arXiv subjects

Mark T. Lusk

Publications and source records attributed to Mark T. Lusk.

At least 19 recordsLinked to original sources

arXiv2026

An Analytical Formula for Gravitational Faraday Rotation in the ADM Split of Spacetime

An analytical expression is derived for the rate of gravitational Faraday rotation measured by Eulerian observers. The reference frame is a Fermi-Walker triad aligned with the spatial wave vector. Attention is restricted to the ADM split of Kerr spacetime and geometric optics. Our exact, closed-form GFR formula is implemented and verified to be consistent with numerical predictions. The approach offers a new perspective on Faraday rotation, and it allows a single Eulerian observer to compare experimentally measured polarization holonomy with analytical prediction. Sliced spacetime does not suffer from a mathematical singularity at the ergosphere associated with Boyer-Lindquist coordinates in the threading decomposition. These physically intuitive coordinates can therefore be used to analytically produce and study GFR predictions for transits of light that pierce the ergosphere.

gr-qc↗

arXiv2025

Gravitational Faraday Holonomy

Closed optical trajectories in Kerr spacetime are engineered to exhibit a marked lack of symmetry. The eccentricity manifests as a holonomy in gravitational Faraday rotation that can be made arbitrarily large by radial translation of the common location of source and receiver. All trajectories are non-equatorial and include a passage through the equatorial plane at the radial turning point, where the trajectory and pseudo-magnetic field are well-aligned. This, combined with path asymmetry, results in a large gravitational Faraday holonomy that lends itself to experimental measurement. Trajectories that start further away from the singularity pass more closely to the ergosphere, thus transiting a more distorted region of spacetime with concomitant amplification of gravitational Coriolis force.

gr-qc↗

arXiv2024

The Influence of Quantum Correlation on the Holonomy of Spatially-Structured Bi-Photons

The manifestation of entanglement within geometric phase is elucidated for spatially-structured bi-photons. Entanglement parameters are shown to influence holonomy in two distinct ways: through statistical superpositions of separable states; and via quantum correlation. These are entwined within geometric phase, motivating the construction of a projective, gauge-invariant measure that allows the manifestation of quantum correlation to be pinpointed and explained. An optical circuit consisting of a pair of misoriented mode converters gives a practical demonstration. This is facilitated by a novel pump engineering method which produces photon pairs with tunable entanglement.

quant-ph↗

arXiv2024

Optical Polarization Holonomy in the Kerr Metric

Polarization holonomy is analytically determined for a class of closed, spherical trajectories of light transiting a black hole in the Kerr metric. The leading order geometric optics approximation admits a closed-form expression of such paths, and sets of source/receiver locations are quantified for a spectrum of black hole angular momenta. A conserved, conformal Yano-Killing scalar is then exploited to determine the evolving polarization. Polarization holonomy, the angle between outgoing and incoming polarizations, is quantified for the spectrum of admissible direct and retrograde trajectories. This offers a means of experimentally measuring Gravitational Faraday Rotation from a single, stationary position.

gr-qc↗

arXiv2024

Entanglement Holonomy for Photon Pairs in Curved Spacetime

Polarization holonomy is analytically determined for maximally entangled photon pairs that transit a class of closed trajectories in the Kerr metric. This is used to define and investigate an entanglement holonomy not associated with constituent product states.

gr-qc↗

arXiv2024

Phase-resolved measurement of entangled states via common-path interferometry

We propose and experimentally demonstrate a method to directly measure the phase of biphoton states using an entangled mode as a collinear reference. The technique is demonstrated with entangled photonic spatial modes in the Laguerre-Gaussian basis, and it is applicable to any pure quantum system containing an exploitable reference state in its entanglement spectrum. As one particularly useful application, we use the new methodology to directly measure the geometric phase accumulation of entangled photons.

quant-ph↗

arXiv2024

Measurement of nonequilibrium vortex propagation dynamics in a nonlinear medium

We observe and measure the nonequilibrium dynamics of optical vortices as a function of propagation distance through a nonlinear medium. The precession of a tilted-core vortex is quantified as is vortex-core sharpening, where the infinite width of a linear core subsequently shrinks and approaches the healing length of this nonlinear optical fluid. Experiments are performed with a variable-length nonlinear medium: a nonlinear fluid in a tank with an output window on a translating tube. This provides control over the distance the light propagates in the fluid and allows for the measurement of the dynamics throughout the entire propagation range. Results are compared to the predictions of a computational simulator to find the equivalent dimensionless nonlinear coefficient.

physics.optics↗

arXiv2024

Trapped Vortex Dynamics Implemented in Composite Bessel Beams

The divergence-free nature of Bessel beams can be harnessed to effectively trap optical vortices in free space laser propagation. We show how to generate arbitrary vortex configurations in Bessel traps to investigate few-body vortex interactions within a dynamically-evolving fluid of light, which is a formal analog to a non-interacting Bose gas. We implement--theoretically and experimentally--initial conditions of vortex configurations first predicted in harmonically-trapped quantum fluids, in the limit of weak atomic interactions, and model and measure the resultant dynamics. These hard trap dynamics are distinct from the harmonic trap predictions due to the non-local interactions that occur among the hard wall boundary and steep phase gradients that nucleate other vortices. By simultaneously presenting experimental demonstrations with the theoretical proposal, we validate the potential application of using Bessel hard wall traps as testing grounds for engineering few-body vortex interactions within trapped, two-dimensional compressible fluids.

physics.optics↗

arXiv2023

Pump-tailored Alternative Bell State Generation in the First-Order Hermite-Gaussian basis

We demonstrate entangled-state swapping, within the Hermite-Gaussian basis of first-order modes, directly from the process of spontaneous parametric down-conversion within a nonlinear crystal. The method works by explicitly tailoring the spatial structure of the pump photon such that it resembles the product of the desired entangled spatial modes exiting the crystal. Importantly, the result is an entangled state of balanced HG modes, which may be beneficial in applications that depend on symmetric accumulations of geometric phase through optics or in applications of quantum sensing and imaging with azimuthal sensitivity. Furthermore, the methods are readily adaptable to other spatial mode bases.

quant-ph↗

arXiv2023

Quantized Optical Vortex-array Eigenstates in a Rotating Frame

Linear combinations of Bessel beams can be used to effectively trap light within cylindrical domains. Such hard traps can be used to produce states that exhibit stationary arrays of optical vortices from the perspective of a steadily rotating frame. These patterned singularities can be engineered to have singularities of the same or mixed charges and the requisite rotation rates are quantized even though the setting is purely linear. A hydrodynamic interpretation is that the vortices are at rest within a compressible, two-dimensional fluid of light.

physics.optics↗

arXiv2023

Experimental measurement of the geometric phase of non-geodesic circles

We present and implement a method for the experimental measurement of geometric phase of non-geodesic (small) circles on any SU(2) parameter space. This phase is measured by subtracting the dynamic phase contribution from the total phase accumulated. Our design does not require theoretical anticipation of this dynamic phase value and the methods are generally applicable to any system accessible to interferometric and projection measurements. Experimental implementations are presented for two settings: (1) the sphere of modes of orbital angular momentum, and (2) the Poincaré sphere of polarizations of Gaussian beams.

physics.optics↗

arXiv2022

The Anatomy of Geometric Phase for an Optical Vortex Transiting a Lens

We present an analytical means of quantifying the fractional accumulation of geometric phase for an optical vortex transiting a cylindrical lens. The standard fiber bundle of a Sphere of Modes is endowed with a Supplementary Product Space at each point so that the beam waists and their positions can be explicitly tracked as functions of lens transit fraction. The method is applied to quantify the accumulation of geometric phase across a single lens as a function of initial state and lens position within the beam. It can be readily applied to a series of lenses as well.

physics.optics↗

arXiv2022

The Peripheral Vortex Biome of Confined Quantum Fluids and Its Influence on Vortex Pair Annihilation

The self-annihilation of oppositely charged optical vortices in a quantum fluid is hindered by nonlinearity and promoted by radial confinement, resulting in rich life-cycle dynamics of such pairs. The competing effects generate a biome of peripheral vortices that can directly interact with the original pair to produce a sequence of surrogation events. Numerical simulation is used to elucidate the role of the vortex biome as a function of nonlinearity strength and the initial spacing between the engineered vortices. The results apply directly to other nonlinear quantum fluids as well and may be useful in the control of complex condensates in which vortex dynamics produce topologically protected phases.

physics.optics↗

arXiv2022

Hydrodynamics Explanation for the Splitting of Higher-charge Optical Vortices

We show that a two-dimensional hydrodynamics model provides a physical explanation for the splitting of higher-charge optical vortices under elliptical deformations. The model is applicable to laser light and quantum fluids alike. The study delineates vortex breakups from vortex unions under different forms of asymmetry in the beam, and it is also applied to explain the motion of intact higher-charge vortices.

physics.optics↗

arXiv2022

Tilted Poincaré Sphere Geodesics

We provide the first experimental demonstration of geometric phase generated in association with closed Poincaré Sphere trajectories comprised of geodesic arcs that do not start, end, or necessarily even include, the north and south poles that represent pure Laguerre- Gaussian modes. Arbitrarily tilted (elliptical) single vortex states are prepared with a spatial light modulator, and Poincaré Sphere circuits are driven by beam transit through a series of π-converters and Dove prisms.

physics.optics↗

arXiv2021

Optical Vortex Braiding with Bessel Beams

We propose the braiding of optical vortices in a laser beam with more than 2π rotation by superposing Bessel modes with a plane wave. We experimentally demonstrate this by using a Bessel-Gaussian beam and a coaxial Gaussian, and we present measurement of three complete braids. The amount of braiding is fundamentally limited only by the numerical aperture of the system and we discuss how braiding can be controlled experimentally for any number of vortices.

physics.optics↗

arXiv2021

Dynamics of elliptical vortices in a trapped quantum fluid

The nonequilibrium dynamics of vortices in 2D quantum fluids can be predicted by accounting for the way in which vortex ellipticity is coupled to the gradient in background fluid density. In the absence of nonlinear interactions, a harmonically trapped fluid can be analyzed analytically to show that single vortices will move in an elliptic trajectory that has the same orientation and aspect ratio as the vortex projection itself. This allows the vortex ellipticity to be estimated through observation of its trajectory. A combination of analysis and numerical simulation is then used to show that nonlinear interactions cause the vortex orientation to precess, and that the rate of vortex precession is once again mimicked by a precession of the elliptical trajectory. Both vortex ellipticity and rate of precession can therefore be inferred by observing its motion in a trap. An ability to anticipate and control local vortex structure and vortex trajectory is expected to prove useful in designing few-vortex systems in which ellipticity is a ubiquitous, as-yet-unharnessed feature.

cond-mat.quant-gas↗

arXiv2021

Hydrodynamics of noncircular vortices in beams of light and other two-dimensional fluids

The motion of noncircular two-dimensional vortices is shown to depend on a form of coupling between vortex ellipticity and the gradient of fluid density. The approach is based on the perspective that an elliptic vortex can be described as the projection of a virtual construct, a circular vortex with a symmetry axis that is tilted with respect to the direction of propagation. The resulting kinetic equation offers insights into how tilt and vortex velocity coevolve in few-body nonequilibrium settings such as vortex pair nucleation and annihilation. The model is developed and applied in association with optical vortices, and optical experiments are used to verify its predictive power. It is valid for quantum fluids and classical hydrodynamics settings as well.

physics.flu-dyn↗