Angular momentum conservation and the cat twist

M Hribar

Xiaoning Zang, Mark T. Lusk

Molecules with ${C}_{N}$ or ${C}_{Nh}$ symmetry can absorb quanta of optical angular momentum to generate twisted excitons with well-defined quasiangular momenta of their own. Angular momentum is conserved in such interactions at the level of a paraxial approximation for the light beam. A sequence of absorption events can thus be used to create a range of excitonic angular momenta. Subsequent decay can produce radiation with a single angular momentum equal to that accumulated. Such molecules can thus be viewed as mediators for changing the angular momentum of light. This sidesteps the need to exploit nonlinear light-matter interactions based on higher-order susceptibilities. A tight-binding paradigm is used to verify angular momentum conservation and demonstrate how it can be exploited to change the angular momentum of light. The approach is then extended to a time-dependent density functional theory setting where the key results are shown to hold in a many-body, multilevel setting.

Niels Geerits, Stephan Sponar

We demonstrate that spin-orbit coupled states are generated in neutral magnetic spin-1/2 particles traveling through an electric field. The quantization axis of the orbital angular momentum is parallel to the electric field; hence both longitudinal and transverse orbital angular momentum can be created. Furthermore, we show that the total angular momentum of the particle is conserved. Finally we propose a neutron optical experiment to measure the transverse effect.

Stephen Paul Robinson

Lele FAN, Feng Wang, Tianhai ZENG

The recent two papers have successively proposed the concepts and more precise expressions of strict conservation or statistical conservation of physical quantities, which are different from the expression of a conserved quantity in quantum mechanics. The Hamiltonian operator of the system discussed in this paper are independent of time, so it is commutative with the operators of an angular momentum itself, its component and its square, so that all these quantities are conserved quantities. In an isolated composite system, one of the angular momentum components of the total system are strictly conserved, while the angular momentum components of the subsystems can only be conserved statistically, both of which can be expressed in terms of eigenvalues and eigenfunctions. Generally, angular momentum itself does not have eigenvalues and eigenfunctions, so it cannot be expressed as strict conservation in terms of these concepts. Although there are eigenvalues and eigenfunctions for the square of angular momentum, they cannot express strict conservation either. And they can only be expressed as statistical conservation.