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Journal of Physics B Atomic Molecular and Optical Physics

Vortical force exerted on atoms in resonance light

V. E. Shapiro

Published Jul 14, 1990• 3 citations
Publisher

Abstract

The work is aimed at drawing attention to peculiar properties and the considerable magnitude of the vortical part of the light force which make it important for light-induced effects of atomic drift, cooling and trapping in gas. The author introduces basic notions that specify the vortical force, determine its properties and the functional structure and give estimates in the weak-field limit. The vortical force like the light gradient force and the light frictional force sharply increases in the light field resonantly exciting the atom, but depends quite differently on the resonance detunings, wavevectors, polarisation and light wave phases. The results give insight into how to control the vortex effect of light under what conditions it dominates critically the effect of light friction and gradient forces.

DOI
10.1088/0953-4075/23/13/032

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The work is aimed at drawing attention to peculiar properties and the considerable magnitude of the vortical part of the light force which make it important for light-induced effects of atomic drift, cooling and trapping in gas. The author introduces basic notions that specify the vortical force, determine its properties and the functional structure and give estimates in the weak-field limit. The vortical force like the light gradient force and the light frictional force sharply increases in the light field resonantly exciting the atom, but depends quite differently on the resonance detunings, wavevectors, polarisation and light wave phases. The results give insight into how to control the vortex effect of light under what conditions it dominates critically the effect of light friction and gradient forces.
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 interdisciplinary 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.
The usual form of electromagnetic forces is given by but for neutral atoms q = 0. The next order of force is the dipole term, but this also vanishes because neutral atoms have no inherent dipole moment. However, a dipole moment can be induced by a field, and this is most efficient if the field is alternating near the atomic resonance frequency. Since these frequencies are typically in the optical range, dipole moments are efficiently induced by shining nearly resonant light on the atoms. Laser cooling and trapping rely on the interaction between laser light and atoms to exert a controllable force on the atoms, and many sophisticated schemes have been developed using the special properties of the interaction. This chapter begins with the simplest schemes for exerting optical forces on atoms, namely a single-frequency light field interacting with a two-level atom. Although this is the simplest possible scheme, it is pedagogically valuable because it shows many of the features that will be encountered further on. The ultimate temperature using such a scheme is limited, but lower temperatures can be achieved with multilevel atoms. This topic is addressed later in the chapter. Two kinds of optical forces When an atom absorbs nearly resonant light, it makes a transition to the excited state, and its subsequent return to the ground state can be either by spontaneous or by stimulated emission. The nature of the optical force that arises from these two different processes is quite different, and will be described separately [1]. The spontaneous emission case is different from the familiar quantum mechanical calculations using state vectors to describe the state of the system, because spontaneous emission causes the state of the system to evolve from a pure state into a mixed state (see Exercise 6.9). Spontaneous emission is an essential ingredient for the dissipative nature of the optical forces in monochromatic light, and the density matrix is needed to describe it (see Chap. 6). When an atom absorbs light, its energy excites the atom and its angular momentum changes the electron's orbit. Both of these are internal atomic properties. However, the linear momentum of the light, can change only the external, translational motion of the atom.
We consider the velocity-dependent light pressure force on a two-level atom interacting with a two-dimensional nearly resonant standing-wave light field. We show that there can be anisotropic cooling-heating forces that will cool the atoms along one field axis while heating them along the perpendicular axis. The force is identified as a spontaneous vortex force associated with the local traveling-wave character of the two-dimensional field. We provide a simple interpretation of this anomalous force in terms of the interplay between the vortical momentum flow of the light field and a motion-induced population transfer between the ground and excited atomic states.
In the previous chapters, we have seen that the cause of the mechanical effects of light on atoms is nothing more than the momentum exchanged between photons and atoms. This exchange determines both the forces exerted on atoms and, ultimately, the atoms’ translational motion. But now things become even more interesting. In this chapter we present to a new generation of laser beams that have been developed over the last few decades. These beams have quite unusual properties and even more exotic and fascinating applications. They contain optical vortices, as do many other physical systems, and, thus, are known as optical vortex beams.
We show that the normally weak optical quadrupole interaction in atoms is enhanced significantly when the atom interacts at near resonance with an optical vortex. In particular, the forces and torque acting on the atom are shown here to scale up with the square of the winding number l of the vortex. Because the integer l can be arranged to be large, this property allows for processes involving dipole-forbidden, but quadrupole-allowed, transitions in atoms, such as cesium and oxygen, to come into play. We show that the mechanical effects of vortex light on atoms involving translational and rotational motion as well as trapping should be significantly enhanced for quadrupole transitions and present novel features with useful implications for the emerging field of atomtronics.
The interaction of neutral atoms in an external resonance field in a wave zone is considered. It is shown that it may be regarded as the result of pressure on the atom exerted by light scattered by the second atom. Depending on the field intensity, the atoms may either attract or repel each other. In a strong field the force obeys the Coulomb-type law with an effective charge which depends on the field intensity and atom velocities. In a finite-density gas the interaction is comparable to the light pressure force. This may be important in studies of the kinetics of atoms in a resonant field.