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European Quantum Electronics Conference (EQEC)

A charged wire interferometer for atoms

S. Nowak, N. Stuhler, Tilman Pfau, J. Mlynek

Published Aug 24, 2005• 0 citations
Publisher

Abstract

Atom interferometers have been successfully applied for precision measurements and the realization of basic gedanken experiments [1]. They consist of three or more atom optical elements to split, redirect, and recombine the motional state of the atoms. These elements are implemented either by freestanding microstructures or by light fields. For high precision applications, such as gyroscopes [2–5], a large throughput of the initial atomic flux is advantageous [6]. In order to efficiently use all atoms in an uncollimated thermal atomic beam, the ideal atom interferometer should produce equally spaced fringes for a wide range of transverse and longitudinal velocities. So called “white light” interferometers solve the problem for different longitudinal velocities by the recombination of only two velocity independent transverse momentum states at the output of the interferometer. Examples for this are the three-grating interferometer [7], operating with a transversely collimated beam, and the Raman interferometer [8]. Operation using a transversely uncollimated atomic beam can also be realized by the Raman interferometer and, for interferometers that do not require light, by the Talbot-Lau interferometer [9]. The latter, in contrast to Ref. [7], operates with three gratings in the Fresnel regime of matter wave diffraction. Since, in this case, many different momentum components build up the interference pattern, the typical length scale of the setup, the Talbot length, depends on the atomic velocity. The Talbot-Lau interferometer is, therefore, chromatic. In this work, we study a charged wire as the central element in an atom interferometer that requires only microstructures, operates in the Fresnel regime, and accepts, therefore, an uncollimated beam of atoms. At the same time, it has essentially white light character over the range of the atomic velocities in our thermal atomic beam. This makes future extensions of our approach based on microstructures potentially as powerful as, for example, the Raman interferometer gyroscope [5]. The attractive interaction between the induced dipole and the charged wire redirects the atomic trajectories to form a simple interferometer with two spatially separated paths. It can, therefore, also be used to measure the recently proposed topological phase shifts for moving electric dipoles [10–13].

DOI
10.1109/eqec.1998.714728

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Abstract : An atom interferometer is constructed in which the atom waves are physically separated prior to being recombined. Fabricated transmission gratings are used as optical elements for the matter waves. Atom interferometers should be useful in studies of atomic properties, tests of basic quantum physics, for metrology, as rotation sensors, and perhaps ultimately as devices to make ultra- small structures using atom holograms. During the last year our atom interferometer has evolved from a rough plan to an essentially complete device. At present all the major components of the interferometer have been built, and tested at least once. The system will be given its first real try in the next year. Our interferometer consists of three 0.2 microns - period diffraction gratings equally spaced approx. 0.65 m apart in our atomic beam machine. The maximum separation of the beams will be approx. 60 microns. The first two gratings separate and redirect the atomic beam forming a standing wave interference pattern in the atomic flux at the third grating, which acts like a mask to sample this pattern. A principle technical obstacle is the mechanical vibrations of our machine which will blur the interference pattern.

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Matter-wave/atom interferometry

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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.

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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.

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This cumulative thesis consists of four publications [1-4], presented as three contributions (I) - (III), where the second one (II) consists of the joint publications [2,3]. All publications were written during the author's research activities at the Institute of Quantum Physics under the supervision of Prof. Dr. W. P. Schleich. All of the presented publications consider light-matter interactions and their potential application in atom interferometry, a comparatively young and rapidly evolving technique. Atom interferometers find application in high-precision measurements, the determination of physical constants, the testing of fundamental physics, and the provision of gravimeters and gyroscopes. The advancement of technology and science has led to significant improvements in performance and the development of ambitious mobile and space-based devices. The recent success of several experiments has led to the proposal of further experiments with the aim of opening up new frontiers. 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It discusses the fundamental differences between the mechanisms and geometries with respect to the diffraction efficiency, taking into account the width of the initial wave function and the duration of the light pulse. Additionally, it explores the transition between the two diffraction geometries when starting from an atom initially at rest and increasing its momentum. The results may serve as a reference for experimentalists in selecting the most suitable configuration, based on their aims and requirements in the realization of more advanced atom interferometers. The second contribution (II) is a follow-up to the previous one, but focuses exclusively on a single diffraction type in microgravity, namely the so-called double Raman diffraction. In contrast to the previous article, where we only discussed single two-photon processes, we consider in this article a six-photon process, also known as third-order diffraction, as well as three subsequent two-photon processes, which both lead to the same amount of transferred momentum and can both be used to realize large-momentum transfer (LMT). We demonstrate that third-order double Raman diffraction is a viable and advantageous method for the diffraction of small momentum distributions like Bose-Einstein condensates (BECs) compared to a sequence of three two-photon processes. Furthermore, we show that third-order Raman pulses can be successfully applied to create higher-order Raman atom interferometers. Third-order diffraction can be perfectly combined with other LMT techniques and, moreover, allows for a reduction in the overall duration of the diffraction process and the complexity of the experimental set-up, as only two distinct laser frequencies are required. 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A new type of hybrid atom-light interferometer is demonstrated with atomic Raman amplification processes replacing the beam splitting elements in a traditional interferometer. This nonconventional interferometer involves correlated optical and atomic waves in the two arms. The correlation between atoms and light developed with the Raman process makes this interferometer different from conventional interferometers with linear beam splitters. It is observed that the high-contrast interference fringes are sensitive to the optical phase via a path change as well as the atomic phase via a magnetic field change. This new atom-light correlated hybrid interferometer is a sensitive probe of the atomic internal state and should find wide applications in precision measurement and quantum control with atoms and photons.

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Atom interferometers have been successfully applied for precision measurements and the realization of basic gedanken experiments [1]. They consist of three or more atom optical elements to split, redirect, and recombine the motional state of the atoms. These elements are implemented either by freestanding microstructures or by light fields. For high precision applications, such as gyroscopes [2–5], a large throughput of the initial atomic flux is advantageous [6]. In order to efficiently use all atoms in an uncollimated thermal atomic beam, the ideal atom interferometer should produce equally spaced fringes for a wide range of transverse and longitudinal velocities. So called “white light” interferometers solve the problem for different longitudinal velocities by the recombination of only two velocity independent transverse momentum states at the output of the interferometer. Examples for this are the three-grating interferometer [7], operating with a transversely collimated beam, and the Raman interferometer [8]. Operation using a transversely uncollimated atomic beam can also be realized by the Raman interferometer and, for interferometers that do not require light, by the Talbot-Lau interferometer [9]. The latter, in contrast to Ref. [7], operates with three gratings in the Fresnel regime of matter wave diffraction. Since, in this case, many different momentum components build up the interference pattern, the typical length scale of the setup, the Talbot length, depends on the atomic velocity. The Talbot-Lau interferometer is, therefore, chromatic. In this work, we study a charged wire as the central element in an atom interferometer that requires only microstructures, operates in the Fresnel regime, and accepts, therefore, an uncollimated beam of atoms. At the same time, it has essentially white light character over the range of the atomic velocities in our thermal atomic beam. This makes future extensions of our approach based on microstructures potentially as powerful as, for example, the Raman interferometer gyroscope [5]. The attractive interaction between the induced dipole and the charged wire redirects the atomic trajectories to form a simple interferometer with two spatially separated paths. It can, therefore, also be used to measure the recently proposed topological phase shifts for moving electric dipoles [10–13].
Abstract : An atom interferometer is constructed in which the atom waves are physically separated prior to being recombined. Fabricated transmission gratings are used as optical elements for the matter waves. Atom interferometers should be useful in studies of atomic properties, tests of basic quantum physics, for metrology, as rotation sensors, and perhaps ultimately as devices to make ultra- small structures using atom holograms. During the last year our atom interferometer has evolved from a rough plan to an essentially complete device. At present all the major components of the interferometer have been built, and tested at least once. The system will be given its first real try in the next year. Our interferometer consists of three 0.2 microns - period diffraction gratings equally spaced approx. 0.65 m apart in our atomic beam machine. The maximum separation of the beams will be approx. 60 microns. The first two gratings separate and redirect the atomic beam forming a standing wave interference pattern in the atomic flux at the third grating, which acts like a mask to sample this pattern. A principle technical obstacle is the mechanical vibrations of our machine which will blur the interference pattern.
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.
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.
This cumulative thesis consists of four publications [1-4], presented as three contributions (I) - (III), where the second one (II) consists of the joint publications [2,3]. All publications were written during the author's research activities at the Institute of Quantum Physics under the supervision of Prof. Dr. W. P. Schleich. All of the presented publications consider light-matter interactions and their potential application in atom interferometry, a comparatively young and rapidly evolving technique. Atom interferometers find application in high-precision measurements, the determination of physical constants, the testing of fundamental physics, and the provision of gravimeters and gyroscopes. The advancement of technology and science has led to significant improvements in performance and the development of ambitious mobile and space-based devices. The recent success of several experiments has led to the proposal of further experiments with the aim of opening up new frontiers. However, the construction of future devices necessitates a decision regarding the employed diffraction mechanism and geometry, depending on the specific technical and scientific requirements. Furthermore, it is necessary to enhance the sensitivity of future devices. The contributions in this dissertation address these issues. The first contribution (I) focuses on the diffraction of atoms by laser pulses which can be employed to generate atom-optical diffraction elements like beam splitters and mirrors. These diffraction elements can be combined to construct atom interferometers, which have been successfully employed for precision measurements regarding fundamental physics as well as practical applications. The article presents a numerical comparison of two distinct diffraction mechanisms (Bragg and Raman) and diffraction geometries (single and double diffraction) in microgravity. It discusses the fundamental differences between the mechanisms and geometries with respect to the diffraction efficiency, taking into account the width of the initial wave function and the duration of the light pulse. Additionally, it explores the transition between the two diffraction geometries when starting from an atom initially at rest and increasing its momentum. The results may serve as a reference for experimentalists in selecting the most suitable configuration, based on their aims and requirements in the realization of more advanced atom interferometers. The second contribution (II) is a follow-up to the previous one, but focuses exclusively on a single diffraction type in microgravity, namely the so-called double Raman diffraction. In contrast to the previous article, where we only discussed single two-photon processes, we consider in this article a six-photon process, also known as third-order diffraction, as well as three subsequent two-photon processes, which both lead to the same amount of transferred momentum and can both be used to realize large-momentum transfer (LMT). We demonstrate that third-order double Raman diffraction is a viable and advantageous method for the diffraction of small momentum distributions like Bose-Einstein condensates (BECs) compared to a sequence of three two-photon processes. Furthermore, we show that third-order Raman pulses can be successfully applied to create higher-order Raman atom interferometers. Third-order diffraction can be perfectly combined with other LMT techniques and, moreover, allows for a reduction in the overall duration of the diffraction process and the complexity of the experimental set-up, as only two distinct laser frequencies are required. Moreover, we present a third-order Mach-Zehnder interferometer with spurious paths being disregarded. As demonstrated later on in [3], this interferometer generates optimal contrast and a substantial amplitude. The third contribution (III) extends the semi-classical λ-scheme of single Raman diffraction, as discussed in detail in contribution (I), into a fully quantized multi-atom multi-λ configuration with center-of-mass motion inside a cavity. Therefore, the incorporation of an internal structure allows for a more realistic modeling of the atoms, which is relevant for multi-photon interaction or cooling processes. We use for our analysis the framework of second quantization, i.e., we take into account the field-theoretical nature of the multi-particle atomic field as well as of the diffracting light field. We reduce this model with a Hamiltonian averaging theory applied to the atomic field operators and obtain an effective Hamiltonian, which determines the time evolution of the system. We demonstrate the efficiency of our model by the application of a typical initial state. Moreover, for a specific input state, we obtain the Hong-Ou-Mandel effect simultaneously in the atomic and the optical system. Our many-body formalism is perfectly suited to theoretically describe contemporary high-precision atom interferometric experiments based on entanglement between the atoms, that aim to surpass the shot-noise limit.
A new type of hybrid atom-light interferometer is demonstrated with atomic Raman amplification processes replacing the beam splitting elements in a traditional interferometer. This nonconventional interferometer involves correlated optical and atomic waves in the two arms. The correlation between atoms and light developed with the Raman process makes this interferometer different from conventional interferometers with linear beam splitters. It is observed that the high-contrast interference fringes are sensitive to the optical phase via a path change as well as the atomic phase via a magnetic field change. This new atom-light correlated hybrid interferometer is a sensitive probe of the atomic internal state and should find wide applications in precision measurement and quantum control with atoms and photons.