Interference with atomic and molecular matter waves is a rich branch of atomic physics and quantum optics. It started with atom diffraction from crystal surfaces and the separated oscillatory fields technique used in atomic clocks. Atom interferometry is now reaching maturity as a powerful art with many applications in modern science. In this review the basic tools for coherent atom optics are described including diffraction by nanostructures and laser light, three-grating interferometers, and double wells on atom chips. Scientific advances in a broad range of fields that have resulted from the application of atom interferometers are reviewed. These are grouped in three categories: ͑i͒ fundamental quantum science, ͑ii͒ precision metrology, and ͑iii͒ atomic and molecular physics. Although some experiments with Bose-Einstein condensates are included, the focus of the review is on linear matter wave optics, i.e., phenomena where each single atom interferes with itself.

We measure the decoherence of a spatially separated atomic superposition due to spontaneous photon scattering. We observe a qualitative change in decoherence versus separation as the number of scattered photons increases, and verify quantitatively the decoherence rate constant in the manyphoton limit. Our results illustrate an evolution of decoherence consistent with general models developed for a broad class of decoherence phenomenon.03.65. Bz,03.75.Dg Decoherence is the result of entanglement between a quantum system and an unobserved environment, and manifests as the reduction of coherent superpositions into incoherent mixtures. This reduction occurs more quickly as the number of particles comprising a quantum system increases, establishing decoherence as a fundamental limit to large-scale quantum computation [1] and communication [2]. Progress in these fields therefore relies upon understanding and correcting for decoherence effects. On a macroscopic scale, decoherence is unavoidable and explains the emergence of classical behavior in a world governed by quantum mechanical laws.

We measured the ground-state electric-dipole polarizability of sodium, potassium, and rubidium using a Mach-Zehnder atom interferometer with an electric-field gradient. We find α Na = 24.11(2) stat (18) sys × 10 −24 cm 3 , α K = 43.06 (14)(33), and α Rb = 47.24(12)(42). Since these measurements were all performed in the same apparatus and subject to the same systematic errors, we can present polarizability ratios with 0.3% uncertainty. We find α Rb /α Na = 1.959(5), α K /α Na = 1.786(6), and α Rb /α K = 1.097(5). We combine our ratio measurements with the higher-precision measurement of sodium polarizability by Ekstrom et al. [Phys. Rev. A 51, 3883 (1995)] to find α K = 43.06(21) and α Rb = 47.24(21).

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