Laser cooling has advanced to the point where atomic motion can no longer be described in terms of discrete particles moving on classical trajectories. Instead, de Broglie wave fields occupy quantum states of a potential created by the interaction between atoms and the light field. Atomic transitions between these quantum states are mediated by optical pumping, in much the same way as transitions were made between internal angular momentum states in Prof. Series' time. Some examples are studied here, with special emphasis on dark states.
Laser cooling has advanced to the point where atomic motion can no longer be described in terms of discrete particles moving on classical trajectories. Instead, de Broglie wave fields occupy quantum states of a potential created by the interaction between atoms and the light field. Atomic transitions between these quantum states are mediated by optical pumping, in much the same way as transitions were made between internal angular momentum states in Prof. Series' time. Some examples are studied here, with special emphasis on dark states.
The techniques of laser cooling have now become sufficiently developed that the focus has shifted toward interesting applications such as the quantum domain of atomic motion.This topic is characterized by the failure of the classical description in which atoms move as point particles whose trajectories can be known: instead, atomic motion must be described as the optics of de Broglie waves.For example, when the de Broglie wavelength λ d B exceeds λορtical, then a classical description is insufficient (Bose condensation is done in the dark, and the quantum condition becomes λdB > nearest.neighbor distance).One of the most fascinating topics of quantized atomic motion in a laser field derives from optical dark states that can even occur in the simplest (two-level) atoms, where there are no magnetic sublevels and the polarization is irrelevant.In spite of the simplicity of this two-level atom case however, the more interesting cases occur in multilevel atoms where the internal magnetic states and external quantum states of atomic motion become truly entangled.Schrödinger called such states "the heart of quantum mechanics" because they led to puzzles such as his famous "cat" and the EPR paradox.
When an atom or a molecule interacts with a light beam, the light emitted or absorbed carries valuable information about the atomic or molecular structure. This phenomenon underlies the whole field of spectroscopy. But the interaction of a photon with an atom can be used to manipulate the atom as well as to probe its structure. For example, in an approach called optical pumping, invented by Alfred Kastler, one can use the resonant exchange of angular momentum between atoms and polarized photons to align or orient the spins of atoms or to put them in nonequilibrium situations. In his original 1950 paper Kastler also proposed using optical pumping to cool and to heat the internal degrees of freedom, calling the phenomena the “effet luminofrigorique” and the “effet luminocalorique.” Another famous example of the use of photon-atom interaction to control atoms is laser cooling. This technique relies on resonant exchange of linear momentum between photons and atoms to control their external degrees of freedom and thus to reduce their kinetic energy. Laser cooling was suggested independently by Theodor Hänsch and Arthur Schawlow for neutral atoms and by David Wineland and Hans Dehmelt for trapped ions. In an article written three years ago for PHYSICS TODAY (June 1987, page 34), Wineland and Wayne Itano presented the principle of laser cooling and the potential applications of cold atoms to fields of physics such as ultrahigh resolution spectroscopy, atomic clocks, collisions, surface physics and collective quantum effects. At that time laser cooling had brought temperatures down to a few hundred microkelvin, but unexpected improvements during the last three years have dramatically lowered those temperatures to only a few microkelvin. We now feel we understand the new physical mechanisms responsible for these very low temperatures.
New laser cooling mechanisms, more efficient than Doppler cooling, allow one to reach new regimes where the quantum nature of the translational degrees of freedom of an atom can no longer be ignored. This paper reviews a few examples of quantum phenomena observable on laser cooled atoms: quantization of atomic motion in an optical potential, de Broglie wavelengths larger than the wavelengths of the laser used to cool the atoms. New theoretical approaches to these problems will be also briefly mentioned.
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.
We propose an alternative method to laser cooling. Our approach utilizes the extreme brightness of a supersonic atomic beam, and the adiabatic atomic coilgun to slow atoms in the beam or to bring them to rest. We show how internal-state optical pumping and stimulated optical transitions, combined with magnetic forces, can be used to cool the translational motion of atoms. This approach does not rely on momentum transfer from photons to atoms, as in laser cooling. We predict that our method can surpass laser cooling in terms of flux of ultracold atoms and phase-space density, with lower required laser power.
As research in quantum optics has advanced, so too has our ability to precisely tailor the quantum state of a system.Indeed, techniques for quantum state preparation have become sufficiently advanced that an entire subfield has appeared which has been given the name "quantum control".. Parallel to these advances have been other striking developments in quantum optics, in particular, laser cooling and trapping of nentral atoms.In this paper we describe some of the recent advancements in laser cooling, particularly in our laboratories, and point out that laser cooling and trapping is also realizing an important form of quantum control.In laser cooling, instead of exercising control over the internal quantum state of an atom or molecule or a laser field, we are instead controlling a complementary set of degrees of freedom: those of the external coordinates of the atom.