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European Journal of Physics

The three-grating Mach Zehnder optical interferometer: a tutorial approach using particle optics

Alain Miffre, R. Delhuille, B. Viaris de Lesegno, M Büchner, Carlo Rizzo, J. Vigué

Published Oct 15, 2002• 12 citations
Publisher

Abstract

In this paper, we present a tutorial set-up based on an optical three-grating Mach–Zehnder interferometer. As this apparatus is very similar in its principle to the Mach–Zehnder interferometers used with matter waves (neutrons, atoms and molecules), it can be used to familiarize students with particle optics, and in our explanations, we use the complementary points of view of wave optics and particle optics. Finally, we have used this interferometer to measure the index of refraction of BK 7 glass for red light at 633 nm, with a technique equivalent to the one used to measure the index of refraction of solid matter for thermal neutrons. The dimensions of this interferometer and its cost make it very interesting for laboratory courses and the experiment described here can be reproduced by students.

DOI
10.1088/0143-0807/23/6/304

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•Nov 8, 2001•17 citations
In this paper, we present a tutorial set-up based on an optical three-grating Mach–Zehnder interferometer. As this apparatus is very similar in its principle to the Mach–Zehnder interferometers used with matter waves (neutrons, atoms and molecules), it can be used to familiarize students with particle optics, and in our explanations, we use the complementary points of view of wave optics and particle optics. Finally, we have used this interferometer to measure the index of refraction of BK 7 glass for red light at 633 nm, with a technique equivalent to the one used to measure the index of refraction of solid matter for thermal neutrons. The dimensions of this interferometer and its cost make it very interesting for laboratory courses and the experiment described here can be reproduced by students.
The wave-particle duality of light plays a fundamental role in introductory courses on quantum mechanics. Traditionally the wave and particle aspects of light are demonstrated in separate experiments which makes it difficult for students to understand their complementary nature. We present an experiment using a single apparatus that demonstrates the wave aspect, the particle aspect, and most importantly, their coexistence. The apparatus is based on a Mach-Zehnder interferometer in which a light beam is attenuated so that at each instant there is only a single photon in the interferometer. In this way the observation of single photon interference becomes possible. By integrating the single photon events in a storage oscilloscope the evolution toward classical interference fringes can be shown in real time. A second strong laser beam, derived from the same pointer, but slightly displaced, traverses the interferometer at the same time, allowing the simultaneous demonstration of wave aspects. Special features of the setup are low cost, simplicity, didactical power and suitability for presentations in large lecture halls using both multimedia projections and audible signals.
Matter - wave interferometry began with the development of electron interferometers and neutron interferometers in the 1950s and 1960s, but it wasn't until 1991 that the first atom matter - wave interferometer was realized. This was followed by a surge of activity sparked by the advent of sources of ultracold laser-cooled atoms. Some of the potential advantages of atom interferometry over neutron interferometry include: much higher particle fluxes, lower particle velocities, larger particle masses, particles with internal states, and laboratory-based sources. This volume is the first text on atom interferometry. It consists of ten comprehensive review articles by leading researchers in the field, many of whom pioneered the first atom interferometers in 1991. The articles describe the different types of atom interferometers developed to date, ranging from the three-grating Mach - Zehnder interferometer based on nanofabricated grating structures (MIT) or standing-wave light-field gratings (Innsbruck), to the Talbot - Lau atom interferometer (Berkeley and Michigan), to atom interferometers based on internal-state labelling such as separated light-field interferometers (PTB, Hannover and Paris-Nord) and light-pulse interferometers (Stanford). Some of the recent applications of atom interferometry described in the articles include high precision measurements of rotations, the gravitational acceleration, and the fine structure constant (Stanford); measurements of topological phases (PTB and Hannover); correlation experiments with atoms and photons (Konstanz) and with pairs of atoms (Tokyo); holographic manipulation of atoms (Tokyo); and experiments on the quantum theory of measurement (Garching, Harvard and Texas A&M). In summary, this volume provides an excellent up-to-date account of atom interferometry and is recommended as essential reading for all researchers and would-be researchers in the field. At the same time it contains sufficient background material and theory to serve as an excellent introduction for the non-specialist. The field is presently moving at such a rapid pace, however, that many of the latest results reported in this volume will already have been superseded by the time it reaches the library shelves.
\nWe have built an atom interferometer of the Mach-Zehnder type, operating with thermal lithium atoms [1]. Its design is largely inspired by previous works done by the groups of D. Pritchard [2], A. Zeilinger [3] and S.A. Lee [4]. In our apparatus, the atomic wave is diffracted in the Bragg regime by three laser sanding waves to achieve a Mach-Zehnder configuration. This paper briefly recalls the diffraction process and shows the experimental results obtained in our group. Our apparatus is able to achieve a high fringe contrast of 74 % with a large mean detected atom flux of 1.5times1041.5 \\times 10^{4}1.5times104s−1^{-1}−1. Finally, the paper ends with the measurement of the velocity distribution of our lithium beam using a light induced fluorescence technique.\n
We have developed a Mach-Zehnder atom interferometer which uses elastic diffraction of lithium atom on laser standing waves for the coherent manipulation of the atom wave. The interference signal is of sufficient quality to achieve a phase sensitivity near 10 milliradians/. With this apparatus, we have recently measured the index of refraction of several gases for lithium waves. The interference signals give access to the real and imaginary parts of () and we have tested the linear dependence of these two quantities with gas density. The measured values of () are in good agreement with calculations and they exhibit glory oscillations, as predicted by theory.
Abstract Among the various areas of neutron optical research, neutron interferometry has provided some of the most challenging and spectacular developments. In most cases, separated coherent beams are used which are produced either by wavefront division (Young’s type) or by amplitude division (Mach− Zehnder type). These beams are subsequently coherently superposed after passing through regions of space where the neutron wavefunction is modified in phase and amplitude by various interactions: nuclear, magnetic, electromagnetic, gravitational, or by geometry and topology (as in Aharonov−Bohm-type experiments). Various types of neutron interferometers that have been tested are shown in Fig. 2.1. The first neutron interferometer was based upon wavefront division and biprism deflection, but it had several constraints for interferometric applications mainly due to the small beam separation (100 μm) (Maier-Leibnitz and Springer 1962). Nevertheless, this method gained further interest for diffraction experiments from macroscopic objects and for the detection of weak interaction effects where the long flight paths (10 m) enhance the sensitivity for the measurements of these effects (Gähler et al. 1980; Klein et al. 1981a). The perfect-crystal interferometer (Rauch et al. 1974) provides widely separated coherent beams and has become a standard method for advanced neutron optical investigations. The development of diffraction and phase grating interferometers extended the Mach-Zehnder interferometer method to very slow neutrons (loffe et al. 1985; Gruber et al. 1989). The superposition of spin-up and spin-down states in the longitudinal direction provides the basis for Larmor and Ramsey interferometry, where no lateral beam splitting is necessary. The well-known spin-echo systems (Mezei 1972) and zero-field spin-echo systems (Gähler and Golub 1987; Dubbers et al. 1989) are examples of such interferometers, which also play an important role in atom interferometry (Bord é 1989; Kasevich and Chu 1991; Riehle et al. 1991).