Oxford University Press eBooks

Atom-Light Forces

J. Weiner, Frederico Dias Nunes

Published Feb 2, 2017• 0 citations

Abstract

Chapter 11 presents the simplest and most intuitive approach to atom-optical interactions: the atom is modelled as a damped harmonic oscillator with spontaneous emission as the damping agent. The semiclassical viewpoint, in which the atom is treated as a quantum object but the fields are classical, is adopted throughout the chapter. Next, the two-level atom is introduced, which sets the stage for establishing light forces at the atomic level: the dipole-gradient force and the radiation pressure force. The Einstein B coefficient is revisited as stimulated dipole emission. Finally, the optical Bloch equations are used to reformulate more generally the appearance of optical forces and to describe the existence of atom Doppler cooling.

DOI: 10.1093/acprof:oso/9780198796664.003.0011

Related papers

Optical forces and laser cooling

P. van der Straten, Harold J. Metcalf

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.

Cambridge University Press eBooksDec 31, 20150 citations

Section 5. OPTICAL FORCES AND TORQUES ON ATOMS

L. Allen, Stephen M. Barnett, Miles J. Padgett

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.

CRC Press eBooksApr 19, 20160 citations

Atoms in Light: Semiclassical Theory

Peter W. Milonni

Abstract The atom-field interaction is treated in semiclassical radiation theory, starting from the transformation from the minimal coupling Hamiltonian to the electric dipole form used extensively in quantum optics. The Heisenberg and density matrix approaches are developed and applied to two-state atoms, Bloch equations, Rabi oscillations, Maxwell-Bloch equations, and transition rates for absorption and emission. Einstein’s theory of blackbody radiation based on momentum fluctuations and dissipation is reviewed. The Einstein fluctuation formula is derived and used to introduce wave-particle duality, Hanbury Brown-Twiss correlations, and photon bunching.

Jan 31, 20190 citations

Fundamentals and applications

J. Weiner, Ping-Tong Ho

Preface.PART I: LIGHT-MATTER INTERACTION: FUNDAMENTALS.Absorption and Emission of Radiation.Semiclassical Treatment of Absorption and Emission.The Optical Bloch Equations.Optical Bloch Equations of a Two-Level Atom.Quantized Fields and Dressed States.Forces from Atom-Light Interaction.The Laser.Elements of Optics.Index.

Wiley eBooksJan 1, 20031,997 citations

Atom–field interaction – semiclassical theory

Marlan O. Scully, Muhammad Suhail Zubairy

One of the simplest nontrivial problems involving the atom–field interaction is the coupling of a two-level atom with a single mode of the electromagnetic field. A two-level atom description is valid if the two atomic levels involved are resonant or nearly resonant with the driving field, while all other levels are highly detuned. Under certain realistic approximations, it is possible to reduce this problem to a form which can be solved exactly; allowing essential features of the atom-field interaction to be extracted. In this chapter we present a semiclassical theory of the interaction of a single two-level atom with a single mode of the field in which the atom is treated as a quantum two-level system and the field is treated classically. A fully quantum mechanical theory will be presented in Chapter 6. A two-level atom is formally analogous to a spin-1/2 system with two possible states. In the dipole approximation, when the field wavelength is larger than the atomic size, the atom–field interaction problem is mathematically equivalent to a spin-1/2 particle interacting with a time-dependent magnetic field. Just as the spin-1/2 system undergoes the so-called Rabi oscillations between the spin-up and spin-down states under the action of an oscillating magnetic field, the two-level atom also undergoes optical Rabi oscillations under the action of the driving electromagnetic field. These oscillations are damped if the atomic levels decay. An understanding of this simple model of the atom–field interaction enables us to consider more complicated problems involving an ensemble of atoms interacting with the field.

Cambridge University Press eBooksSep 4, 19975 citations

The interaction of atoms with radiation

Christopher J. Foot

Abstract To describe the interaction of a two-level atom with radiation we shall use a semiclassical treatment, i.e. the radiation is treated as a classical electric field but we use quantum mechanics to treat the atom. From the theory of the interaction with radiation, we will be able to find the conditions for which the equations reduce to a set of rate equations that describe the populations of the atomic energy levels (with a steady-state solution). In particular, for an atom illuminated by broad band radiation, this approach allows us to make a connection with Einstein’s treatment of radiation that was presented in Chapter 1; we shall find the Einstein B coefficient in terms of the matrix element for the transition.

Nov 25, 20041 citation