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Physical Review A

Theory of radiation forces and momenta for mobile atoms in light fields

V. E. Lembessis, M. Babiker, C. Baxter, R. Loudon

Published Aug 1, 1993• 65 citations
Publisher

Abstract

A theory for a bound system of charges interacting with electromagnetic fields is developed, with special emphasis on the radiation-pressure effects imposed by the fields on the gross motion of the charges. The theory is particularly simple and transparent for the case of two opposite charges of finite mass M in the electric-dipole approximation. This enables a rigorous description to be given for the quantum electrodynamics of the problem with the various interaction terms affecting the gross motion being easily identified. Here, too, it becomes clear that, even in the dipole approximation, the conventional interaction term should be supplemented by the so-called R\"ontgen term. Besides ensuring the consistency of the theory for the overall (charges plus fields) system regarding conservation laws, the R\"ontgen term has dynamical consequences. This is established by explicit calculations of the expectation values of the mechanical momentum 〈MR\ifmmode \dot{}\else \.{}\fi{}〉 and the radiation pressure force 〈MR\ifmmode\ddot\else\textasciidieresis\fi{}〉 on a two-level atom in the dipole approximation. Results of calculations are displayed for the case of a single light beam and for counterpropagating beams. The feasibility of experimentally observing the transverse force is explored. Generalizations of the well-known friction force arising in one-dimensional optical molasses are given and discussed.

DOI
10.1103/physreva.48.1594

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CRC Press eBooks•Apr 19, 2016•0 citations
A theory for a bound system of charges interacting with electromagnetic fields is developed, with special emphasis on the radiation-pressure effects imposed by the fields on the gross motion of the charges. The theory is particularly simple and transparent for the case of two opposite charges of finite mass M in the electric-dipole approximation. This enables a rigorous description to be given for the quantum electrodynamics of the problem with the various interaction terms affecting the gross motion being easily identified. Here, too, it becomes clear that, even in the dipole approximation, the conventional interaction term should be supplemented by the so-called R"ontgen term. Besides ensuring the consistency of the theory for the overall (charges plus fields) system regarding conservation laws, the R"ontgen term has dynamical consequences. This is established by explicit calculations of the expectation values of the mechanical momentum 〈MR\ifmmode \dot{}\else .{}\fi{}〉 and the radiation pressure force 〈MR\ifmmode\ddot\else\textasciidieresis\fi{}〉 on a two-level atom in the dipole approximation. Results of calculations are displayed for the case of a single light beam and for counterpropagating beams. The feasibility of experimentally observing the transverse force is explored. Generalizations of the well-known friction force arising in one-dimensional optical molasses are given and discussed.
A theory of radiation pressure and its effects on the gross motion of an aggregrate of charges is established within a canonical framework. The theory indicates the existence of radiation-pressure effects arising from an additional interaction--the R\"ontgen interaction--whose origin is the classical R\"ontgen current. A careful development of the formalism reveals the importance of distinguishing between the canonical and mechanical momenta of the gross motion of the aggregate and of incorporating the R\"ontgen-type interaction terms when calculating the gross-motion dynamics. A form of the R\"ontgen interaction is present even in the dipole approximation: an effect which has previously been ignored but which is necessary to ensure gauge invariance of the radiation-induced mechanical force. Explicit calculations of the rates of change of canonical and mechanical momenta are presented for a general atomic dipole, with specializations to a two-level atom, revealing the presence of velocity-dependent terms in a natural way. The formalism is consistent with the Minkowski form of the classical momentum density of an electromagnetic field.
The Röntgen term is an often neglected contribution to the interaction between an atom and an electromagnetic field in the electric dipole approximation. In this work we discuss how this interaction term leads to a difference between the kinetic and canonical momentum of an atom which, in turn, leads to surprising radiation forces acting on the atom. We use a number of examples to explore the main features of this interaction, namely forces acting against the expected dipole force or accelerations perpendicular to the beam propagation axis.
A general theory of the motion of a two-level atom in a resonant or near-resonant electromagnetic wave of arbitrary amplitude and phase, including effects of radiative relaxation due to interaction with the quantized vacuum field, is developed from first principles. Particular emphasis is placed on the effects of quantum-mechanical fluctuations of the radiation force and on the associated diffusion of atomic momentum due to spontaneous and induced absorption and emission processes. Analytic results and numerical examples are presented for (1) the lower bound on the temperature achievable by radiation cooling in a standing wave tuned below resonance, (2) the heating rate in a strong resonant standing wave, (3) the maximum confinement time for an atom in a Gaussian radiation trap, (4) the deflection and spreading of an atomic beam transversely illuminated by a strong resonant running wave, and (5) the transverse cooling of an atomic beam by a strong running wave tuned below resonance.
A theory of the changes in momenta suffered by the translational motion of a two-level atom due to interaction near resonance within uniform light, is presented. The leading changes in the translational energy are first derived and the changes in the momenta due to the irradiation are then deduced from these in a simple and transparent manner. The derivation depends on the inclusion of a quantum interaction term whose classical origin is the Rontgen current in the electric dipole approximation. Thus the theory presented differs considerably from conventional approaches which are normally based on considerations of the transition rates and do not include the effects of the Rontgen term. The momentum changes obtained can be expressed in terms of the susceptibility and its first derivative, and are shown to be independent of the state of the atomic translation. They depend, mainly in sign, on whether the atom is in its ground or excited state. These features lead to a simple derivation of the average momentum changes induced by the irradiation of an atomic system.
A theory is developed that leads to the description of the internal and gross motions of an atom interacting with an arbitrary light field. The general results are then applied to the case of a Laguerre-Gaussian (LG) mode, one of a class of modes of electromagnetic radiation that possess orbital angular momentum. A number of effects are predicted, notably, an azimuthal shift in the atomic resonance, a modified radiation pressure force, and an associated torque on the atom. It is pointed out that the effects originate in the processes of the transfer of linear and orbital angular momentum from the field to the atomic gross motion. The strengths of the effects are assessed in relation to the normal axial Doppler shift and the linear light pressure force. The motion of atoms and ions subject to the LG pressure force is studied by solving the classical equation of motion. Trajectories clearly exhibiting the effects of orbital angular momentum are displayed for a free atom and for an ion in a two-dimensional trap and in a Paul trap.
It has been known for some time that the interaction of laser light with a free atom can give rise to electromagnetic pressure forces that act on its centre of mass. These forces have been extensively examined both theoretically and experimentally: see, for example Metcalf and van der Straten (5.1) or Adams and Riis (5.2). A simple model of a two-level atom subject to a plane electromagnetic wave may be shown to give rise to two kinds of force acting on the atom centre of mass. These are, a dissipative force arising from the absorption of the light by the atom and its subsequent spontaneous emission in a random direction and a dipole force arising from the non-uniformity of the field distribution which can attract the atom to the regions of intense field. These forces underpin the manipulation of atoms by lasers in a variety of beam configurations. The dissipative force has been exploited in the Doppler cooling of the atomic motion (5.3, 5.4) and the dipole force used for trapping (5.5), while a combination of these effects has led to the realisation of Bose-Einstein condensation (5.6). These forces are, of course, closely related to the ones discussed in Section 4.