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Application of Fourier-Fresnel Imaging to Neutral - Atom Interferometry

John F. Clauser

Published Oct 3, 1990• 0 citations
OpenAlex

Abstract

Abstract : This note provides a brief summary of the use of Fourier-Fresnel imaging to neutral atom interferometry. In applications of neutral-atom interferometry not requiring the interferometer to have an open (multiply connected) topology, the use of this imaging has significant advantages, notably ease of alignment, significantly increased through-put flux, ability to work with very short wavelength (and/or high velocity atoms). The results are primarily interesting in that they span the boundary between trapezoidal moire fringes and sinusoidal wave-interference fringes. Their limited applicability, perhaps accounts for the relative obscurity of many of the results to typical curricula of modern-day optics. The emphasis in this note is thus to put existing results (along with some additions that are needed for clarity) in a form suitable for use by techniques available for neutral-atom interferometry.

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Matter-wave/atom interferometry

John F. Clauser, Shifang Li

Although interferometry's earliest and most familiar use is with photons, the discovery of matter-wave (deBroglie-wave) interference for electrons demanded the development of quantum mechanics. Since then, matter-wave interferometry has been performed with neutrons, Cooper electron-pairs, and most recently, with whole atoms and diatomic molecules. This talk describes our recent high-flux atom interferometry experiments using the generalized Talbot-vonLau effect. Our interferometer consists of a sequence of three planar vacuum-slit diffraction gratings, microfabricated from silicon nitride membranes. DeBroglie-wave interference fringes are sensed by measuring the transmission of potassium atoms on a hot- wire as a function of grating relative position. Different spatial Fourier components (up to sixth) in the diffraction pattern are resonant in the interferometer at different atomic velocities (i.e., at different wavelengths). When a laser cooled slow atomic beam is incident, various different diffraction patterns are observed as a function of atomic velocity. In an alternative `Heisenberg Microscope' configuration an incident thermal beam produces a velocity average over different fringe Fourier components. AC modulated weak laser light passing through the interferometer interacts selectively with atoms at a specific velocity. The associated fringe pattern is then ac modulated and revealed by its selective destruction.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Dec 12, 1994•0 citations

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Atom interferometry utilizes wavelike nature of matter and benefits from the short de Broile wavelength of the matterwave.Recently, neutral atoms which are laser cooled down to a few μK or even to a few nK, are used widening the applications of the atomic interferometers.Optical interferometers have been greatly used in precision measurements and atom interferometer can replace the optical interferometers providing better precision.In addition, atomic interferometers have unique feature that

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Atom optics: from basic science to applications

Alain Aspect

Atom Optics is a new branch of Atomic Physics, where one tries to act upon atoms, likewise one can act upon light (photons) in ordinary optics. The goal is therefore to reflect, focus, diffract, make interfere atoms1 .Afew years ago, this was considered as a fundamental goal, as had been the case decades ago for electron optics, or neutron optics. Indeed, it is always important to investigate the quantum behaviour of larger and larger objects, and studying the wave like behaviour of atoms has attracted a lot of attention. Moreover, atoms are objects that are coupled with the environment in a controlable way, in particular via quasi-resonant interaction with light. There is thus a hope to investigate how this coupling with the environment is relevant to the old problem of the division between the quantum world and the classical world2 ,and how it is related to the question of quantum decoherence. To keep in the domain of Atom Optics, the question of the preservation of coherence of the de Brogue waves describing the atomic motion is crucial. Another basic issue is the question of the collisions between atoms, or between an atom and a surface, when the atom is described as a matter-wave. From this point of view, the very interesting recent results in the domain of cold atoms collisions are only a part of what will probably come out, and new approaches may be fruitful. For instance, some collision effects may be considered as non-linear effects of atom optics... On the other hand, almost from the start, Atom Optics has been a domain where the question of applications has been raised. The experience of the many useful applications existing in the domain of electron and neutron optics has clearly shown the way. A first reason for expecting interesting applications to atom optics is the small value of the de Brogue wavelength, in the nanometer range or below, even at very low energies. This opens for instance the possibility of high resolution lithography, or of nanoprobes, at energies low enough to have a soft, non damaging interaction with a surface. Another important class of applications is in atomic interferometry. It can be shown that atomic interferometers (using atoms of mass Mat) are much more sensitive to inertial or gravitational effects3 than photonic interferometers (using photon of energy hw), by a ratio of the order of MatC2 / ho) . Note that this statement is true only under the condtion that the atomic and photonic interferometers under comparison have equivalent geometries, so that present day interferometers do not yet take full advantage of the 1011 factor of potential improvement. However, impressive results have already be demonstrated6. As a matter of fact, many of the papers presented in this symposium are linked to applications, either with atomic interferometers, or related to the possibility of deep focusing of an atomic beams. Most of these applications a Unite de recherche associée au CNRS can be easily understood by analogy with photon optics. However, there are also several features of atom optics that have no analogy in photon optics. The most important one is probably the possibility to increase the luminosity of an atomic beam (i.e. the flux of atoms per per unit time, surface, and solid angle) or —equivalently — to increase the atomic density in the phase space. This is possible by use of laser cooling, which is a dissipative process, and therefore is not constrained by the Liouville theorem. Another distinctive feature of atom optics —this one not particularly an advantage —is the lack of a sudden interface, that would be analogous to a glass-vacuum interface for light. By sudden interface, we mean that some characteristic parameter relevant to the propagation (the index of refraction in the case of light) changes on a scale small compared to the wavelength of the waves that propagate. In atom optics, the interfaces are usually soft, since the potentials acting on the atomic motion usually change on a scale large compared to the de Broglie wavelengths. In this overview, I intend to recall some basic principles of atom optics, and to point out some important analogies and differences with photon optics4 .Iexpect this discussion to be illustrated by the various presentations at this symposium, for which I hope to offer a framework. In addition, I will take the liberty to illustrate my presentation by some examples chosen among results obtained recently in my laboratory, on the subject of atomic mirrors. The comparison between atom optics and photon optics would of course be incomplete if I would not adress the question of the impact of Bose Einstein condensates onto Atom Optics. As many of us, I am convinced that we are assisting to a revolution as important for Atom Optics as the invention of the laser in the domain of Photon Optics, and we are lucky to have a full session on this hot subject.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 1, 1997•0 citations

Atom Interferometry

Peter Hannaford

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.

Measurement Science and Technology•Sep 1, 1997•1 citation

‘‘Heisenberg microscope’’ decoherence atom interferometry

John F. Clauser, Shifang Li

Atom de Broglie--wave interference fringes are revealed by their selective destruction. A thermal potassium beam is transmitted through a Talbot-Lau atom interferometer. Different fringe Fourier components resonate in the interferometer at different atomic velocities. The thermal velocity distribution averages and washes out the high-frequency components. ac-modulated laser light passes through the interferometer, is scattered by atoms at one velocity, and destroys, and thereby reveals via the ac modulation, the associated high-frequency fringe contribution.

Physical Review A•Sep 1, 1994•28 citations

Atom Interferometry

Tim Byrnes, Ebubechukwu O. Ilo-Okeke

This chapter describes the Bose--Einstein condensate (BEC) interferometry. We first introduce the optical interferometer, briefly discussing the role of fringe contrast in observing interference patterns. Next, we examine a BEC interferometer in a Michelson geometry that consists of a BEC in a trapping potential well. The BEC cloud in the potential well is put into a linear superposition of two clouds that travel along different paths in the trap and are recombined using the same light beams. By studying the population of atoms in the different motional states of the BEC clouds that emerge after recombination, we obtain information about the relative phase shift accumulated by the two traveling superposed condensates during the interferometry. We then characterize the atom distribution that is found in the output of the interferometer by finding the probability density distribution and calculating the features of the probability density such as the mean, the variance, and the interference fringe contrast. Finally, we parameterize the effect of two-body collisional interactions on the observed interference fringes in a way that can be directly controlled in an experiment.

Cambridge University Press eBooks•Jul 23, 2021•0 citations
Abstract : This note provides a brief summary of the use of Fourier-Fresnel imaging to neutral atom interferometry. In applications of neutral-atom interferometry not requiring the interferometer to have an open (multiply connected) topology, the use of this imaging has significant advantages, notably ease of alignment, significantly increased through-put flux, ability to work with very short wavelength (and/or high velocity atoms). The results are primarily interesting in that they span the boundary between trapezoidal moire fringes and sinusoidal wave-interference fringes. Their limited applicability, perhaps accounts for the relative obscurity of many of the results to typical curricula of modern-day optics. The emphasis in this note is thus to put existing results (along with some additions that are needed for clarity) in a form suitable for use by techniques available for neutral-atom interferometry.
Although interferometry's earliest and most familiar use is with photons, the discovery of matter-wave (deBroglie-wave) interference for electrons demanded the development of quantum mechanics. Since then, matter-wave interferometry has been performed with neutrons, Cooper electron-pairs, and most recently, with whole atoms and diatomic molecules. This talk describes our recent high-flux atom interferometry experiments using the generalized Talbot-vonLau effect. Our interferometer consists of a sequence of three planar vacuum-slit diffraction gratings, microfabricated from silicon nitride membranes. DeBroglie-wave interference fringes are sensed by measuring the transmission of potassium atoms on a hot- wire as a function of grating relative position. Different spatial Fourier components (up to sixth) in the diffraction pattern are resonant in the interferometer at different atomic velocities (i.e., at different wavelengths). When a laser cooled slow atomic beam is incident, various different diffraction patterns are observed as a function of atomic velocity. In an alternative `Heisenberg Microscope' configuration an incident thermal beam produces a velocity average over different fringe Fourier components. AC modulated weak laser light passing through the interferometer interacts selectively with atoms at a specific velocity. The associated fringe pattern is then ac modulated and revealed by its selective destruction.
Atom Optics is a new branch of Atomic Physics, where one tries to act upon atoms, likewise one can act upon light (photons) in ordinary optics. The goal is therefore to reflect, focus, diffract, make interfere atoms1 .Afew years ago, this was considered as a fundamental goal, as had been the case decades ago for electron optics, or neutron optics. Indeed, it is always important to investigate the quantum behaviour of larger and larger objects, and studying the wave like behaviour of atoms has attracted a lot of attention. Moreover, atoms are objects that are coupled with the environment in a controlable way, in particular via quasi-resonant interaction with light. There is thus a hope to investigate how this coupling with the environment is relevant to the old problem of the division between the quantum world and the classical world2 ,and how it is related to the question of quantum decoherence. To keep in the domain of Atom Optics, the question of the preservation of coherence of the de Brogue waves describing the atomic motion is crucial. Another basic issue is the question of the collisions between atoms, or between an atom and a surface, when the atom is described as a matter-wave. From this point of view, the very interesting recent results in the domain of cold atoms collisions are only a part of what will probably come out, and new approaches may be fruitful. For instance, some collision effects may be considered as non-linear effects of atom optics... On the other hand, almost from the start, Atom Optics has been a domain where the question of applications has been raised. The experience of the many useful applications existing in the domain of electron and neutron optics has clearly shown the way. A first reason for expecting interesting applications to atom optics is the small value of the de Brogue wavelength, in the nanometer range or below, even at very low energies. This opens for instance the possibility of high resolution lithography, or of nanoprobes, at energies low enough to have a soft, non damaging interaction with a surface. Another important class of applications is in atomic interferometry. It can be shown that atomic interferometers (using atoms of mass Mat) are much more sensitive to inertial or gravitational effects3 than photonic interferometers (using photon of energy hw), by a ratio of the order of MatC2 / ho) . Note that this statement is true only under the condtion that the atomic and photonic interferometers under comparison have equivalent geometries, so that present day interferometers do not yet take full advantage of the 1011 factor of potential improvement. However, impressive results have already be demonstrated6. As a matter of fact, many of the papers presented in this symposium are linked to applications, either with atomic interferometers, or related to the possibility of deep focusing of an atomic beams. Most of these applications a Unite de recherche associée au CNRS can be easily understood by analogy with photon optics. However, there are also several features of atom optics that have no analogy in photon optics. The most important one is probably the possibility to increase the luminosity of an atomic beam (i.e. the flux of atoms per per unit time, surface, and solid angle) or —equivalently — to increase the atomic density in the phase space. This is possible by use of laser cooling, which is a dissipative process, and therefore is not constrained by the Liouville theorem. Another distinctive feature of atom optics —this one not particularly an advantage —is the lack of a sudden interface, that would be analogous to a glass-vacuum interface for light. By sudden interface, we mean that some characteristic parameter relevant to the propagation (the index of refraction in the case of light) changes on a scale small compared to the wavelength of the waves that propagate. In atom optics, the interfaces are usually soft, since the potentials acting on the atomic motion usually change on a scale large compared to the de Broglie wavelengths. In this overview, I intend to recall some basic principles of atom optics, and to point out some important analogies and differences with photon optics4 .Iexpect this discussion to be illustrated by the various presentations at this symposium, for which I hope to offer a framework. In addition, I will take the liberty to illustrate my presentation by some examples chosen among results obtained recently in my laboratory, on the subject of atomic mirrors. The comparison between atom optics and photon optics would of course be incomplete if I would not adress the question of the impact of Bose Einstein condensates onto Atom Optics. As many of us, I am convinced that we are assisting to a revolution as important for Atom Optics as the invention of the laser in the domain of Photon Optics, and we are lucky to have a full session on this hot subject.
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.
Atom de Broglie--wave interference fringes are revealed by their selective destruction. A thermal potassium beam is transmitted through a Talbot-Lau atom interferometer. Different fringe Fourier components resonate in the interferometer at different atomic velocities. The thermal velocity distribution averages and washes out the high-frequency components. ac-modulated laser light passes through the interferometer, is scattered by atoms at one velocity, and destroys, and thereby reveals via the ac modulation, the associated high-frequency fringe contribution.
This chapter describes the Bose--Einstein condensate (BEC) interferometry. We first introduce the optical interferometer, briefly discussing the role of fringe contrast in observing interference patterns. Next, we examine a BEC interferometer in a Michelson geometry that consists of a BEC in a trapping potential well. The BEC cloud in the potential well is put into a linear superposition of two clouds that travel along different paths in the trap and are recombined using the same light beams. By studying the population of atoms in the different motional states of the BEC clouds that emerge after recombination, we obtain information about the relative phase shift accumulated by the two traveling superposed condensates during the interferometry. We then characterize the atom distribution that is found in the output of the interferometer by finding the probability density distribution and calculating the features of the probability density such as the mean, the variance, and the interference fringe contrast. Finally, we parameterize the effect of two-body collisional interactions on the observed interference fringes in a way that can be directly controlled in an experiment.