How ICFO Engineers Control Motion at Quantum Limit

Researchers at ICFO, Institut de Ciències Fotòniques in Barcelona and Universite de Bordeaux, University of Chicago and Argonne National Laboratory have achieved control of motion at the zero-point motion scale, manipulating movement at the fundamental limit imposed by quantum mechanics. The team, led by C. B. Møller and R. Tormo-Queralt, demonstrated tunable nonlinear electromechanics by coupling a nanotube mechanical oscillator with a double-quantum-dot electronic two-level system, enabling a mechanical Kerr nonlinearity at this previously theoretical scale. This work yields a mechanical anharmonicity three orders of magnitude larger than in previous work while preserving the predominantly mechanical nature of the lowest energy states. The results establish a tunable platform for strong mechanical anharmonicity and nonlinear continuous readout at the zero-point motion scale.

Researchers have demonstrated control of mechanical motion at the zero-point motion scale, a capability realized through tunable nonlinear electromechanics within a carbon nanotube device. This advance, detailed in a recent publication, relies on ultrastrong coupling between the nanotube, acting as a mechanical oscillator, and a double-quantum-dot electronic two-level system. This work yields a mechanical anharmonicity three orders of magnitude larger than in previous work, a substantial increase crucial for accessing nonlinear mechanics at extremely small amplitudes and opening possibilities for precise control and readout of nanomechanical systems. The system’s design incorporates a suspended carbon nanotube hosting a double-quantum dot, tuned to create a tunable electronic two-level system. Researchers led by C. B. Møller and R. Tormo-Queralt demonstrated a purely quadratic cavity-based continuous readout of the mechanical motion, enabled by a double-quantum dot symmetry that can be broken via gate tuning to introduce a large linear transduction. As they explain, “The purely quadratic dependence of the readout provides direct access to the oscillator’s energy and thus to its averaged phonon number.”

Researchers C. B. Møller and R. Tormo-Queralt demonstrated a mechanical Kerr nonlinearity, effectively engineering a frequency shift dependent on the amplitude of oscillation, a phenomenon crucial for advanced control schemes. The system’s design prioritizes ultrastrong coupling, satisfying conditions for the experiment while remaining within the dispersive regime.

This readout method is enabled by a double-quantum dot symmetry, which can be actively tuned using gate voltages to introduce a substantial linear transduction. The system’s performance is described by a Hamiltonian incorporating mechanical and cavity modes, alongside Pauli operators representing the two-level system, enabling a sizeable Kerr nonlinearity even at the zero-point motion scale. The origin of this nonlinearity stems from the system’s symmetry; opposite mechanical displacements produce the same energy change, resulting in a frequency shift that scales quadratically with displacement.

The ability to manipulate mechanical systems at the zero-point motion scale, the fundamental limit of quantum movement, relies on achieving a specific operational regime known as dispersive coupling. This configuration centers on a carbon nanotube mechanical oscillator interacting with an electronic two-level system (ETLS), and crucially, a readout cavity. The team highlights that this readout method provides a purely quadratic cavity-based continuous readout of the mechanical motion. This continuous nonlinear optomechanical readout is enabled by a double-quantum dot symmetry, which can be broken by gate tuning to introduce a large linear transduction.

Researchers established a specific parameter set, a bare mechanical frequency, an electromechanical coupling strength, and an electronically tunable two-level system frequency, to operate within the far-detuned dispersive regime while simultaneously fulfilling the ultrastrong coupling criterion. This configuration, detailed in their recent work, ensures a mechanical Kerr nonlinearity remains sizeable even at the quantum limit of motion. Specifically, the team targeted a scenario where the electronic two-level system frequency is larger than both the mechanical and cavity frequencies. Maintaining this balance, they report, “enables both a large Kerr nonlinearity and a purely quadratic readout,” as detailed in their supporting information. Crucially, this parameter selection preserves the validity of the dispersive approximation, allowing for precise control and measurement.

Conventional mechanical resonators often require large displacements to detect signals, introducing noise and limiting sensitivity. This quadratic dependence is crucial, as it provides an absolute measure of displacement in units of zero-point motion, potentially revolutionizing nanoscale displacement sensors and opening doors for more complex quantum devices.