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 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.
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 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.
An atomic electron, in the vacuum of photons, can emit and reabsorb photons of any frequency. Such processes give rise to well known radiative corrections (Lamb—shift, g — 2, natural width of excited states...). We review in this paper similar effects which can be induced by the interaction of an atomic electron with an incident electromagnetic wave, and we try to get some physical insight in radiative processes by comparing these two types of « spontaneous » and « induced » effects. Optical pumping methods have been very useful for studying how atoms are perturbed by optical or RF photons. The Zeeman sublevels of an atomic ground state are broadened and shifted by a resonant or quasiresonant optical irradiation. The corresponding light-shifts (or « Lamp-shifts » as A. Kastler called them) are due to virtual absorptions and reemissions of incident photons. Another example of an induced effect is the modification of the magnetic properties of an atomic level due to a high frequency non resonant RF irradiation. The Larmor precession is slowed down and becomes anisotropic. The two previous examples correspond to two situations leading to simple calculations. For a resonant or quasiresonant excitation, a single atomic transition needs to be considered. Non perturbative treatments can be given which include the effect of the atom field coupling to all orders. For example, the « dressed atom » approach allows a unified treatment of various effects such as light shifts, Autler-Townes doublets resonance fluorescence triplets... On the other hand, for a high frequency irradiation, all atomic transitions must be included. It is possible in this case to derive an effective hamiltonian describing, to lowest order in the fine structure constant α, how electronic energy levels are perturbed in the presence of N photons ω. The remaining part of the paper is devoted to the analysis of such a situation. The terms of the effective hamiltonian proportional to the number N of incident photons correspond to the induced effects. They can be fully interpreted in semiclassical terms and they describe how the slow motion of the electron in the external static fields is modified by the high frequency vibration in the incident monochromatic wave. For example, the vibrating electron averages the static potential over a finite length, the angular oscillation of the spin reduces the effective magnetic moment. The remaining terms, which are independent of N, exist even in the vacuum of photons (N = 0) and describe the contribution of the mode ω to spontaneous radiative corrections. It is possible to split them into two parts. The first one has the same structure as the N-dependent terms, with N replaced by 1/2. It describes the corrections due to the vibration of the electron in vacuum fluctuations which have a spectral power density ħω/2 per mode. The second part represents the effect of radiation reaction, i.e. the interaction of the electron with its self field. Such an interpretation is confirmed by a Heisenberg equations approach where the total force acting upon the electron is split into two physical (i.e. hermitian) parts representing respectively the effect of the vacuum « free » field and the effect of the « source » field produced by the electron itself. These considerations are finally applied to the problem of the positive sign of g - 2. The g-factor can be written as 2 ωL/ωc, where ω L is the Larmor frequency of the spin and ωc the cyclotron frequency of the charge for an electron in a weak static field B 0. In the absence of radiative corrections, g = 2, and ω L = ωc. To lowest order in 1/c (order zero), radiation reaction slows down ωc but not ωL (a charge is more coupled to its self field than a magnetic moment). The effect of vacuum fluctuations appears only at order 2 in 1/c and corresponds to relativistic and magnetic effects which slow down both ωL and ωc. Therefore, it appears that, in the non relativistic domain, the main effect is a reduction of ωc by radiation reaction and this explains why 2 ωL/ωc becomes larger than 2. A complete relativistic calculation (to all orders in 1/ c, but to lowest order in α) does not change this conclusion since the contribution of non relativistic modes (ħω < mc2) is predominant in the integral giving g — 2.
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.
In this chapter a quantum mechanical treatment of atomic response to the fields of an electromagnetic wave is presented. Absorption and emission of energy by atoms involves transition between their quantized energy levels driven by an interaction Hamiltonian. Schrodinger equation is used to derive the equations of motion for the density matrix of the atom, which is better suited to include the effects of mechanisms other than the interaction Hamiltonian – collisions, level decays, level shifts, etc. that also affect the state of the atom. Using the density matrix equation of motion and focusing on two atomic levels, induced dipole moment for a single two-level atom and polarization and susceptibility for a collection of two-level atoms, including the effects of level decays, and collisions, are calculated. Equations of motion for level populations are also derived. These expressions naturally predict stimulated emission as well as absorption. Expressed in terms of spontaneous emission rate they confirm the validity of equations derived in Chapter 5 using the dipole oscillator model of atomic response. The limit in which quantum mechanical equations for atomic response reduce to the classical dipole oscillator equations is also discussed.
A detailed investigation of the momentum absorbed by an atom from resonant light is presented in this thesis. The major topic to be addressed concerns the dependence of absorbed momentum upon the initial quantum state of the atom. This dependence is exploited for the purpose of showing that the absorbed momentum can be used to investigate processes where determining this initial state is important. A specific example where this technique can be applied, electron -atom collision studies, is discussed. It is found that in this case, where the determination of coherences between substates of the electron excited level is critical, the method based upon momentum absorption produces the same general formalism as experiments using the superelastic and electron -photon coincidence techniques. A method for creating coherences between substates in the ground level with rf magnetic fields is described. This is proposed as a way of testing the sensitivity of the optical forces to ground state coherences. A quantum electrodynamic theory is used to describe the photon -atom interaction. This allows all of the atomic states that are important in the interaction to be included. The QED theory provides a solution to the density matrix of the atoms as a function of time, which in turn is used to calculate the average momentum transferred to the atom. Several different atomic systems are considered some hypothetical and some real. The systems to be examined include: a two level system, a J=1 J=2 transition, and the 32S111 (F=2) -> 32P312 transition of atomic sodium. Although the latter example is a complex system requiring the solution to a set of at least 59 first order partial differential equations, its theoretical consideration is vital for comparison to the experimental data.