Atoms in complex twisted light

The physics of optical vortices, also known as twisted light, is now a well-established and a growing branch of optical physics with a number of important applications and significant inter-disciplinary connections. Optical vortex fields of widely varying forms and degrees of complexity can be realised in the laboratory by a host of different means. The interference between such beams with designated orbital angular momenta and optical spins (the latter is associated with wave polarisations) can be structured to conform to various geometrical arrangements. The focus of this review is on how such tailored forms of light can exert a controllable influence on atoms with which they interact. The main physical effects involve atoms in motion due to application of optical forces. The now mature area of atom optics has had notable successes both of fundamental nature and in applications such as atom lasers, atom guides and Bose-Einstein condensates. The concepts in atom optics encompass not only atomic beams interacting with light, but atomic motion in general as influenced by optical and other fields. Our primary concern in this review is on atoms in structured light where, in particular, the twisted nature of the light is made highly complex with additional features due to wave polarisation. These features bring to the fore a variety of physical phenomena not realisable in the context of atomic motion in more conventional forms of laser light. Atoms near resonance with such structured light fields become subject to electromagnetic fields with complex polarisation and phase distributions, as well as intricately structured intensity gradients and radiative forces. From the combined effect of optical spin and orbital angular momenta, atoms may also experience forces and torques involving an interplay between the internal and centre of mass degrees of freedom. Such interactions lead to new forms of processes including scattering, trapping and rotation and, as a result, they exhibit characteristic new features at the micro-scale and below. A number of distinctive properties involving angular momentum exchange between the light and the atoms are highlighted, and prospective applications are discussed. Comparison is made between the theoretical predictions in this area and the corresponding experiments that have been reported to date.