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Physical Review A

Laser cooling of atoms

David J. Wineland, Wayne M. Itano

Published Oct 1, 1979• 798 citations
Publisher

Abstract

Various aspects of the laser cooling of atoms are investigated theoretically. More generally, the authors investigate a process through which the kinetic energy of a collection of resonant absorbers can be reduced by irradiating these absorbers with near-resonant electromagnetic radiation. The process is described here as anti-Stokes spontaneous Raman scattering. Cooling mechanisms, rates, and limits are discussed for both free and bound atoms.

DOI
10.1103/physreva.20.1521

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Various aspects of the laser cooling of atoms are investigated theoretically. More generally, the authors investigate a process through which the kinetic energy of a collection of resonant absorbers can be reduced by irradiating these absorbers with near-resonant electromagnetic radiation. The process is described here as anti-Stokes spontaneous Raman scattering. Cooling mechanisms, rates, and limits are discussed for both free and bound atoms.
Publisher Summary This chapter focuses on the concept of laser cooling of a solid, which may occur when the average energy of the photons emitted by the solid is larger than the energy of the ones it absorbs. More formally, the anti-Stokes emission, which occurs at frequencies larger than that of the pump laser, must dominate the Stokes emission that occurs at smaller frequencies. A crucial additional requirement is that the nonradiative decay rates of the laser-pumped states be negligible in comparison to their radiative decay rates. For the sake of specificity, these states will be taken to be those of a set of isolated ions embedded within an insulating host, although in general they could equally well be those of gas-, liquid-, or solid-phase neutral atoms or molecules, or even those of the energy bands of intrinsic semiconductors. Outside the realm of impurity-doped insulators, recent experiments with semiconductors make net anti-Stokes fluorescence cooling of these materials appear achievable. A long-term idea for improving laser cooling of solids takes advantage of photonic band gap materials. The idea is to fabricate a refractive-index structure within the cooling element that would establish a three-dimensional photonic gap immediately below the pump frequency. In this way, emission at Stokes frequencies falling within the gap would be inhibited, thereby enhancing the cooling power derived from the anti-Stokes emission.
A new method is analyzed for 3-D cooling of solids based on near-resonant, stimulated Raman scattering on a narrowband transition together with optical pumping on a broadband transition. Estimates of achievable cooling rates indicate that Raman cooling offers significant improvement over anti-Stkes fluorescence cooling at cryogenic temperatures and should enable the attainment of sub-Kelvin termperatures, starting from ambient conditions in bulk samples. Also the method is not restricted to ions with small Stokes shifts, and should therefore lead to diversification of the material platforms used for optical refrigeration.
The laser cooling of vibrational states of solids has been achieved through photoluminescence in rare-earth elements, optical forces in optomechanics, and the Brillouin scattering light-sound interaction. The net cooling of solids through spontaneous Raman scattering, and laser refrigeration of indirect band gap semiconductors, both remain unsolved challenges. Here, we analytically show that photonic density of states (DoS) engineering can address the two fundamental requirements for achieving spontaneous Raman cooling: suppressing the dominance of Stokes (heating) transitions, and the enhancement of anti-Stokes (cooling) efficiency beyond the natural optical absorption of the material. We develop a general model for the DoS modification to spontaneous Raman scattering probabilities, and elucidate the necessary and minimum condition required for achieving net Raman cooling. With a suitably engineered DoS, we establish the enticing possibility of refrigeration of intrinsic silicon by annihilating phonons from all its Raman-active modes simultaneously, through a single telecom wavelength pump. This result points to a highly flexible approach for laser cooling of any transparent semiconductor, including indirect band gap semiconductors, far away from significant optical absorption, band-edge states, excitons, or atomic resonances.
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.
The results of a recent experiment on the mechanical interaction of a bichromatic light beam with a single three-level ion serve to redefine laser cooling of ions in a trap and of atoms in standing light waves. Novel variants of light forces are demonstrated. They are caused by stimulated Raman-type two-photon transitions combined with spontaneous Raman scattering and by all-stimulated parametric interaction. These efficient processes parallel the generation of a stimulated light force in a standing wave and the operation of a free-electron laser, respectively. The latter force imposes no natural limit on the residual excitation energy of trapped particles.