Atom Interferometry

C.S. Adams; O. Carnal1; J. Mlynek    Fakultät für Physik, Universität Konstanz, Konstanz, Germany
1 Norman Bridge Laboratory of Physics, California Institute of Technology, Pasadena, California 91125.

I Introduction

The essential character of a wave is the property of interference. The wave nature of light was established by Young’s demonstration of interference using a double slit in 1802. Interferometry with light soon developed into an important tool for precision measurement. Soon after de Broglie’s suggestion in 1925 that massive particles can behave as waves, diffraction of both electrons (Davisson and Germer, 1927; Thomson, 1927) and atoms (Estermann and Stern, 1930) was demonstrated. However, some time passed before interference between spatially separated particle beams was observed. In 1954 Marton et al. demonstrated the first massive particle interferometer by diffraction of electrons from thin metal films. A similar three-grating interferometer for neutrons based on Bragg diffraction from crystals was realized by Rauch et al. (1974).

Progress on interferometry with atoms was hindered by the short de Broglie wavelength and because, unlike neutrons, atoms do not penetrate through matter. However, recently an explosion of activity has occurred in atom interferometry that was stimulated by two main developments: First, progress in microfabrication technology now permits the production of structures sufficiently fine to diffract thermal atomic beams to significant angles. Second, the development of intense tunable lasers allowed rapid progress in techniques to manipulate the trajectories of neutral atoms by means of light forces. In 1991 atom interferometers based on diffraction from microfabricated structures were reported by Carnal and Mlynek (1991) and Keith et al. (1991). Not long after, Riehle et al. (1991) applied the technique of optical Ramsey excitation to demonstrate the Sagnac effect for atoms, and Kasevich and Chu (1991) reported a high sensitivity to gravitational fields using the Ramsey technique in an atomic fountain. Atomic interference has also been observed by nonadiabatic passage of an atomic beam through separated regions with static electric (Sokolov and Yakolov, 1982) and magnetic (Robert et al., 1991) field gradients. The considerable potential of atom interferometry for precision measurement of gravitational or inertial effects (Kasevich and Chu, 1992) and atomic properties (Weiss et al., 1993a) has been demonstrated. In addition, the first experiments to exploit the spatial separation of an atomic wave function have been reported (Ekstrom, 1993).

The rapid development of atom interferometry raises the question of the advantages of atoms compared to electrons or neutrons. Precision measurement with electron interferometry is difficult due to stray fields and long-range Coulomb interactions with the walls of the vacuum chamber. However, atoms are neutral and therefore much less sensitive to perturbations by static electromagnetic fields. Whereas neutron interferometry requires a particle accelerator or nuclear reactor, atomic beams are relatively easy to produce. There are many species of atoms with a considerable range of properties and masses. Atoms have a complex internal structure that can be probed and modified by means of resonant laser light or static electromagnetic fields. The internal structure allows precision measurement by spectroscopic techniques. The interaction between excited atoms and the vacuum field induces spontaneous relaxation. This is a dissipative process that permits cooling of the atomic system. For atom interferometry, laser cooling is useful for the preparation of slow atomic sources. As demonstrated by Weiss et al. (1993a), a Ramsey-type interferometry based on slow atoms in an atomic fountain has a sensitivity a million times higher than that of a conventional atomic beam. In the interferometer itself, spontaneous emission is undesirable because it degrades the atomic coherence.

This chapter is organized as follows: In Section II we present an elementary treatment of the underlying principles of atom interferometry. The phase evolution of an atomic de Broglie wave and the coherence of an atomic beam are discussed. A beam splitter is a key component in an interferometer. The main techniques used to split an atomic beam coherently are considered in Section III. In Section IV we discuss possible applications of atom interferometry. The second part of the chapter concentrates on existing experiments in atom interferometry. Atom interferometers that have been realized are described, and experiments that use these devices are discussed. The chapter concludes with a summary and outlook. Other reviews of atom interferometry may be found in Levy (1991), Helmcke et al. (1992), and Pritchard (1993).

II General Principles

In quantum mechanics a wave function |Ψ〉 is introduced to describe the statistical properties of an ensemble of similarly prepared systems. The wave function contains information about the internal state and the external motion of the atomic ensemble. For a discrete spectrum of internal states, a pure state may be written as

Ψ〉=Σn|cn〉⊗|n〉

where |cn〉 and |n〉 are the center of mass and the internal wave function of state n. Two classes of interference may be distinguished: interference between different components of the center-of-mass wave function (scalar interference) and interference between different internal states (spinor interference). An example of spinor interference is the Ramsey technique of separated oscillatory fields (Ramsey, 1956): The first interaction generates a superposition of internal states that follow different paths in Hilbert space and interfere in the second interaction. Knowledge of the internal state between the two interaction regions destroys the interference, analogous to “which path” information in a double-slit experiment (see Section II.C). However, whereas Ramsey fringes may be interpreted classically as the precession of a dipole moment or spin, interference between spatially separated paths has no classical analogue. For optical Ramsey excitation (see Section V.C), the distinction between scalar and spinor interference is less clear cut, because the larger photon recoil can result in spatial separation of the paths. This has led to some debate over what qualifies as an atom interferometer, particularly because, at least until now, no experiment based on the optical Ramsey technique has exploited the spatial separation.

The wave function is characterized by an amplitude and a phase. Whereas most experiments measure amplitudes, interferometry measures phase. Two factors determine the sensitivity of an interferometer, the magnitude of the induced phase shift and the accuracy of the phase measurement. For some applications, for example, an atom gyroscope (Section IV.A), the sensitivity can be increased by increasing the area of the interferometer. The detection of atoms follows Poissonian statistics; therefore, the phase uncertainty for a measurement time t is

φ=1Jt

where is the atomic flux. Compared to conventional optics, atomic fluxes are relatively low. Consequently, the sensitivity of an atom interferometer is often limited by counting statistics.

A PHASE EVOLUTION OF AN ATOMIC WAVE

The evolution of the wave function is described by the Schrödinger equation:

|Ψ〉=iℏ∂t|Ψ〉

where H = T + V, T is the kinetic energy operator, and V represents an external perturbation. In an interferometer, V may represent the beam-splitting process or a selective interaction with one arm. Processes that do not conserve the atomic flux, for example, diffraction from a slit, cannot be represented by a Hermitian operator. In this case, the interaction with the slit may be thought of as a state preparation, in which the state subsequently evolves according to the Schrödinger equation.

It is often convenient to express the internal states in terms of the interaction eigenstates. In this basis, the potential energy operator is diagonal but the kinetic energy operator may contain nondiagonal elements that give rise to transitions between the eigenstates. However, if the time dependence of the external perturbation is slow compared to the characteristic time scale for the internal evolution, the off-diagonal terms may be neglected. This is commonly referred to as the adiabatic approximation. In this case, the vector Schrödinger equation decouples into independent scalar equations for each eigenstate. In the following we limit the discussion to one internal state.

An elegant approach to the phase evolution in an atom interferometer is provided by the path-integral approach to quantum mechanics (Feynman and Gibbs, 1965). The path-integral wave function is...