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Annalen der Physik

Atomic interferometry as two‐level particle scattering by a periodic potential

Christian Bordé, Cláus Lämmerzahl

Published Jan 1, 1999• 3 citations
Publisher

Abstract

Abstract The beam splitting process of an atomic beam is described by an exactly solvable theory. We use exact plane wave solutions of an atomic two‐level system interacting with laser beams and employ appropriate jump conditions between regions with and without laser beam. The transmission matrix as well as the reflection matrix are given explicitely. Also, the conditions for atom optical analogues of the Borrmann effect and of the pendellösung effect are treated exactly. The high‐energy limit of these phenomena is discussed which is sufficient for many practical purposes.

DOI
10.1002/andp.19995110106

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The beam splitting process of an atomic beam is described by an exactly solvable theory. We use exact plane wave solutions of an atomic two-level system interacting with laser beams and employ appropriate jump conditions between regions with and without laser beam. The transmission matrix as well as the reflection matrix are given explicitely. Also, the conditions for atom optical analogues of the Borrmann effect and of the pendellösung effect are treated exactly. The high-energy limit of these phenomena is discussed which is sufficient for many practical purposes.

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Kluwer Academic Publishers eBooks•Dec 11, 2005•1 citation
Abstract The beam splitting process of an atomic beam is described by an exactly solvable theory. We use exact plane wave solutions of an atomic two‐level system interacting with laser beams and employ appropriate jump conditions between regions with and without laser beam. The transmission matrix as well as the reflection matrix are given explicitely. Also, the conditions for atom optical analogues of the Borrmann effect and of the pendellösung effect are treated exactly. The high‐energy limit of these phenomena is discussed which is sufficient for many practical purposes.
The beam splitting process of an atomic beam is described by an exactly solvable theory. We use exact plane wave solutions of an atomic two-level system interacting with laser beams and employ appropriate jump conditions between regions with and without laser beam. The transmission matrix as well as the reflection matrix are given explicitely. Also, the conditions for atom optical analogues of the Borrmann effect and of the pendellösung effect are treated exactly. The high-energy limit of these phenomena is discussed which is sufficient for many practical purposes.
Two recent experiments demonstrating novel atomic lenses—one using a free standing Fresnel zone plate and the other using an optical standing wave with large (40 μm) period—will be discussed. In addition, an experiment demonstrating the splitting of an atomic beam by the optical Stern–Gerlach effect will be described. In this effect, a beam of (two-level) atoms is coherently split into two paths by an exactly resonant optical field gradient, each path containing atoms in one of the two dressed states. The field gradient was derived from a large period standing wave, produced by bouncing a laser beam from a glass surface at grazing incidence. The experiments were carried out with metastable He atoms interacting through the 23S1to 23P2 transition with an optical field at 1.083 μm. The interaction times were significantly less than the 23P natural lifetime of 100 ns, so spontaneous emission played no role during the interaction.
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 set of coupled equations for the particle scattering by a two level atom in a strong near resonant radiation field is derived from the time dependent Schrodinger equation. This set of equations is discussed in a first and second order approximation. The result can be visualized in terms of a scheme in which the two well separated (nondegenerate) atomic states split, each into two energy levels. The splitting depends on the strength of the field and on the difference between the resonance frequency and the frequency of the incident light and is typically a few meV. In this scheme all possible elastic, quasielastic, inelastic and superelastic transitions between the four levels can be induced by collision processes. In addition, multiphoton processes may occur if the scattered particle remains long enough in the interaction region. Estimates of the two photon gain process for electron and heavy particle scattering by sodium atoms in a dye laser field are given. It is suggested that the superelastic processes may play an important role in laser induced gas breakdown, even if the laser frequency does not coincide with any atomic transition. Spontaneous emission of atoms in laser fields is also treated. The results are similar to the particle scattering processes.
We are concerned with an analytic separation approach of the optical Bloch equations in the case of the two-level atom interacting with a classical light. The conditions that permit a complete separation of these equations are extracted in a natural manner and the exact solutions are obtained. A theoretical comparison with Torrey method is given. In this context, we find that the transient regime, valid from the instant of the application of the laser on atom, is significant for the evolution of forces and the dynamics before the steady-state regime will be reached. The case of Eu3 + ion moving in plane-light wave and standing-wave is treated with some details. The implications of the results for operating atoms and ions using laser light are discussed.
New levels of control over the atomic motion have been attained through the development of the atom laser. The unique properties of these coherent atomic sources open up a wide range of new possibilities in the fields of atom optics and precision measurement. In this article we have discussed the high contrast interference pattern obtained from an atom laser with two output modes of different energies. It should be possible to create a highly complex interference pattern in the output beam of an atom laser by applying a correspondingly tailored radio wave field for output coupling. A novel atom optical manipulation method allowed us to reflect, recapture and focus an atom laser beam. Due to its simplicity and precision the technique is ideally suited for creating an interferometer for the atom laser beam. It seems feasible to split the atom laser beam into two components and recombine it after delaying one of the two components. The resulting interference pattern would reveal the coherence properties of the atom laser beam.