sensing applications. Since the QPC transducer is sensitive to local modifications of the nearby electric field, our approach is in principle compatible with any nanoscale resonator, without requiring any functionalization to activate the coupling. By improving the performance of the QPC as a one-dimensional conductor and the cantilever-QPC capacitive coupling, our system has the potential to achieve quantum-limited displacement resolution and ground state cooling. We then report on some ongoing attempts to overcome the current limitations of our system and couple mechanical motion to different mesoscopic transport devices. \n \nWe remark that our demonstration of an as-grown quantum-dot-in-nanowire hybrid system opens up bright prospects on future experiments, as also testified by the very recent ferment of the scientific community around this topic. We find that the opto-mechanical coupling rate is not far from the nanowire mechanical frequency. This fact makes our system particularly promising for the quantum non-demolition readout of a quantum dot state through a measurement of the nanowire position. On the other hand, we show that the coupling can be further optimized, and the nanowire mechanical heating rate reduced, thus disclosing the captivating perspective of using quantum dots to probe and control the mechanical state of a nanowire. In this context, it would be important to investigate a possible spin-oscillator coupling in our system, given the long coherence time offered by a spin state in a quantum dot. The wide range of control over the quantum dots emission energy and the ability to tune two neighboring dots into resonance pave the way to mechanically induced emitter-emitter coupling. In addition, our monolithic opto-mechanical system constitutes a good candidate for recent proposals of a tripartite hybrid system, which would integrate an optical cavity, a quantum two-level system and a mechanical resonator. The intrinsically strong coupling between the quantum dots and the nanowire motion would enhance the interaction between the mechanics and the cavity field, leading for instance to efficient cooling of the resonator to the ground state. Finally, the quantum dot sensitivity to the nanowire resonant vibration could also support the use of our system as an integrated force probe or as a nanomechanical mass sensor. In other words, the results reported in this dissertation constitute not only a relevant proof-of-principle, moreover they open up intriguing challenges for future research.