Optics and interferometry with atoms and molecules The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Cronin, Alexander D., Jörg Schmiedmayer, and David E. Pritchard. “Optics and interferometry with atoms and molecules.” Reviews of Modern Physics 81.3 (2009): 1051. © 2009 The American Physical Society As Published http://dx.doi.org/10.1103/RevModPhys.81.1051 Publisher American Physical Society Version Final published version Citable link http://hdl.handle.net/1721.1/52372 Terms of Use Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. REVIEWS OF MODERN PHYSICS, VOLUME 81, JULY–SEPTEMBER 2009 Optics and interferometry with atoms and molecules Alexander D. Cronin* Department of Physics, University of Arizona, Tucson, Arizona 85721, USA Jörg Schmiedmayer† Atominstitut Österreichischen Universitäten, TU-Wien, Austria David E. Pritchard‡ Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA ͑Published 28 July 2009͒ 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. DOI: 10.1103/RevModPhys.81.1051 PACS number͑s͒: 03.75.Be, 03.75.Dg, 37.25.ϩk, 03.75.Pp CONTENTS III. Atom Interferometers 1067 A. Introduction 1067 1. General design considerations 1067 I. Introduction 1052 2. White light interferometetry 1067 A. Interferometers for translational states 1052 3. Types and categories 1068 B. Preparation, manipulation, and detection 1053 B. Three-grating interferometers 1069 C. Scientific promise of atom interferometers 1054 1. Mechanical gratings 1069 II. Atom Diffraction 1055 2. Interferometers with light gratings 1070 A. Early diffraction experiments 1055 3. Time-domain and contrast interferometers 1071 B. Nanostructures 1055 4. Talbot-Lau ͑near-field͒ interferometer 1072 1. Transmission gratings 1056 C. Interferometers with path-entangled states 1073 2. Young’s experiment with atoms 1057 1. Optical Ramsey-Bordé interferometers 1073 3. Charged-wire interferometer 1057 2. Raman interferometry 1074 4. Zone plates 1057 D. Longitudinal interferometry 1075 5. Atom holography 1058 1. Stern-Gerlach interferometry 1075 C. Gratings of light 1058 2. Spin echo 1076 1. Thin gratings: Kapitza-Dirac scattering 1059 3. Longitudinal rf interferometry 1076 2. Diffraction with on-resonant light 1060 4. Stückelberg interferometers 1077 3. Thick gratings: Bragg diffraction 1060 E. Coherent reflection 1077 4. Bloch oscillations 1062 F. Confined atom interferometers with BECs 1077 5. Coherent channeling 1063 1. Interference with guided atoms 1078 D. The Talbot effect 1063 2. Coherent splitting in a double well 1079 E. Time-dependent diffraction 1064 3. Interferometry on atom chips 1080 1. Vibrating mirrors 1064 IV. Fundamental Studies 1081 2. Oscillating potentials 1065 A. Basic questions: How large a particle can interfere? 1081 3. Modulated light crystals 1065 B. Decoherence 1082 F. Summary of diffractive Atom Optics 1066 1. Interference and “welcher-weg” information 1082 G. Other coherent beam splitters 1066 2. Internal state marking 1083 3. Coupling to an environment 1084 a. Decoherence in diffraction 1084 *[email protected] b. Decoherence in Talbot-Lau interferometer 1084 †[email protected] c. Photon scattering in an interferometer 1084 ‡[email protected] d. Scattering from background gas in an 0034-6861/2009/81͑3͒/1051͑79͒ 1051 ©2009 The American Physical Society 1052 Cronin, Schmiedmayer, and Pritchard: Optics and interferometry with atoms and molecules interferometer 1084 observed and exploited for scientific gain. Atom inter- 4. Realization of Feynman’s gedanken ferometers are now valuable tools for studying funda- experiment 1085 mental quantum mechanical phenomena, probing 5. Realization of Einstein’s recoiling slit atomic and material properties, and measuring inertial experiment 1087 displacements. C. Origins of phase shifts 1088 In historical perspective, coherent atom optics is an 1. Dynamical phase shifts 1088 extension of techniques that were developed for ma- 2. Aharonov-Bohm and Aharonov-Casher nipulating internal quantum states of atoms. Broadly effects 1089 speaking, at the start of the 20th century atomic beams 3. Berry phase 1090 were developed to isolate atoms from their environ- 4. Inertial displacements 1091 ment; this is a requirement for maintaining quantum co- D. Extended coherence and BECs 1091 herence of any sort. Hanle ͑1924͒ studied coherent su- 1. Atom lasers 1091 perpositions of atomic internal states that lasted for tens 2. Studies of BEC wave functions 1092 of nanoseconds in atomic vapors. But with atomic 3. Many-particle coherence in BECs 1092 beams, Stern-Gerlach magnets were used to select and 4. Coupling two BECs with light 1094 preserve atoms in specific quantum states for several ms. E. Studies with and of BECs 1095 A big step forward was the ability to change atoms’ in- 1. Josephson oscillations 1096 ternal quantum states using rf resonance as demon- 2. Spontaneous decoherence and number strated by Rabi et al. ͑1938͒. Subsequently, long-lived squeezing 1096 coherent superpositions of internal quantum states were 3. Structure studies of BEC 1097 intentionally created and detected by Ramsey ͑1949͒. 4. Dynamics of coherence in 1D systems 1097 The generalization and application of these techniques 5. Measuring noise by interference 1097 has created or advanced many scientific and technical 6. Momentum of a photon in a medium 1098 fields ͑e.g., precise frequency standards, nuclear mag- F. Testing the charge neutrality of atoms 1099 netic resonance spectroscopy, and quantum information V. Precision Measurements 1099 gates͒. A. Gravimeters, gryroscopes, and gradiometers 1099 Applying these ideas to translational motion required B. Newton’s constant G 1101 the development of techniques to localize atoms and C. Tests of relativity 1101 transfer atoms coherently between two localities. In this D. Interferometers in orbit 1102 view, localities in position and momentum are just an- E. Fine structure constant and ប/M 1102 other quantum mechanical degree of freedom analogous VI. Atomic Physics Applications 1104 to discrete internal quantum states. We discuss these co- A. Discovery of He2 molecules 1104 herent atom optics techniques in Sec. II and the interfer- B. Polarizability measurements 1104 ometers that result in Sec. III. Then we discuss applica- 1. Ground-state dc scalar polarizability 1104 tions for atom interferometers in Secs. IV–VI. 2. Transition dc and ac Stark shifts 1106 C. Index of refraction due to dilute gases 1106 ͑ ͒ D. Casimir-Polder atom-surface potentials 1107 A. Interferometers for translational states 1. vdW-modified diffraction 1108 2. Interferometer vdW and CP measurements 1109 “Atom Optics” is so named because coherent manipu- VII. Outlook 1110 lation of atomic motion requires that the atoms be Acknowledgments 1114 treated as waves. Consequently, many techniques to con- References 1114 trol atom waves borrow seminal ideas from light optics. To make atom interferometers the following compo- nents of an optical interferometer must be replicated: I. INTRODUCTION ͑1͒ state selection to localize the initial state ͑gener- ally in momentum space͒; Atom interferometry is the art of coherently manipu- ͑ ͒ lating the translational motion of atoms ͑and molecules͒ 2 coherent splitting, typically using diffraction to together with the scientific advances that result from ap- produce at least two localized maxima of the wave plying this art. We begin by stressing that motion here function with a well-defined relative phase; refers to center of mass displacements and that coher- ͑3͒ free propagation so that interactions can be ap- ently means with respect for ͑and often based on͒ the plied to one “arm,” i.e., one of the two localized phase of the de Broglie wave that represents this mo- components of the wave function; tion. The most pervasive consequence of this coherence ͑ ͒ is interference, and the most scientifically fruitful appli- 4 coherent recombination so that phase informa- cation of this interference is in interferometers. In an tion gets converted back into state populations; interferometer atom waves are deliberately offered the ͑5͒ detection of a specific population, so the relative option of traversing an apparatus via two or more alter- phase of the wave-function components can be de- nate paths and the resulting interference pattern is termined from interference fringes. Rev. Mod. Phys., Vol. 81, No. 3, July–September 2009 Cronin, Schmiedmayer, and Pritchard: