Nano Photonics Models Frequency-Dependent Torque Scaling for Anisotropic Particle Rotation

A quantum theory of rotational vacuum friction, developed by F. Javier García de Abajo and Alejandro Manjavacas at The Barcelona Institute of Science and Technology and IQF, reveals that particle symmetry dramatically alters energy dissipation. The findings show anisotropic particles experience frictional torque scaling with rotation frequency to the power of seven at zero temperature, driven by correlated photon pair emission. Axisymmetric particles avoid this photon-assisted friction entirely, irrespective of temperature, offering key insight into nanoscale rotational dynamics and potential applications in precision measurement.

Rotational symmetry governs frictional torque and photon emission from nanoscale particles

A dramatic difference in frictional torque exists between particle types; anisotropic particles experience a torque scaling with rotation frequency to the power of seven, whereas axisymmetric particles exhibit no torque at any temperature. This represents a key advance, as previous semiclassical treatments failed to predict the complete absence of friction for symmetrical shapes. Classical physics often approximates interactions as instantaneous, neglecting the finite speed of light and quantum effects. This new research demonstrates the necessity of a fully quantum mechanical treatment to accurately describe energy dissipation at the nanoscale, where these effects become dominant. This discovery establishes a clear threshold where particle symmetry dictates energy loss during rotation in a vacuum, opening avenues for designing nanoscale devices immune to photon-assisted friction. The implications extend to areas such as the development of highly sensitive gyroscopes and persistent rotational systems, where minimising energy loss is paramount. Understanding this fundamental limit on rotational motion is crucial for advancing nanotechnology.

Detailed modelling revealed that two-photon emission dominates energy loss at low temperatures, while photon scattering becomes significant at higher temperatures, specifically when thermal energy exceeds the particle’s internal energy gap. The emission of correlated photon pairs, a distinctly quantum mechanical phenomenon, is the primary mechanism driving friction in anisotropic particles. These photons are emitted in pairs to conserve momentum, and their frequency is related to the particle’s rotational frequency. At higher temperatures, the increased thermal fluctuations lead to a greater probability of single photon scattering events, contributing to the overall frictional torque. For a prolate diamond ellipsoid with semi-axes of 100nm and 76nm rotating at 6GHz, the predicted torque was approximately 2 × 10−33 Newton metres at 300 Kelvin, a value six orders of magnitude below current levitated torque sensor sensitivity. This suggests that detecting this rotational vacuum friction experimentally is extremely challenging, requiring highly sensitive measurement techniques. Current levitated torque sensors, which utilise optically trapped nanoparticles, are approaching the sensitivity required to observe these effects. The models currently address ‘small lossless particles’ and leave unanswered how larger or absorbing materials behave under rotational vacuum friction. The assumption of lossless particles simplifies the calculations, but real materials will inevitably exhibit some degree of absorption, which would introduce additional energy dissipation channels. Isolation and subsequent investigation of the additional effects introduced by asymmetry or material properties are now possible through understanding how symmetrical particles behave. Earlier semiclassical treatments predicted some degree of friction even for symmetrical particles, a prediction demonstrably incorrect according to this new quantum mechanical description. These earlier models failed to account for the quantum nature of light and the specific symmetries of the rotating particle.

Modelling light-matter interaction via retarded dipole-response formalism describes rotational behaviour

Retarded dipole-response formalism was employed to model light-matter interaction with the rotating particles; this approach calculates the particle’s response to electromagnetic fields, accounting for the time it takes light to travel, which is important for understanding energy dissipation. Unlike instantaneous dipole models, the retarded formalism considers the finite propagation speed of electromagnetic waves, leading to a more accurate description of the dynamic interactions between the particle and the vacuum electromagnetic field. This method allows for the calculation of the particle’s polarizability, a measure of how easily its electrons distort in an electric field, and links it to internal excitations and transition dipoles, the direction of electron movement within the particle. The transition dipole moment represents the strength of the interaction between the particle and the electromagnetic field, and its orientation determines the direction of emitted photons. By accurately modelling the particle’s polarizability and transition dipoles, researchers can predict the rate of photon emission and, consequently, the frictional torque. It provides a firm foundation for modelling more complex scenarios, extending beyond perfectly symmetrical, non-absorbing particles. Future work could incorporate material dispersion, allowing for the investigation of particles with frequency-dependent dielectric properties. Furthermore, the formalism can be extended to consider particles with more complex shapes and compositions, paving the way for a more comprehensive understanding of rotational vacuum friction in diverse nanoscale systems.

Quantum mechanics refutes predicted friction in rotating nanoscale particles

The Barcelona Institute of Science and Technology’s findings offer a pathway towards designing microscopic rotating devices with predictable energy dissipation, vital for precision measurement and novel micro-mechanical systems. Particles lacking symmetrical axes experience frictional forces, with the rate of energy loss increasing rapidly as the rotation speed increases, scaling with the seventh power of rotational frequency. This steep dependence on rotational frequency highlights the importance of minimising rotational speed in applications where energy efficiency is critical. Perfectly symmetrical particles are immune to this particular form of friction, irrespective of temperature, a finding that challenges previous theoretical predictions. This immunity stems from the conservation of angular momentum; the particle’s symmetry prevents the emission of photons that would carry away angular momentum. It is important to acknowledge that these calculations currently apply only to perfectly symmetrical, non-absorbing particles. Deviations from perfect symmetry or the presence of absorption will introduce additional frictional forces. The Barcelona Institute of Science and Technology has revealed a fundamental connection between an object’s shape and its energy loss when rotating in a vacuum; this energy loss occurs through the emission of light, converting rotational motion into electromagnetic radiation. This process, known as rotational vacuum friction, is a manifestation of the zero-point energy of the electromagnetic field and the interaction between the rotating particle and virtual photons. The research underscores the importance of considering quantum effects when designing and analysing nanoscale devices, and opens up new possibilities for manipulating rotational motion at the atomic and molecular level.

The research demonstrated that the shape of a rotating particle influences its energy loss in a vacuum. Particles without axial symmetry experience a frictional force that increases rapidly with rotation speed, while those with perfect symmetry are protected from this effect regardless of temperature. This finding refutes prior theoretical predictions and highlights how a particle’s symmetry impacts its interaction with the electromagnetic field. The authors suggest this understanding is vital for designing nanoscale rotating devices with predictable energy dissipation.