Colloquium : Geometric phases of light: Insights from fiber bundle theory

Using Rotations to Control Observable Relativistic Effects

“…This mechanism of boostrotation entanglement, known more generally as Wigner rotation, is quite similar to the Coriolis effect and may be attributed to a classical geometric phase [7,8]. The same pattern is observed in many areas of theoretical physics and engineering: from classical mechanics to geometric optics and even quantum computation [9][10][11][12][13]. A particularly curious context with plenty of practical implementations lies within the realm of electrodynamics [14][15][16], where the magnetic force itself may be regarded as a consequence of such inertial effect and thus linked to a geometric phase following a mechanical analogy [16][17][18].…”

“…In [27] we consider the Wigner rotation in this setting and its various physical applications: from quantum scattering to the falling cat problem [9,10]. The latter may be regarded as yet another application of classical geometric phases.…”

Dirac equation for photons in a fibre: Origin of polarisation

“…In particular, we focus on the difference between the SU(2) wavefunction of spin states and SO(3) expectation values. Mathematically, the fundamental theorem of homomorphism [103] [104] [105] [106] [107] gives their relationship as SU(2)/ SO(3), where . This means that the phase change of −1 for the SU(2) wavefunction is expected upon a 2 π rotation on the Poincaré sphere, described by SO(3).…”

Quantum commutation relationship for photonic orbital angular momentum

“…The nature of structured light is attracting significant attention, these days [18][19][20][21][22][23]. The increased bandwidth in fibre optic communication would be one of the most promising near-term application [20,24].…”