Tying knots in light fields

We construct a new family of null solutions to Maxwell's equations in free space whose field lines encode all torus knots and links. The evolution of these null fields, analogous to a compressible flow along the Poynting vector that is both geodesic and shear-free, preserves the topology of the knots and links. Our approach combines the Bateman and spinor formalisms for the construction of null fields with complex polynomials on $\mathbb{S}^3$. We examine and illustrate the geometry and evolution of the solutions, making manifest the structure of nested knotted tori filled by the field lines.Comment: 5 pages, 3 figure

Deterministic ratchet from stationary light fields

Ratchets are dynamic systems where particle transport is induced by zero-average forces due to the interplay between nonlinearity and asymmetry. Generally, they rely on the effect of a strong external driving. We show that stationary optical lattices can be designed to generate particle flow in one direction while requiring neither noise nor driving. Such optical fields must be arranged to yield a combination of conservative (dipole) and nonconservative (radiation pressure) forces. Under strong friction all paths converge to a discrete set of limit periodic trajectories flowing in the same direction.Comment: 6 pages, 4 figure

Qubit-Programmable Operations on Quantum Light Fields

Engineering quantum operations is one of the main abilities we need for developing quantum technologies and designing new fundamental tests. Here we propose a scheme for realising a controlled operation acting on a travelling quantum field, whose functioning is determined by an input qubit. This study introduces new concepts and methods in the interface of continuous- and discrete-variable quantum optical systems.Comment: Comments welcom

Maximally polarized states for quantum light fields

The degree of polarization of a quantum state can be defined as its Hilbert-Schmidt distance to the set of unpolarized states. We demonstrate that the states optimizing this degree for a fixed average number of photons $\bar{N}$ present a fairly symmetric, parabolic photon statistics, with a variance scaling as $\bar{N}^2$. Although no standard optical process yields such a statistics, we show that, to an excellent approximation, a highly squeezed vacuum can be considered as maximally polarized.Comment: 4 pages, 3 eps-color figure