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arXiv:physics/0309003 · Physical Review A

Wave mechanics of a two-wire atomic beam splitter

Daniele C. E. Bortolotti, John L. Bohn

Published Mar 18, 2004• 12 citations
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Abstract

We consider the problem of an atomic beam propagating quantum mechanically through an atom beam splitter. Casting the problem in an adiabatic representation (in the spirit of the Born-Oppenheimer approximation in molecular physics) sheds light on explicit effects due to nonadiabatic passage of the atoms through the splitter region. We are thus able to probe the fully three-dimensional structure of the beam splitter, gathering quantitative information about mode mixing, splitting ratios, and reflection and transmission probabilities.

DOI
10.1103/physreva.69.033607

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We consider the problem of an atomic beam propagating quantum mechanically through an atom beam splitter. Casting the problem in an adiabatic representation (in the spirit of the Born-Oppenheimer approximation in molecular physics) sheds light on explicit effects due to nonadiabatic passage of the atoms through the splitter region. We are thus able to probe the fully three-dimensional structure of the beam splitter, gathering quantitative information about mode mixing, splitting ratios, and reflection and transmission probabilities.
Atom interferometry allows for new precision limits in measurement and a key component of it is the beam-splitter. In this thesis we look at the properties of an all optical beam-splitter, which is created by the overlap of two Gaussian laser beams,which also function as waveguides for the Bose-Einstein condensate. For this mainly the split step Fourier method is used to model the propagation of a low density Bose-Einstein condensate of atoms. The two main areas of interest are the splitting and recombination properties. \nThe splitting is studied both in two and one dimensions. For the one-dimensional case both standing and propagating waves are used to find the ideal splitting conditions of a balanced splitting and transmission. The result of these methods are in general agreement with the exception that for the propagating wave some of the atoms can become localised inside the beam-splitter. For the propagation it was found that the splitting is not perfectly coherent as the outputs are slightly deformed. However, when looking at the two-dimensional case we see that the splitting is not even close to being coherent. This is because the beam-splitter excites the incoming wave into higher transverse modes of the waveguides. To compensate for this the depth of the waveguides was lowered and the width narrowed to reduce the potential kinetic energy that the atoms could acquire and to increase the separation between the eigenstates to lower the probability of excitation into higher modes, respectively. Nonetheless, these investigations improved the splitting balance but it is still not coherent. Another method investigated was the introduction of a third laser which acts as a filling to reduce the depth of the potential well where the lasers generate the beam-splitter. This approach does not improve the splitting. \nHence instead of recombining single mode waves we used a multimode approach. For this we found that the mirror position is crucial for certain parameters as the longitudinal momentum is not necessarily the same in the reflection and transmission waveguide. Our investigations have generated interference fringes in this model \nsystem with a fractional height up to 33%.
A laser-cooled neutral-atom beam from a low-velocity intense source is split into two beams while it is guided by a magnetic-field potential. We generate our multimode beam-splitter potential with two current-carrying wires upon a glass substrate combined with an external transverse bias field. The atoms are guided around curves and a beam-splitter region within a 10-cm guide length. We achieve a maximum integrated flux of 1.5x10(5)atoms/s with a current density of 5x10(4)amp/cm (2) in the 100-microm -diameter wires. The initial beam can be split into two beams with a 50/50 splitting ratio.
A novel atomic beam splitter, using reflection of atoms off an evanescent light wave, is investigated theoretically. The intensity or frequency of the light is modulated in order to create sidebands on the reflected de Broglie wave. The weights and phases of the various sidebands are calculated using three different approaches: the Born approximation, a semiclassical path integral approach, and a numerical solution of the time-dependent Schrödinger equation. We show how this modulated mirror could be used to build practical atomic interferometers.
A novel atomic beam splitter, using reflection of atoms off an evanescent light wave, is investigated theoretically. The intensity or frequency of the light is modulated in order to create sidebands on the reflected de Broglie wave. The weights and phases of the various sidebands are calculated using three different approaches: the Born approximation, a semiclassical path integral approach, and a numerical solution of the time-dependent Schrödinger equation. We show how this modulated mirror could be used to build practical atomic interferometers.