arXiv subjects

Francis J. Headley

Publications and source records attributed to Francis J. Headley.

7 recordsLinked to original sources

arXiv2026

Magnetic Dipole in a Cuboidal Superconducting Trap

We derive the exact image-dipole potential of a point dipole inside a closed cuboidal superconducting trap. The construction generalises the parallel-plate result to a geometry that confines every translational degree of freedom, and we prove that the image lattice satisfies the Meissner boundary condition on all six walls. For a centred dipole the orientational energy reduces to a diagonal quadratic form whose three coefficients are Epstein-zeta-type lattice sums. We show that in both the infinite and finite rectangular traps the dipole orientation aligns with the \emph{short} cross-sectional axis over a finite range of aspect ratios. The equilibrium orientation in both cases is described by a phase diagram whose degeneracies we classify. Every prediction is verified against finite-element solutions of the same boundary-value problem, with agreement better than $0.16\%$.

cond-mat.supr-con↗

arXiv2026

Detection of the Earth Tides by Diamagnetic Levitation

The detection of mass distributions and mass transport via gravity mapping is a key geophysical tool for understanding the structure and dynamics of the earth. Changes in mass distribution, driven by natural processes and human activity (e.g., extraction of oil, gas, and minerals), contribute to observable phenomena such as sea-level rise (3 mm per year), increased flooding, landslides, and ice mass loss (hundreds of giga-tons per year). These processes generate gravity variations detectable by gravimeters and gradiometers on ground and in space. Current instruments achieve sensitivities of 10-100 micro-GAL per square root of Hz and enable applications including hydrocarbon exploration, volcanic monitoring, and subsurface detection. They also measure Earth tides (100-300 micro-GAL amplitude), requiring long-term stability over days. However, existing systems are limited by size (more than 8 kg) and cost (more than 100,000 USD), restricting widespread deployment. Here we demonstrate a levitated mechanical sensor (LOMS) with a demonstrated sensitivity of 18 micro-GAL, a large dynamical range, and an integration time of 6 s, with an expected sensitivity of smaller than 200 nano-GAL per square root of Hz in a volume of only a few cubic cm. We resolve earth tide signals, demonstrating stability comparable to state-of-the-art instruments. Unlike conventional accelerometers (micro-g sensitivity, low stability), our device operates as a true gravimeter. Its compact size and low projected cost enable scalable deployment, including drone-based surveys (10-100 m altitude), distributed sensor networks, and multipixel gravity imaging arrays. This platform enables high-resolution, cost-effective gravity mapping with potential for large-scale geophysical monitoring.

physics.geo-ph↗

arXiv2026

Rotational Quantum Tunneling of a Magnetic Dipole in a Superconducting Trap

We study the quantum dynamics of the rotational degree of freedom of a nano-magnet trapped in a superconducting trap. The nano-magnet is modeled as a magnetic dipole with magnetization pinned to the easy axis of the particle. The magnetic trap then leads to a potential barrier that hinders free rotation of the particle, but through which it can tunnel. We identified rest-gas scattering as the most important decoherence mechanism at low temperatures. A shape of the particle sufficiently close to perfect rotational symmetry about the rotational axis can protect the rotational tunneling against this decoherence mechanism, and we identify experimentally feasible parameter regimes where rotational tunneling should be observable.

quant-ph↗

arXiv2026

Path Integral Approach to Quantum Fisher Information

We present a real-time path-integral formulation of the quantum Fisher information for dynamical parameter estimation. For pure states undergoing unitary evolution, we show that the quantum Fisher information can be expressed as a connected symmetrized covariance of a time-integrated action deformation, equivalently as an integrated insertion of $\partial_λS$ in the propagator. This reformulation avoids explicit state reconstruction by rewriting the quantum Fisher information in terms of real-time correlators that are natural targets for many-body methods. We further embed the construction into the Schwinger-Keldysh closed-time-path formalism, identifying the quantum Fisher information with the Keldysh component of an appropriate contour-ordered correlator generated by forward and backward propagating sources. Finally, using the Van Vleck-Gutzwiller approximation we re-derive the compact semiclassical quantum Fisher information expression, clarifying how classical trajectory data control leading-order metrological sensitivity.

quant-ph↗

arXiv2026

Quantum Fisher Information for Entropy of Gibbs States

We derive the quantum Fisher information for entropy estimation in a Gibbs state and show that it equals the inverse of the heat capacity, which is dual to the temperature Fisher information given by the heat capacity divided by the square of the temperature. Their product is independent of the Hamiltonian and depends only on the temperature, leading to a metrological uncertainty relation between the variances of entropy and temperature estimators in which all system-specific quantities cancel. This relation arises from the dually-flat structure of the Gibbs exponential family expressed in thermodynamic coordinates, and holds for all standard thermodynamically conjugate pairs. We identify energy measurement as the optimal protocol for entropy estimation, analyse critical-point scaling where the entropy Fisher information vanishes, and connect it to the Ruppeiner metric in entropy coordinates. We lastly examine the distinguished role of the von Neumann entropy within the Rényi family. Generalisations to the grand canonical and generalised Gibbs ensembles are given.

quant-ph↗

arXiv2026

Quantum Metrology of Newton's Constant with Levitated Mechanical Systems

Newton's constant is the least well-measured among the fundamental constants of Nature, and, indeed, its accurate measurement has long served an experimental challenge. Levitated mechanical systems are attracting growing attention for their promising applications in sensing and as an experimental platform for exploring the intersection between quantum physics and gravitation. Here we propose a mechanical interferometric scheme of interacting levitated oscillators for the accurate estimation of Newton's constant. Our scheme promises to beat the current standard by several orders of magnitude.

quant-ph↗

arXiv2025

Magnetic Dipole Trapping Potential between Infinite Superconducting Plates

We derive the exact analytic form of the potential experienced by a magnetic dipole trapped between two infinite parallel superconducting plates using the method of image dipoles, providing a benchmark for numerical methods and a foundation for studying the stability and dynamics of magnetically levitated systems in precision measurements and fundamental physics experiments.

cond-mat.supr-con↗