Optical properties of radially-polarised twisted light

We show that, in general, any type of radially-polarised paraxial twisted optical mode carries only an axial total optical angular momentum (AM) ${\bar {\cal J}_z}=\ell{\cal L}_0$ where $\ell$ is the winding number and ${\cal L}_0$ is a constant. This mode, however, is shown to have zero spin angular momentum (SAM), so it is endowed only with orbital angular momentum (OAM) and no SAM. The helicity is found to be proportional to $\ell$, hence radially-polarised modes display chirality. When applied to a Laguerre-Gaussian (LG) mode our treatment leads to a total helicity equal to $(\ell/|\ell|){\cal Q}$, where ${\cal Q}$ is the action constant. The factor $(\ell/|\ell|)=\pm 1$, depends on the sign, not the magnitude of $\ell$ and so the result holds for any radially-polarised LG mode however large the magnitude of its winding number $\ell$ is. The magnitude of the action constant ${\cal Q}$ and hence the helicity are diminished for all such LG modes of large beam waist $w_0$.Comment: 4 figure

Radiation pattern of two identical emitters driven by a Laguerre-Gaussian beam: An atom nanoantenna

We study the directional properties of a radiation field emitted by a geometrically small system composed of two identical two-level emitters located at short distances and driven by an optical vortex beam, a Laguerre-Gaussian beam which possesses a structured phase and amplitude. We find that the system may operate as a nanoantenna for controlled and tunable directional emission. Polar diagrams of the radiation intensity are presented showing that a constant phase or amplitude difference at the positions of the emitters plays an essential role in the directivity of the emission. We find that the radiation patterns may differ dramatically for different phase and amplitude differences at the positions of the emitters. As a result the system may operate as a two- or one-sided nanoantenna. In particular, a two-sided highly focused directional emission can be achieved when the emitters experience the same amplitude and a constant phase difference of the driving field. We find a general directional property of the emitted field that when the phase differences at the positions of the emitters equal an even multiple of \pi/4, the system behaves as a two-sided antenna. When the phase difference equals an odd multiple of \pi/4, the system behaves as an one-sided antenna. The case when the emitters experience the same phase but different amplitudes of the driving field is also considered and it is found that the effect of different amplitudes is to cause the system to behave as a uni-directional antenna radiating along the interatomic axis.Comment: published versio

Quantum Hall Physics with Cold Atoms in Cylindrical Optical Lattices

We propose and study various realizations of a Hofstadter-Hubbard model on a cylinder geometry with fermionic cold atoms in optical lattices. The cylindrical optical lattice is created by copropagating Laguerre-Gauss beams, i.e.~light beams carrying orbital angular momentum. By strong focusing of the light beams we create a real space optical lattice in the form of rings, which are offset in energy. A second set of Laguerre-Gauss beams then induces a Raman-hopping between these rings, imprinting phases corresponding to a synthetic magnetic field (artificial gauge field). In addition, by rotating the lattice potential, we achieve a slowly varying flux through the hole of the cylinder, which allows us to probe the Hall response of the system as a realization of Laughlin's thought experiment. We study how in the presence of interactions fractional quantum Hall physics could be observed in this setup.Comment: 10 pages, 9 figure