Angular Momentum Research Articles

Kerr black hole energy extraction, irreducible mass feedback, and the effect of captured particles charge

AbstractWe analyze the extraction of the rotational energy of a Kerr black hole (BH) endowed with a test charge and surrounded by an external test magnetic field and ionized low-density matter. For a magnetic field parallel to the BH spin, electrons move outward(inward) and protons inward(outward) in a region around the BH poles(equator). For zero charge, the polar region comprises spherical polar angles $$-60^\circ \lesssim \theta \lesssim 60^\circ $$ - 60 ∘ ≲ θ ≲ 60 ∘ and the equatorial region $$60^\circ \lesssim \theta \lesssim 120^\circ $$ 60 ∘ ≲ θ ≲ 120 ∘ . The polar region shrinks for positive charge, and the equatorial region enlarges. For an isotropic particle density, we argue the BH could experience a cyclic behavior: starting from a zero charge, it accretes more polar protons than equatorial electrons, gaining net positive charge, energy and angular momentum. Then, the shrinking(enlarging) of the polar(equatorial) region makes it accrete more equatorial electrons than polar protons, gaining net negative charge, energy, and angular momentum. In this phase, the BH rotational energy is extracted. The extraction process continues until the new enlargement of the polar region reverses the situation, and the cycle repeats. We show that this electrodynamical process produces a relatively limited increase of the BH irreducible mass compared to gravitational mechanisms like the Penrose process, hence being a more efficient and promising mechanism for extracting the BH rotational energy.

Proton acceleration driven by relativistic femtosecond Laguerre–Gaussian lasers

AbstractWith the advancement of ultra-intense and ultra-short laser technology, lasers have achieved new parameters in femtosecond (10–15 s) and petawatt (1015 W) ranges. Ion acceleration driven by these lasers has become a prominent research area. However, most research still relies on traditional Gaussian lasers, posing challenges in enhancing the low divergence angle, high flux, and high collimation of ion beams. This paper reviews a novel laser mode—the Laguerre–Gaussian (LG) laser in the relativistic domain. LG lasers feature a hollow intensity distribution and angular momentum, offering centripetal force and phase modulation at the axis center, reducing particle beam divergence and enabling focused acceleration. High-quality proton beams driven by ultra-intense, ultra-short LG lasers have promising applications in proton therapy, fast ignition in inertial confinement fusion, proton imaging, particle injection in accelerators, and astrophysics.

Dynamics of massive and massless particles in the spacetime of a wiggly cosmic dislocation

AbstractIn this paper, we investigate the spacetime containing both small-scale structures (wiggles) and spatial dislocation, forming a wiggly cosmic dislocation. We study the combined effects of these features on the dynamics of massive and massless particles. Our results show that while wiggles alone lead to bound states and dislocation introduces angular momentum corrections, their coupling produces more complex effects, influencing both particle motion and wave propagation. Notably, this coupling significantly modifies radial solutions and eigenvalues, with the direction of motion or propagation becoming a critical factor in determining the outcomes. Numerical solutions reveal detailed aspects of particle dynamics as functions of dislocation and string parameters, including plots of trajectories, probability densities, and energy levels. These findings deepen our understanding of how a wiggly cosmic dislocation shapes particle dynamics, suggesting new directions for theoretical exploration in cosmological models.

Mode entanglement and isospin pairing in two-nucleon systems

Abstract In this study, we explore the entanglement and correlation in two-nucleon systems using isospin formalism. With the help of Slater decomposition, we derive analytical expressions for various entanglement measures. Specifically, we analyse the one- and two-mode entropies, mutual informations, and a basis-independent characteristic known as the one-body entanglement entropy.

To understand the impact of pairing, we consider interactions involving isovector and isoscalar L=0 pairing terms. Our findings show that certain pairing interactions can maximize one-body entanglement entropy of ground states when both total angular momentum and total isospin have zero projections.

We provide numerical examples for the sd shell and explore the mutual informations in LS coupled and jj coupled single-particle bases. We find that the shell structure and angular momentum coupling significantly impact the measures of entanglement. We outline the implications of conserving angular momentum and isospin on one-mode entropies, irrespective of particle number.

Chirality-induced phonon spin selectivity by elastic spin–orbit interaction

Spin and orbital degrees of freedom are crucial in not only fundamental particles but also classical waves such as optical systems, wherein the spin-orbit interaction (SOI) of light provides new perspectives for manipulating electromagnetic waves. Elastic waves possess similar spin angular momentum (SAM) and orbital angular momentum (OAM). However, the elastic counterpart of SOI remains unexplored, even for ubiquitous elastic waveguides (WG). Here, we demonstrate the existence of elastic SOI in helical WG. We prove that the torsion and curvature of helical WG induces synthetic gauge potentials in describing the elastic vibrations. Through analytical theory and simulations, we unveil the interplay among elastic SAM, intrinsic OAM, and extrinsic OAM, impacted by the elastic SOI. Importantly, results show that elastic SOI can introduce the Chirality-Induced Phonon Spin Selectivity. These findings advance our understanding of angular momentum physics in elastic waves and enable practical strategies for wave manipulation.

Kinetic Energy and Angular Momentum of Free Particles in a Class of Rotating Cylindrical Gravitational Waves using the Noether Symmetry Approach

Kinetic Energy and Angular Momentum of Free Particles in a Class of Rotating Cylindrical Gravitational Waves using the Noether Symmetry Approach

On the non-dissipative orbital evolution of a binary system comprising non-compact components with misaligned spin and orbital angular momenta

Abstract In this Paper we determine the non-dissipative tidal evolution of a close binary system with an arbitrary eccentricity in which the spin angular momenta of both components is misaligned with the orbital angular momentum. We focus on the situation where the orbital angular momentum dominates the spin angular momenta and so remains at small inclination to the conserved total angular momentum. Torques arising from rotational distortion and tidal distortion taking account of Coriolis forces are included. This extends the previous work of Ivanov & Papaloizou relaxing the limitation resulting from the assumption that one of the components is compact and has zero spin angular momentum. Unlike the above study, the evolution of spin-orbit inclination angles is driven by both types of torque. We develop a simple analytic theory describing the evolution of orbital angles and compare it with direct numerical simulations. We find that the tidal torque prevails near ’critical curves’ in parameter space where the time-averaged apsidal precession rate is close to zero. In the limit of small spin, these curves exist only for systems that have at least one component with retrograde rotation. As in our previous work, we find solutions close to these curves for which the apsidal angle librates. As noted there, this could result in oscillation between prograde and retrograde states. We consider the application of our approach to systems with parameters similar to those of the misaligned binary DI Herc.

Selection of OAM signal constellations for atmospheric channels using optimal transport theory

We describe a method for determining optimal selections of orbital angular momentum (OAM) superpositions for OAM signal modulation in free-space optical communications using a measure of distance in the context of the Optimal Transport theory. Within the range of topological charges ℓ = −20 to ℓ = 20 we design OAM constellations using 16 to 128 symbols consisting of solos, duets, trios, and quartets of OAM modes. We propose a classification strategy requiring relatively low complexity to evaluate the performance of these constellations, achieving a classification error smaller than 1/1000 in weak to strong turbulence conditions for the 16-OAM constellation. We have found that the optimal set shows some dependence on the receiver’s architecture, so we offer results for optical detectors based on the conjugate projection, the mode sorter, and the Shack-Hartmann sensor.

Biaxial Gaussian Beams, Hermite–Gaussian Beams, and Laguerre–Gaussian Vortex Beams in Isotropy-Broken Materials

We have developed the paraxial approximation for electromagnetic fields in arbitrary isotropy-broken media in terms of the ray–wave tilt and the curvature of materials’ Fresnel wave surfaces. We have obtained solutions of the paraxial equation in the form of biaxial Gaussian beams, which is a novel class of electromagnetic field distributions in generic isotropy-broken materials. Such beams have been previously observed experimentally and numerically in hyperbolic metamaterials but have evaded theoretical analysis in the literature up to now. Biaxial Gaussian beams have two axes: one in the direction of the Abraham momentum, corresponding to the ray propagation, and another in the direction of the Minkowski momentum, corresponding to the wave propagation, in agreement with the recent theory of refraction, ray–wave tilt, and hidden momentum [Durach, 2024]. We show that the curvature of the wavefronts in the biaxial Gaussian beams correspond to the curvature of the Fresnel wave surface at the central wave vector of the beam. We obtain the higher-order modes of the biaxial beams, including the biaxial Hermite–Gaussian and Laguerre–Gaussian vortex beams, which opens avenues toward studies of the optical angular momentum (OAM) in isotropy-broken media, including generic anisotropic and bianisotropic materials.

Illumination diversity in multiwavelength extreme ultraviolet ptychography

With the development of high harmonic generation (HHG), lensless extreme-ultraviolet (XUV) imaging at nanoscale resolution has become possible with table-top systems. Specifically, ptychographic phase retrieval using monochromatic XUV illumination exhibits extraordinary robustness and accuracy to computationally reconstruct the object and the illumination beam profile. In ptychography, using structured illumination has been shown to improve reconstruction robustness and image resolution by enhancing high spatial-frequency diffraction. However, broadband imaging has remained challenging, as the required multiwavelength algorithms become increasingly demanding. One major aspect is the ability to separate the available information into different physically meaningful states, such as different spectral components. Here, we show that introducing spatial diversity between spectral components of an HHG beam can significantly improve the reconstruction quality in multiwavelength XUV ptychography. We quantify the diversity in the polychromatic illumination by analyzing the diffraction patterns using established geometry- and information-theory-based dissimilarity metrics. We experimentally verify the major influence of diversity by comparing ptychography measurements using HHG beams with Gaussian and binary structured profiles as well as with beams carrying wavelength-dependent orbital angular momentum. Our results demonstrate how structured illumination acts in twofold by separating the spectral information in a single diffraction pattern while providing maximized added information with every new scan position. We anticipate our work to be a starting point for high-fidelity polychromatic imaging of next-generation nanostructured devices at XUV and soft-X-ray wavelengths.

A Conjugate Linearly Polarized Light Wave Along an Optical Fiber with the Berry Phase Model and Its Magnetic Trajectories According to the Conjugate Frame

In this article, we study how a linear polarized wave that is going along an optical fiber works, which is known not only as a curve on a Lie group but also as a rotation of the polarization plane. What we are trying to show in this article is that linear polarized light waves (PLWs) are related to the Berry phase. Moreover, we give magnetic curves created by N traveling in the electromagnetic trajectories and the optical fiber generated by the electric field N of the PLW moving through the optical fiber. With this described method, we present a mathematical model to conveniently generate the relationships between an optical fiber and the optical angular momentum in a three-dimensional Lie group. The conjugate frame we used in this article removes unnecessary bending around the tangent and enables a more dynamic characterization, which can still be applied even when the second derivative of the curve is zero.

Saturated absorption spectroscopy of 87Rb atoms using structured light: Observation of narrow hyperfine and crossover resonances

Abstract An experiment on the saturated absorption spectroscopy (SAS) of 87Rb-D2 line is performed using the Laguerre-Gaussian (LG) beam as structured light. The theoretical simulation of which is done by considering a four-level atom-laser coupled system. The theoretically simulated spectra fairly match with the experimentally observed spectra. The line-width narrowing behavior of both the observed hyperfine and crossover resonances in the Doppler-broadened probe absorption spectra is attributed by the spatially dependent Rabi frequency of the pump LG beam irrespective of the characteristics of the probe beam. The results also illustrated that the narrowing behavior of the line shapes of the hyperfine structure using the LG beam is universal in nature, i.e. irrespective of hyperfine or crossover transitions. This structured light-induced narrowing of line-width of the sub Doppler hyperfine and crossover resonances can be utilized for high-precision laser frequency locking at a particular hyperfine or crossover transition. Moreover, a significant narrowing of hyperfine and crossover resonances with the variation of the orbital angular momentum (OAM) number of the LG beam shows that the generated SAS signal can be manipulated by using the OAM of the structured light as a control knob.

The hydrogen atom perturbed by a 1-dimensional Simple Harmonic Oscillator (1d-SHO) potential

Abstract The hydrogen atom perturbed by a constant 1-dimensional weak quadratic potential λz2 is solved at first-order perturbation theory using the eigenstates of the total angular momentum operator - the coupled basis. Physical applications of this result could be found, for example, in the study of a quadratic Zeeman effect weaker than fine-structure effects, or in a perturbation caused by instantaneous generalised van der Waals interactions.

Periodic orbits and KAM tori of a particle around a homogeneous elongated body

We analyse the dynamics of an infinitesimal particle around an elongated body, which is modelled as a homogeneous fixed straight segment centred at the origin. We assume that the length of the segment is small compared with the distance to the particle. After a Lie–Deprit normalization, we end up with a Hamiltonian that has not only the mean anomaly but also the argument of the perigee relegated to terms or third order or higher. We employ invariant and reduction theories to reduce the artificial symmetries associated with the Kepler flow and the central action of the angular momentum. Analysing the relative equilibria in the first and second reduced spaces allows us to determine the existence of near-polar circular periodic orbits and KAM tori.

Origin of the black hole spin in lower-mass-gap black hole-neutron star binaries

During the fourth observing run, the LIGO-Virgo-KAGRA Collaboration reported the detection of a coalescing compact binary (GW230529$_ $181500) with component masses estimated at $2.5-4.5\, M_ and $1.2-2.0\, M_ with 90<!PCT!> credibility. Given the current constraints on the maximum neutron star (NS) mass, this event is most likely a lower-mass-gap (LMG) black hole-neutron star (BHNS) binary. The spin magnitude of the BH, especially when aligned with the orbital angular momentum, is critical in determining whether the NS is tidally disrupted. An LMG BHNS merger with a rapidly spinning BH is an ideal candidate for producing electromagnetic counterparts. However, no such signals have been detected. In this study, we employ a detailed binary evolution model that incorporates new dynamical tide implementations to explore the origin of BH spin in an LMG BHNS binary. If the NS forms first, the BH progenitor (He-rich star) must begin in orbit shorter than 0.35 days to spin up efficiently, potentially achieving a spin magnitude of $ BH > 0.3$. Alternatively, if a nonspinning BH (e.g., $M_ BH = 3.6\, M_ forms first, it can accrete up to $ 0.2\, M_ via case BA mass transfer (MT), reaching a spin magnitude of $ BH 0.18$ under Eddington-limited accretion. With a higher Eddington accretion limit (i.e., 10.0 $ M Edd $), the BH can attain a significantly higher spin magnitude of $ BH by accreting approximately $1.0\, M_ during case BA MT phase.

Universal analyzer for measuring orbital angular momentum spectrum of randomly fluctuated beam

Universal analyzer for measuring orbital angular momentum spectrum of randomly fluctuated beam

Design and implementation of broadband optical vortices in photonic crystal slabs

We propose and discuss a simple method to generate broadband optical vortices, utilizing the inherent topological vortex structures of polarization around bound states in the continuum supported by a photonic crystal slab in the momentum space to induce the generation of vortex beams. Since the proposed structure is composed of silicon pillars arranged periodically, it lacks a true optical geometric center. It is insensitive to the position of the incident light and does not require a specific optical alignment process compared to traditional spiral phase plates. Furthermore, because it is composed of dielectric pillars, it can achieve vortex beam generation at any desired working wavelength. We also discuss the robustness of its structure, showing that it can be immune to certain manufacturing defects. Therefore, the proposed structure not only provides a new method for manipulating the angular momentum of photons but also has potential new applications in integrated optical information processing and optical tweezers.

Electric-magnetic duality of dyonic Kerr-Newman-NUT-AdS spacetimes

We study the (anti-)self-duality conditions under which the electric and magnetic parts of the conserved charges of the dyonic Kerr-Newman-NUT-anti-de Sitter solution become equivalent. Within a holographic framework, the stress tensor and the boundary Cotton tensor are computed from the electric/magnetic content of the Weyl tensor. The holographic stress tensor/Cotton tensor duality is recovered along the (anti-)self-dual curve in parameter space. We show that the latter not only implies a duality relation for the mass but also for the angular momentum. The partition function is computed to first order in the saddle-point approximation and a Bogomol’nyi-Prasad-Sommerfield bound is obtained. The ground state of the theory is enlarged to all the (anti-)self-dual configurations when the SO(4) and U(1) Pontryagin densities are introduced. We demonstrate this at the level of the action and variations thereof. Published by the American Physical Society 2024

One loop effective actions in Kerr-(A)dS black holes

We compute new exact analytic expressions for one-loop scalar effective actions in Kerr (A)dS black hole (BH) backgrounds in four and five dimensions. These are computed by the connection coefficients of the Heun equation via a generalization of the Gelfand-Yaglom formalism to second-order linear ordinary differential equations with regular singularities. The expressions we find are in terms of Nekrasov-Shatashvili special functions, making explicit the analytic properties of the one-loop effective actions with respect to the gravitational parameters and the precise contributions of the quasinormal modes. The latter arise via an associated integrable system. In particular, we prove asymptotic formulas for large angular momenta in terms of hypergeometric functions and give a precise mathematical meaning to Rindler-like region contributions. Moreover, we identify the leading terms in the large distance expansion as the point particle approximation of the BH and their finite size corrections as encoding the BH tidal response. We also discuss the exact properties of the thermal version of the BH effective actions by providing a proof of the Denef-Hartnoll-Sachdev formula and explicitly computing it for new relevant cases. Although we focus on the real scalar field in dS-Kerr and (A)dS-Schwarzschild in four and five dimensions, similar formulas can be given for higher spin matter and radiation fields in more general gravitational backgrounds. Published by the American Physical Society 2024

Systematic bias due to mismodeling precessing binary black hole ringdown

Accurate waveform modeling is crucial for parameter estimation in gravitational wave astronomy, impacting our understanding of source properties and the testing of general relativity. The precession of orbital and spin angular momenta in binary black hole (BBH) systems with misaligned spins presents a complex challenge for gravitational waveform modeling. Current precessing BBH waveform models employ a coprecessing frame, which precesses along with the binary. In this paper, we investigate a source of bias stemming from the mismodeling of ringdown frequency in the coprecessing frame. We find that this mismodeling of the coprecessing frame ringdown frequency introduces systematic biases in parameter estimation, for high-mass systems in particular, and in the inspiral-merger-ringdown (IMR)-consistency test of general relativity. Employing the waveform model henom, we conduct an IMR-consistency test using a Fisher matrix analysis across parameter space, as well as full injected signal parameter estimation studies. Our results show that this mismodeling particularly affects BBH systems with high-mass ratios, high-spin magnitudes, and highly inclined spins. These findings suggest inconsistencies for all waveform models which do not address this issue. Published by the American Physical Society 2024