arXiv subjects

Robert Hart

Publications and source records attributed to Robert Hart.

4 recordsLinked to original sources

arXiv2026

Visualizing Mathieu-Type Dynamics in a Tabletop Magnetic Trap: A Coil-Driven Parametric Oscillator

We present a tabletop demonstration of dynamic stabilization and ponderomotive-like trapping using a pair of sinusoidally-driven anti-Helmholtz coils and a suspended permanent magnet. The oscillating field produces a rapid micromotion superimposed on a slower secular oscillation, with micromotion amplitude increasing with displacement and peaking near the turning points. This behavior reveals a ponderomotive-like mechanism: a spatial gradient of micromotion amplitude that drives slow secular motion. The time-averaged effect provides a time-averaged harmonic (ponderomotive) restoring force that confines the magnet between the coils. Driving at 12-18 Hz places the system in a small-q regime where the two time scales are clearly separated and directly visible to the eye. Video tracking (included with this article) quantifies the motion and reveals a stability edge as the drive frequency is lowered (near 6-7 Hz in our apparatus). From trajectories in the 12-18 Hz range, we extract an effective Mathieu parameter q ~ 0.16 from the measured timescale separation of the secular versus drive frequencies. The apparatus uses inexpensive, readily available parts, and we provide a concise materials list, analysis code, field-gradient calibration data, and demonstration videos.

physics.atom-ph↗

arXiv2025

Demonstrating Dynamic Stability in Paul Traps: Exploring Rotating Saddles with Liquid Nitrogen Droplets

Rotating saddle potentials provide a compelling visual demonstration of dynamic stability, widely used in undergraduate physics as mechanical analogs to the RF Paul trap. Traditional demonstrations typically rely on rolling ball bearings, whose frictional effects and internal rotation obscure fundamental particle dynamics. We introduce a simple yet significant improvement by employing droplets of liquid nitrogen LN2, which levitate via the Leidenfrost effect, eliminating rolling dynamics and greatly reducing friction. LN2 droplets clearly illustrate the rotating ponderomotive-like force, producing trajectories closely consistent with theoretical predictions. Using experimental data, we compare the stability threshold and particle trajectories of LN2 droplets and traditional ball bearings. LN2 droplets exhibit a sharply defined and visually distinct stability threshold, transitioning abruptly from unstable to stable motion at a critical rotation frequency. In contrast, ball bearings demonstrate a more gradual threshold, accompanied by trajectories complicated by friction-induced deviations. We present detailed measurements of particle lifetimes and trajectories as functions of dimensionless stability parameters for both symmetric and intentionally asymmetric saddles. These improvements significantly enhance visual and conceptual clarity, reduce common misconceptions related to frictional dynamics, and provide natural opportunities for exploring related phenomena such as the Leidenfrost effect. We also offer practical guidance on assembling and implementing this enhanced demonstration for effective classroom and laboratory instruction.

physics.ed-ph↗

arXiv2025

The asymmetric rotating saddle potential as a mechanical analog to the RF Paul trap

Under specific conditions, a rotating saddle potential can confine the motion of a particle on its surface. This time-varying hyperbolic potential shares key characteristics with the RF electric quadrupole ion trap (RF Paul trap), making it a valuable mechanical analog. Previous work has primarily focused on symmetric saddles, characterized by equal curvatures along the trapping and anti-trapping directions. However, most applications of RF Paul traps-such as atomic clocks, quantum computing, and quantum simulations-require asymmetry in the quadrupole potential to break the degeneracy of motional modes, which is essential for processes like laser cooling and other quantum manipulations. In this paper, we investigate the motion of trapped particles in asymmetric rotating saddles. We demonstrate that even minor asymmetries, including those arising from manufacturing imperfections, can significantly affect particle trajectories and stability. Our analysis includes both theoretical modeling and experimental measurements. We derive the equations of motion for asymmetric saddles and solve them to explore stability and precession effects. Additionally, we present lifetime measurements of particles in saddles with varying degrees of asymmetry to map key features of the a-q stability diagram, including counterintuitive demonstrations of stability for saddles with negative asymmetry. This study underscores the importance of incorporating asymmetry into mechanical models of ion traps to better reflect real-world implementations. Although motivated primarily by RF Paul traps, these asymmetry-related results are also relevant to emerging gravitational analogs, such as rotating saddle potentials in certain binary black hole systems.

physics.atom-ph↗

arXiv2016

Using single nanoparticle tracking obtained by nanophotonic force microscopy to simultaneously characterize nanoparticle size distribution and nanoparticle-surface interactions

Comprehensive characterization of nanomaterials for medical applications is a challenging and complex task due to the multitude of parameters which need to be taken into consideration in a broad range of conditions. Routine methods such as dynamic light scattering or nanoparticle tracking analysis provide some insight into the physicochemical properties of particle dispersions. For nanomedicine applications the information they supply can be of limited use. For this reason, there is a need for new methodologies and instruments that can provide additional data on nanoparticle properties such as their interactions with surfaces. Nanophotonic force microscopy has been shown as a viable method for measuring the force between surfaces and individual particles in the nano-size range. Here we outline a further application of this technique to measure the size of single particles and based on these measurement build the distribution of a sample. We demonstrate its efficacy by comparing the size distribution obtained with nanophotonic force microscopy to established instruments, such as dynamic light scattering and differential centrifugal sedimentation. Our results were in good agreement to those observed with all other instruments. Furthermore, we demonstrate that the methodology developed in this work can be used to study complex particle mixtures and the surface alteration of materials. For all cases studied, we were able to obtain both the size and the interaction potential of the particles with a surface in a single measurement.

cond-mat.soft↗