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arXiv:physics/0206029

Nanometer scale period sinusoidal atom gratings produced by a Stern-Gerlach beam splitter

B. Dubetsky, Georg A. Raithel

Published Jun 11, 2002• 1 citation
arXivHTMLPDF

Abstract

An atom interferometer based on a Stern-Gerlach beam splitter is proposed. Atom scattering from a combination of magnetic quadrupole and homogeneous magnetic fields is considered. Using Raman transitions, atoms are coherently excited into and de-excited from sublevels having nonzero magnetic quantum numbers. The spatial regions in which the atoms are in such sublevels are small and have magnetic fields designed to have constant gradients. Therefore, the atoms experience position-independent accelerations, and the aberration of the coherently separated and recombined atomic beams remains small. We find that because of these properties it is possible to envision an apparatus producing atomic density gratings with nm-scale periods and large contrasts over 10-100 $μ$m. We use a new method of describing the atomic interaction with a pulsed spatially homogeneous field. In our detailed analysis, we calculate corrections caused by the non-linear part of the potential and the finite value of the de-Broglie wave length. The chromatic aberration and the effects of an angular beam divergence are analyzed, and optimal conditions for an experimental demonstration of the technique are identified.%The $lin\bot %lin$ combination of resonant co-propagating traveling waves splits %atoms between different Zeeman sublevels. %For a given desirable atom %grating period and length, characteristics of the atomic beam and %magnetic field are found from requirements that corrections remain %below $10%.$

DOI
10.48550/arxiv.physics/0206029

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An atom interferometer based on a Stern-Gerlach beam splitter is proposed. Atom scattering from a combination of magnetic quadrupole and homogeneous magnetic fields is considered. Using Raman transitions, atoms are coherently excited into and de-excited from sublevels having nonzero magnetic quantum numbers. The spatial regions in which the atoms are in such sublevels are small and have magnetic fields designed to have constant gradients. Therefore, the atoms experience position-independent accelerations, and the aberration of the coherently separated and recombined atomic beams remains small. We find that because of these properties it is possible to envision an apparatus producing atomic density gratings with nm-scale periods and large contrasts over 10-100 μμμm. We use a new method of describing the atomic interaction with a pulsed spatially homogeneous field. In our detailed analysis, we calculate corrections caused by the non-linear part of the potential and the finite value of the de-Broglie wave length. The chromatic aberration and the effects of an angular beam divergence are analyzed, and optimal conditions for an experimental demonstration of the technique are identified.%The lin⊥lin\bot %linlin⊥ combination of resonant co-propagating traveling waves splits %atoms between different Zeeman sublevels. %For a given desirable atom %grating period and length, characteristics of the atomic beam and %magnetic field are found from requirements that corrections remain %below 1010%.10
An atom interferometer using two Stern-Gerlach magnets as polariser and analyser is described. The interferometer was first operated with a thermal beam of ground state potassium atoms. In that case the beam splitters are two radio-frequency zones within a transverse homogeneous magnetic field building a coherent superposition of Zeeman states. Ramsey fringes are obtained by scanning the RF-frequency through the resonance profile. Pulsing the RF power allows to get the time-of-flight distribution of the beam. Atomic interference fringes (``Stern-Gerlach fringes'') are observed when the magnitude of an inhomogeneous magnetic field located in between the beam splitters is scanned. When the inhomogeneous field is also pulsed, the scalar Bohm-Aharonov effect is observed. The use of metastable helium atoms (He*23S) in place of potassium atoms is proposed. In addition to the usual advantages provided by metastable atoms of high internal energy, this atom offers the specific advantage to behave as an ideal spin-one particle. This allows us to greatly simplify the polarisation scheme of the interferometer. Possible applications involving transversally inhomogeneous magnetic fields are given and limitations due to the finite source size and angular aperture are discussed.
Here we propose and demonstrate a new way of using SG type methods in order to split and recombine matter waves. We use Rabi oscillations and magnetic field gradients in order to split87Rb atoms into two momentum components while keeping the two outputs of the beam splitter (BS) in the same spin state (Zeeman sublevels). After recombining the two outputs of the BS a spatial fringe pattern is observed. The new BS may enable a wide range of applications, such as, fundamental studies of many-body entanglement and dephasing processes, probing classical and quantum properties of nearby solids, and metrology of rotation, acceleration and gravity on a chip scale.
Since the advent of quantum mechanics and the idea that massive particles exhibit wave properties, physicists have made efforts to make use of the short deBroglie wave length of matter waves for fundamental as well as practical studies. Among these are the precise measurements allowed by interference, diffraction, and microscopy as well as the study of more fundamental aspects of quantum theory such as the Aharonov-Bohm effects or the Stern-Gerlach effect, which are described below. However, in order to use matter waves to observe any of these effects it is necessary to produce and maintain coherence in the waves which are used for measurement. With a grasp of what coherence is and how it may be achieved and maintained one can move forward to study the interesting phenomena associated with coherent matter waves. More specifically in this work the interference and diffraction of electron matter waves are considered. The phenomena under consideration are those associated with the interaction of the electric charge and magnetic dipole moment of the electron with external fields and potentials while in the process of interfering or diffracting. Namely the focus of this dissertation is the Aharonov-Bohm effect, the Aharonov-Casher effect, and the Stern-Gerlach effect. Additionally, a wide-angle electron beam-splitter capable of producing two centimeter beam separation at the detection plane is discussed. The beam-splitter utilizes a nanofabricated periodic grating in combination with a bi-prism element. Contrary to devices utilizing only bi-prism elements, the use of the periodic grating causes amplitude, and not wave front, splitting. Even at maximum separation, beam profiles remain undistorted, providing evidence that coherence is intact. This is a step towards the realization of a large area electron interferometer using such a grating bi-prism combination. Such an interferometer could, in principle, be used to test the dispersionless nature of the Aharonov-Bohm effect. Work towards such an interferometer and possible future work are also discussed. Advisor: Herman Batelaan
The paper presents an experiment based on an efficient coupling between atomic Zeeman states (for atoms with internal angular momentum) allowed by the quadrupolar component of the surface- induced van der Waals (vdW) interaction. This exo-energetic "vdW - Zeeman" transition provides a tuneable (magnetic field intensity dependent) beam splitter that was theoretically illustrated by the simplest possible interferometer: an atomic counterpart of Fresnel biprism. The velocity - adjustable atomic beam is here coming across two opposite surfaces (single slit of a nano-grating). For a transverse coherent radius large enough, the atom wave packet is strongly inelastically diffracted by the two opposite surfaces at some distances from the slit to yield non localised interference fringes. The calculation has been done for Ar metastable atoms with a grating of 100 nm period and different velocities of the atoms (560 to 10 m/s). Via the interference pattern (Schlieren image), this device should give access to such novel information as the oscillating part of the complex vdW - interaction transition amplitude. This simplest configuration is not sensitive to inertial effect. As a next step, a loop - closing transmission grating was added to realize a new type of compact interferometer.
The key elements for atom interferometers are atomic beam splitters and recombiners. An atomic beam splitter separates a single atomic wave function into a superposition state corresponding to two center of mass wavepackets that propagate in different spatial directions and a recombiner reunites the atomic beams. We report here on the investigation of 1) an atomic beam splitter with large separation angle based on the optical Stern Gerlach effect, 2) an atomic mirror based on the reflection of atoms by different types of evanescent waves (a simple evanescent wave and a surface plasmon wave), 3) an atomic beam splitter realized by the partial spatial reflection of an atom by an evanescent wave and 4) diffraction of atoms by a standing evanescent wave.
Summary form only given. Spatial coherences are measured by means of a new atom interferometry technique. First, a coherent superposition of the Zeeman components of the atom is built by means of well-controlled magnetic interactions. Second, pulsed inhomogeneous magnetic fields are employed to coherently separate and reunite the atomic substates via the Stern-Gerlach induced forces. Finally, atomic interference fringes are recorded on the state-selected outcoming sample by changing the spatial separation. This method bears strong similarities with the Fourier-transform spectroscopy of light. The interferogram visibility curve yields the atom sample spatial coherences. For example, when the applied magnetic gradients are parallel to the atom trajectory, one gets the coherence length by varying the overlap of the separated wavepackets. Several experiments on cold cesium atoms have been performed and are presented. Furthermore, we have used our magnetic cooling method to prepare the atom cloud upstream from the interferometer. Large enhancements of the coherence length are demonstrated.