Atom Optics with Laser Light

V.S. Letokhov

• Publisher: CRC Press
• Year: 2020
• ISBN:
  9781000674361
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

This book deals specifically with the manipulation of atoms by laser light, describing the focusing, channeling and reflection of atoms by laser fields. It also describes the potential fields required to cause the phase change of the wave function necessary for the atomic interactions to occur.

1. INTRODUCTION

The term of atom optics is due to the natural analogy with light optics or the optics of photons. Light optics is based on the two fundamental principles: (a) the wave properties of light and (b) the electromagnetic interaction between light field and matter or, in other words, between light and bound charged particles (electrons or ions) in a medium. Owing to this interaction, the light field can be reflected by the medium or diffracted by it, or else light can propagate through the medium with some velocity other than the velocity of light in a vacuum, and so on (Bom and Wolf, 1984).

1.1 TYPES OF MASSIVE-PARTICLE OPTICS

According to the de Broglie theory, wavelike properties are associated with any particles of matter, and the de Broglie wavelength is defined by the fundamental relation

${\text{λ}}_{\text{Br}}=\text{h/p}=\text{h/Mv}$

(1.1)

where h is Planck’s constant and p, M, and v are the momentum, mass, and velocity of particle, respectively. The wave properties of massive particles were verified in experiments on the diffraction of electrons and used in the first light optics analog for particles — electron optics (Grivet, 1972). Electron optics is based on (a) the wave properties of electrons and (b) the electromagnetic interaction between moving electronic charge and electrical and magnetic fields of appropriate configuration (Grivet, 1972). The most familiar application of electron optics is electron microscopy (Ruska, 1980).

Another light optics analog is neutron optics based again on (a) the wave properties of ultra cold neutron and (b) the interaction between neutrons and atomic nuclei, which can be described by means of what is known as the optical potential [Sears, 1989]. As distinct from electron optics we deal here with more massive particles (ultra-cold neutrons) whose wave properties manifest themselves at low temperatures; [Shapiro, 1976]. The effect of gravitation and low intensity of ultracold neutron sources make experiment in neutron optics more complex than in electron optics. Nevertheless neutron interferometers [Bonze and Rauch, 1979] and microscopes [Shutz et al., 1980; Frank, 1987, 1991] have already been successfully realized.

The next natural object are neutral atoms or molecules. The wave properties of atoms and molecules and various types of their interaction with matter and electromagnetic fields (from static to optical) make it possible to implement atom and molecular optics. It is precisely the great variety of methods for exerting effect on an atom (or molecule) possessing a static electrical or magnetic moment, a quadruple moment and optic resonance transitions (or a high frequency dipole moment) that form the basis for several possible ways to realize atomic (molecular) optics. Let us consider them briefly.

1.2 METHODS OF REALIZATION OF ATOM OPTICS

The known methods to implement atom optics (atomic–optical effects) can be classed in the following three categories:

(a) methods based on the interaction between atoms and matter;

(b) methods based on the interaction between atoms having a magnetic or electrical dipole moment and a static electrical magnetic field of a suitable configuration;

(c) methods based on the resonance (or quasiresonance) interaction between atom and a laser field.

The first experiment on atom optics realized by method (a) and (b) were succesfully conducted almost a century ago. The advent of tunable laser allowed the possibility to demonstrate atom optics based on the atom-light interaction. It is exactly this type of atom optics that the present review is devoted to. However, for the sake of generality of the physical picture, it seems advisable to recall briefly the milestones in all approaches to atom (molecular) optics.

1.2.1 Interaction Between Atoms and Matter

In his classical monograph, Ramsey (1956) (Chap. 2, Sect. 5) considered the mirror reflection and diffraction of molecular beams on the surface of a solid. According to Ramsey (1956), for mirror reflection to occur, it is necessary that the following two conditions be satisfied.

(a) The projection of the height of surface irregularities on the direction of molecular beam must be shorter than the de Broglie wavelength. Recall an example from light optics: smoked glass is a poor reflector in the case of perpendicular incidence and a good reflector in the case grazing incidence. If δ is the average height of surface irregularities and ϕ is the grazing angle of incident beam, the above requirement may be expressed as (Fig. 1a).

$\delta \text{sin}\varphi {\text{< λ}}_{\text{Br}}$

(1.2)

(b) The average residence time of the particle on the surface must be short. In this case, the state of reflected particles will be the same as that of incident particles.

Fig. 1 Reflection of atom in grazing incidence upon the surface of a solid: (a) requirement for the surface roughness δ, the glancing angle of the incident beam ϕ and the de Broglie wavelength; (b) reflectivity of a beam of He atoms from the surface of LiF crystal at two different temperatures (1 — 295 K; 2 — 100 K), (Estermann and Stern, 1930).

The roughness of most thoroughly mechanically polished surfaces is of the order 10⁻⁵ cm, whereas the de Broglie wavelength of hydrogen at 300 K amounts to 10⁻⁸ cm. Therefore, according to (1.1) and (1.2), the condition for the reflection has the form ϕ < 10 ⁻³ rad.

It was more than 50 years ago that they managed to observe a 5% reflection of hydrogen beam from polished bronze mirror at the grazing angle of ϕ = 10⁻³ grad (Krauer and Stern, 1929). Cleaved crystal surfaces are much more smoother. The thermal vibrations of the crystal lattice limits the roughness of the surface to about 10⁻⁸ cm. In that case a beam of He atoms should undergo reflection at grazing angles less than 20-30 grad. This was confirmed in the experiments (Estermann and Stern, 1930) with He atoms and LiF crystal. (Fig. 1b). The temperature dependence of the grazing angle marking the onset of simple reflection of atoms bears witness of the fact that thermal vibrations have an effect on the surface roughness of crystal.

Experiment on the simple reflection of atoms at the surface of condensed medium continue to draw investigator’s attention. Recall the experiments on the reflection of ⁴He atoms grazing the surface of liquid ⁴He [Nayak et al., 1983] and thermal Cs atoms grazing a polished glass surface [Anderson et al., 1986].

The first experiment aimed at observing the diffraction of atoms by a cleaved crystal surface acting as a two-dimensional, plane grating were conducted by Stern [1929] and the results of detailed research into this phenomena were presented in [Frish and Stern, 1933]. The diffraction of atoms by a fabricated periodic structure (a slotted membrane) with a much more grating period was observed in the work reported in [Keith etal., 1988].

The effect of quantum reflection of ⁴He and ³He beams at a liquid-helium-vacuum interface was successfully used to focus hydrogen atoms with a concave mirror [Berkhout et al., 1989], and the authors of [Carnal et al., 1991] were successful in conducting an experiment on focusing a beam He atoms by means of a zone plate. In [Ekstrum et al., 1992] was proposed the several optical elements based on the microfabricated structures.

Atomic interferometry based on the microfabricated structures was realized in two elegant experiments: The atomic Young’s two slit interferometer [Carnal and Mlynek, 1991] and the atom...