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International Laser Science Conference

Light traps using spontaneous forces

David E. Pritchard, Carl Wieman, Eric L. Raab, Richard N. Watts, Vanderlei Salvador Bagnato, Richard E. Stoner

Published Jan 1, 1986• 1 citation
Publisher

Abstract

We propose several ideas for neutral atom traps which utilize spontaneous light forces produced by static laser beams. Although the “optical Earnshaw theorem”1 would seem to prohibit such traps, the theorem does not apply if the proportionality constant between force and light intensity is made to vary with position. We suggest possible ways to accomplish this: Zeeman tuning the atom’s resonant frequency by applying a changing magnetic field; varying the quantization axis of the system via a magnetic field cork-screw; utilizing optical pumping effects which arise from matrix element imbalances between hyperfine sublevels in certain atoms. These traps are true in the sense that they provide a potential energy minimum in three dimensions, as well as dissipative cooling. Compared with gradient force light traps, these traps are many times deeper, a million times larger, and can be operated cw.

DOI
10.1364/ils.1986.wf4

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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.

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We propose several ideas for neutral atom traps which utilize spontaneous light forces produced by static laser beams. Although the “optical Earnshaw theorem”1 would seem to prohibit such traps, the theorem does not apply if the proportionality constant between force and light intensity is made to vary with position. We suggest possible ways to accomplish this: Zeeman tuning the atom’s resonant frequency by applying a changing magnetic field; varying the quantization axis of the system via a magnetic field cork-screw; utilizing optical pumping effects which arise from matrix element imbalances between hyperfine sublevels in certain atoms. These traps are true in the sense that they provide a potential energy minimum in three dimensions, as well as dissipative cooling. Compared with gradient force light traps, these traps are many times deeper, a million times larger, and can be operated cw.
We show that the optical Earnshaw theorem does not always apply to atoms and that it is possible to confine atoms by spontaneous light forces produced by static laser beams. A necessary condition for such traps is that the atomic transition rate cannot depend only on the light intensity. We give several general approaches by which this condition can be met and present a number of specific trap designs illustrating these approaches. These traps have depths on the order of a kelvin and volumes of several cubic centimeters.
Radiation pressure forces have been proposed for making stable optical traps for neutral atoms and other dielectric particles. Recently introduced optodynamic or alternating beam traps based on the scattering force are compared with cw traps based on the gradient force. Trapping experiments on micron-sized dielectric particles are described which demonstrate the basic principles of alternating beam light trapping. The relationship of these traps to the optical Earnshaw theorem is considered. The implications for trapping of recently demonstrated sources of slow atoms are also discussed.
Atom traps Light forces It is well known that a light beam carries momentum and that the scattering of light by an object produces a force. This property of light was first demonstrated by Frish [139] through the observation of a very small transverse deflection (3 × 10 –5 rad) in a sodium atomic beam exposed to light from a resonance lamp. With the invention of the laser, it became easier to observe effects of this kind because the strength of the force is greatly enhanced by the use of intense and highly directional light fields, as demonstrated by Ashkin [20, 21] with the manipulation of transparent dielectric spheres suspended in water. The results obtained by Frish and Ashkin raised the possibility of using light forces to control the motion of neutral atoms. Although the understanding of light forces acting on atoms was already established by the end of the 1970s, unambiguous demonstration of atom cooling and trapping was not accomplished before the mid 1980s. In this section we discuss some fundamental aspects of light forces and schemes employed to cool and trap neutral atoms. The light force exerted on an atom can be of two types: a dissipative, spontaneous force and a conservative, dipole force. The spontaneous force arises from the impulse experienced by an atom when it absorbs or emits a quantum of photon momentum.
There has been considerable activity recently on cooling and trapping atoms using laser light. This work raises expectations that laser manipulation of atoms will be an important new tool for atomic physics. However, up to now, almost all the work has been on sodium atoms using light from dye lasers. The expense and complication of a narrowband dye laser system is a considerable limitation on the possible uses of this tool. In response to this we have been exploring the use of inexpensive diode lasers for the manipulation of atoms. We have found that diode lasers work very well for this purpose and even have some advantages over dye lasers in addition to cost and ease of use. We previously reported using light from diode lasers to stop a beam of atomic cesium. Here we discuss our more recent work using diode lasers to produce extremely cold cesium vapor via optical molasses cooling and the demonstration of a new type of optical trap. This is a purely optical spontaneous force trap which uses spatially inhomogeneous optical pumping to circumvent the optical Earnshaw theorem.
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.