arXiv subjects

Dan-Dan Lian

Publications and source records attributed to Dan-Dan Lian.

7 recordsLinked to original sources

arXiv2025

The Hall effects of vortex light in optical materials

For light, its spin can be independent of the spatial distribution of its wave function, whereas its intrinsic orbital angular momentum does depend on this distribution. This difference suggests that the spin Hall effect might differ from the orbital Hall effect as light propagates through optical materials. In this paper, we model optical materials as curved space-time and investigate light propagation in two specific materials by solving the covariant Maxwell equations. We find that the trajectory of light with spin $σ$ and intrinsic orbital angular momentum $\ell$ deviates from that of light without angular momentum ($σ=0$ and $\ell=0$) by an angle $θ_{σ,\ell} \propto 2σ+\ell$. In particular, the contribution of spin $σ$ to angle $θ_{σ,\ell}$ is twice that of the intrinsic orbital angular momentum $\ell$, highlighting their differing effects on light propagation in optical materials. Furthermore, this angle $θ_{σ,\ell}$ could potentially be observed experimentally, enhancing our understanding of the role of angular momentum in light propagation.

physics.optics↗

arXiv2024

Effective ray equations for vortex light and their application in an optical waveguide

Beyond its spin, light can also carry intrinsic orbital angular momentum (IOAM), termed as vortex light. In this study, we derive effective ray equations for vortex light by applying the WKB approximation to the covariant Maxwell equations. According to these equations, the propagation of vortex light can be significantly affected by its IOAM, as suggested by numerous studies. To examine the effects of IOAM, we solve the effective ray equations for vortex light and investigate its ray trajectory within a specific optical waveguide. Our findings indicate that the ray trajectory of vortex light exhibits a divergence perpendicular to the normal propagation plane, akin to the spin Hall effect in light. This divergence, termed as the orbital Hall effect, stems from the IOAM of the light. In this study, the effective ray equations are derived by modeling the interaction between light and media as light's free fall in a curved spacetime. Therefore, observing the orbital Hall effect could not only enhance our understanding of light's spin and IOAM, but also offer novel insights into the coupling between light and gravitational fields.

gr-qc↗

arXiv2024

Gravitational spin Hall effect of electrons in Schwarzschild metric

In this study, we derive the non-relativistic Hamiltonian for electrons within the Schwarzschild metric from covariant Dirac equations, using both the weak field approximation and the Foldy-Wouthuysen transformation. This Hamiltonian incorporates a gravitational spin-orbit coupling term, resulting in the gravitational spin Hall effect (SHE), which separates electrons by their spin. By solving the Schrödinger equation for these electrons, we investigate the gravitational SHE as they orbit a non-rotating gravitational source. Our findings reveal that the spin-dependent separation of electrons increases in proportion to their orbital periods, significantly improving the detectability of gravitational SHE. Specifically, for electrons in a low Earth orbit, the separation is estimated to be $3.0\times 10^{-12}\, \text{m}$ annually. These results indicate the practicality of detecting the gravitational SHE in electrons orbiting Earth, especially with prolonged orbital durations, underscoring the potential for quantum test of the Weak Equivalence Principle.

gr-qc↗

arXiv2024

Gravitational orbital Hall effect of vortex light in Lense-Thirring metric

Vortex light, characterized by an intrinsic orbital angular momentum aligned with its propagation direction, is described through vortex electromagnetic waves. Similar to the gravitational spin Hall effect (SHE), vortex light is expected to exhibit intrinsic orbital angular momentum dependent trajectories and deviations from the null geodesic plane when propagating through a gravitational field, a phenomenon termed the gravitational orbital Hall effect (OHE). In this work, we model the vortex light as vortex Laguerre-Gaussian electromagnetic wave packets and analyze its motion by solving covariant Maxwell equations within the Lense-Thirring metric. Our findings reveal that the trajectory of vortex light with an intrinsic orbital angular momentum deviates from the null geodesic in two ways. It deviates both perpendicular to, and within, the null geodesic plane. This behavior contrasts with the gravitational SHE, where spin-polarized light primarily deviates perpendicular to the null geodesic plane. Moreover, the relationship between the deviation and intrinsic orbital angular momentum differs significantly from that between the deviation and spin. These results suggest a unique interaction between intrinsic orbital angular momentum and gravity, distinct from the spin-gravity coupling, indicating that the gravitational OHE of light might not be precisely predicted by merely substituting spin with intrinsic orbital angular momentum in the gravitational SHE of light.

gr-qc↗

arXiv2024

The motion of twisted particles in a stellar gravitational field

In this work, we explore the motion of a twisted particle possessing intrinsic orbital angular momentum (OAM) as it traverses a weak stellar gravitational field, which we approximate using a polytropic model. We disregard the spin characteristic of the twisted particle, modeling it as a massless complex twisted scalar wave packet to simplify its interaction with gravitational fields. Building on this simplification, we determine the trajectory of this twisted particle by using the center of its energy density and investigate the gravitational birefringence induced by its OAM. In a weak field approximation, we find the gravitational birefringence-OAM relationship parallels that with spin, as described by the Mathisson-Papapetrou-Dixon equations. This indicates that the gravitational birefringence induced by OAM can potentially exceed that induced by spin by several orders of magnitude, significantly enhancing its detectability. To broaden our analysis, we introduce a nonminimal coupling term, $λR|ϕ|^2$, into the Lagrangian, resulting in the modified expression $\mathcal{L}=-\frac{1}{2}\nabla _ρϕ\nabla^ρϕ^*-\frac{1}{2}λR|ϕ|^2$. This adjustment is necessitated by the quantization of the scalar field in curved spacetime. We then explore the effects of this term on the motion of the twisted particle. Our findings show that the trajectory of the twisted particle under nonminimal coupling ($λ\neq 0$) differs from that in the minimal coupling scenario ($λ=0$). Specifically, for a positive nonminimal coupling constant $λ$, the trajectory of the twisted particle is expected to deviate away from the stellar center, compared to the minimal coupling scenario.

gr-qc↗

arXiv2022

Repeatedly readable state, spontaneous collapse, and quantum/classical boundary

We propose a model to identify the quantum/classical boundary. The model introduces a spontaneous collapse of state superposition: $\frac{d}{dt} ρ_{ij} =-\frac{i}{\hbar}[H,ρ]_{ij}-ρ_{ij}/τ_{ij}$. Different from other collapse models, the collapsing scale $τ_{ij}$ here does not contain a universal parameter, but is specified by the two states $| i\rangle $ and $ | j\rangle$: If each state is {\em in principle} repeatedly readable (typically by a QND measurement), then $τ_{ij}$ is the {\em potentially} needed measuring time to discriminate the two states, and the collapse occurs spontaneously {\em without} any actual monitoring. Otherwise, $τ_{ij}=\infty$, which means no collapse and everlasting superposition. This happens if one state is not repeatedly readable, or if the two states cannot possibly be discriminated in a particular circumstance (for example in the Rabi oscillation). Detailed analysis shows that for a "trapped Schr{ö}dinger's cat", the superposition of $|{\rm here} \rangle$ and $| {\rm there} \rangle $ is forbidden if $E D \gg 4π\hbar c$, and allowed if $E D \le 4π\hbar c$, where $D$ is the trap separation and $ E$ is the energy gap, which can be estimated with $ M v^2$. The model also constrains a "free Schr{ö}dinger's cat" to display double-slit interference if $pθD\ge 8\hbar$, where $p= Mv$, $θ$ is the angle spanned by the two trajectories, and $D$ is the slit separation. In contrast, this model sets no limit on the coherent length of massless photon, thus the arm of a Michelson interferometer can be arbitrarily long. The spontaneous collapse which we propose can occur for an isolated system, and parallels the decoherence induced by interaction with environment.

quant-ph↗

arXiv2018

Extraordinary spin density and energy back-flow under interference

A novel phenomenon was reported recently that the "local optical spin density" based on Poynting vector might be counter-intuitively opposite to the integrated spin orientation while the one related to the canonical expression might not [Leader, Phys. Lett. B 779, 385-387 (2018)]. However, the "local optical spin density" of the canonical expression can also be counter-intuitively opposite to the integrated spin orientation under the interference of plane waves, even if all of the plane waves possess the same polarization handedness. Moreover, the interference fields might acquire a transverse spin density (perpendicular to the propagation plane), which can have more well-controlled relations with the polarization. Meantime, in such a case its energy flux exhibits counter-intuitive back-flow and a circular motion (vortex) in the propagation plane locally, which implies a transverse local orbital angular momentum density.

physics.optics↗