Nested SU(2) symmetry of photonic orbital angular momentum

Frontiers in Physics, Journal Year: 2023, Volume and Issue: 11

Published: Oct. 19, 2023

The polarization state is described by a quantum mechanical two-level system, which known as special unitary group of degree 2 [SU(2)]. Polarization attributed to an internal spin freedom inherent photons, while photons also possess orbital freedom. A fundamental understanding the nature and angular momentum significant utilize degrees for various applications in optical communications, computations, sensing, laser-patterning. Here, we show that coherent emitted from laser diode can be incremented using vortex lens, magnitude increases with increase topological charge inside mode. superposition left right vortices SU(2) state, similar polarization; however, radius corresponding Poincaré sphere depends on charge. Consequently, expect nested structure describe states different magnitudes momentum. We have experimentally developed simple system realize arbitrary controlling both amplitudes phases freedom, whose interplays were confirmed expected far-field images dipoles quadruples.

Language: Английский

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Topological Polarisation States

arXiv (Cornell University), Journal Year: 2023, Volume and Issue: unknown

Published: Jan. 1, 2023

Polarisation states are described by spin expectation values, known as Stokes parameters, whose trajectories in a rotationally symmetric system form sphere named after Poincaré. Here, we show that the of broken rotational systems can exhibit distinct topological structures polarisation states. We use phase-shifter to circle (${\mathbb S}^1$), which interferes with original input due phase change output state upon rotation. By rotating using rotator, become torus S}^1 \times {\mathbb was experimentally confirmed simple set-up passive optical components together Mach-Zehnder interferometers. also discuss about realisations other features, such Möbius strip, Hopf-links, and Dirac bosons bulk-edge correspondence.

Language: Английский

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Spin textures of coherent photons with SU(4) symmetry

Results in Physics, Journal Year: 2024, Volume and Issue: 61, P. 107745 - 107745

Published: May 9, 2024

We show coherent photons with spin and orbital angular momentum have symmetry of special unitary group degree four, SU(4), both theoretically experimentally. the polarisation could be a measure to characterise quantum coherency state, which was significantly affected by partial trace out freedom. By changing amplitudes classically entangled we observed crossover from Heisenberg classical Ising spin. also demonstrated projections states, recover while SU(4) state is projected simple product SU(2)×SU(2). Based on developed platform, explored texture photons, found unique profile reminiscent Bengal cat upon wrapping three-dimensional sphere. controlled phase between singlet triplet states rotated increasing phase.

Language: Английский

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SU(N) symmetry of coherent photons controlled by rotated waveplates

Heliyon, Journal Year: 2024, Volume and Issue: 10(14), P. e34423 - e34423

Published: July 1, 2024

The coherent state from a laser source has spin and orbital degrees of freedom, which allow an arbitrary superposition among orthogonal states with varying amplitudes phases. Here, we theoretically show photons SU(N) symmetry are characterised by expectation values angular momentum shown on hypersphere in SO(N2−1) space. To demonstrate expected unitary transformations experiments, have constructed generators the Lie group simply combining widely available optical components such as waveplates vortex lenses. We between twisted Gaussian is dynamics topological charge upon transformation SU(3) states. also realised photonic singlet triplet corresponding to SU(4) states, were projected SU(2)×SU(2) passing through rotated polariser.

Language: Английский

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Special Theory of Relativity for a Graded Index Fibre

arXiv (Cornell University), Journal Year: 2023, Volume and Issue: unknown

Published: Jan. 1, 2023

The speed of light ($c$) in a vacuum is independent on choice frames to describe the propagation, according theory relativity. We consider how characterised material, where different from that due finite dielectric constant. phase velocity material smaller than $c$, such moving frame can be larger velocity, move faster material. Consequently, an unusual Doppler effect expected, and wavelength changes red-shift blue-shift upon increasing frame. corresponding energy also sign positive negative, while momentum always positive, leading sings for helicity. In graded index fibre, exact solution available, even more complicated phenomena are effective mass photons. Upon increase gap, generated by optical confinements orbital angular momentum, photons increases. If gap large enough, starts change positive. this case, diverges if agreement with fame velocity. Contrary behaviours group below $c$. This thought-experiment might useful insight polarisation sate light.

Language: Английский

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Photonic Quantum Chromo-Dynamics

arXiv (Cornell University), Journal Year: 2023, Volume and Issue: unknown

Published: Jan. 1, 2023

Vortexed photons with finite orbital angular momentum have a distinct mode profile topological charge at the centre of mode, while propagating in certain direction. Each different $m$ is orthogonal, sense that overlap integral vanishes among modes values $m$. Here, we theoretically consider superposition state 3 left- and right-vorticies Gaussian without vortex. These states are considered to be assigned quantum states, thus, employed $\mathfrak{su}(3)$ Lie algebra associated SU(3) group classify photonic states. We calculated expectation 8 generators algebra, which should observable, since Hermite. proposed call these parameters as Gell-Mann parameters, named after theoretical physicist, Murray Gell-Mann, who established Quantum Chromo-Dynamics (QCD) for quarks. The represented on 8-dimensional hypersphere its radius fixed due conservation law Casimir operator. discussed possibility explore QCD experiments classified embed SO(6) SO(5).

Language: Английский

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