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Nonlinear atom optics of an ultracold atomic beam

Weiping Zhang, Daniel F. Walls

Published May 8, 1994• 0 citations
OpenAlex

Abstract

It is well known that light waves have a mechanical effect on atoms. Such a mechanical effect is employed to manipulate the center of mass of atoms in atom optics. As a result, light waves can act as mirrors, gratings and lens for atoms. In this sense, atoms and photons in atom optics exchange their roles in conventional optics. The current research in atom optics is concerned with atomic beams with low densities which are theoretically described by a single-atom approach.

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It is well known that light waves have a mechanical effect on atoms. Such a mechanical effect is employed to manipulate the center of mass of atoms in atom optics. As a result, light waves can act as mirrors, gratings and lens for atoms. In this sense, atoms and photons in atom optics exchange their roles in conventional optics. The current research in atom optics is concerned with atomic beams with low densities which are theoretically described by a single-atom approach.
Two of the major classes of atom optical elements are microfabricated structures and light beams. For instance, a standing light wave can act as a phase grating for atoms, as each absorption and emission process is accompanied by a coherent atomic recoil. After a simple discussion of the mechanical effects of light on atoms, we use a band-theoretical approach to categorize the main resonances (Bragg and Doppleron) that can be exploited to operate such a grating effectively. We discuss the incoherent effects of spontaneous emission, showing when and how they lead from a diffractive to a diffusive regime of atom–field interactions. We turn next to the diffraction of atoms by quantized fields and show the sensitivity of the resulting atomic diffraction pattern to the field photon statistics. In this quantized regime, the atom–field interaction leaves the system in an entangled state. We conclude by reviewing some proposals that exploit this property to perform measurements on the field (atom) to prepare and/or monitor specific atomic (field) states.
A vector quantum field theory is developed to describe the interaction of an ultracold atomic ensemble with a laser field. The ultracold atomic ensemble is composed of either bosonic atoms or fermionic atoms. The photon exchanges between different ultracold atoms result in a long-range interatom interaction. Under appropriate conditions, such a many-body interaction leads to an effective ``Kerr-type'' nonlinearity of atomic waves. In terms of the nonlinearity, we construct a general formalism of nonlinear atom optics for an ultracold atomic beam. Applying the formalism to the diffraction of an ultracold atomic beam composed of bosonic atoms by a standing-wave laser field, we find that the many-body nonlinearity induces self-phase and cross-phase modulation of diffracted atomic waves. As a result, a standing-wave laser acts as a nonlinear atomic grating which diffracts atoms in the same way as a nonlinear periodic medium diffracts photons.
A large-aperture liquid-He coated spherical mirror and a room-temperature bent-gold crystal have been used to focus atom beams of H and He, respectively. They are described elsewhere in this symposium. Many of the new optical elements for atoms rely on the mechanical forces of light; mirrors are one example. When atoms approach the surface of glass that has intense blue-detuned light inside, they recoil from the evanescent wave that extends several wavelengths past the surface and into the vacuum. The atoms are never close enough to the surface to be affected by its atomic attraction or its small-scale irregularities. When a highly collimated beam of sodium atoms is directed at a standing wave of light near its resonance frequency, the angular scattering pattern of the atoms exhibits the characteristics of diffraction from a short sinusoidal grating. Diffraction orders up to ~20 have been observed at high light intensities. In contrast to phase gratings made with light, material absorption gratings are amplitude gratings.
Starting from the first principles of nonrelativistic QED we have derived the system of Maxwell-Schr\"odinger equations which can be used for theoretical description of atom optical phenomena at high densities of atoms and high intensities of the laser radiation. The role of multiple atomic transitions between ground and excited states in atom optics has been investigated. Nonlinear optical properties of interacting Bose gases are studied and an equation for the refractive index has been derived. We have investigated the role of light-induced and collisional nonlinearities in the diffraction of an ultracold atomic beam from an intense standing laser wave in the Raman-Nath and in the Bragg regimes.
Abstract : It is well known that ultracold atoms (T < 1 milliKelvin) are promising candidates for nextgeneration inertial sensors and magnetometers. An interferometer measures accelerations and rotations in much the same way as does a laser-based interferometer, except that the recorded interferograms are due to matter wave interference rather than optical interference. Large laboratory-based atom interferometers using thermal atom beams have demonstrated unparalleled performance, but the most promising path to making such technology practical is to use ultracold atoms: unlike room temperature atoms, cold atoms can be guided along controlled trajectories, analogous to fiber optics for light. The roles of matter and light are reversed - whereas material guides photons in fiber optics, photons guide atoms in atom optics. To realize high sensitivities with cold atoms, we must: (1) obtain a large flux of cold atoms and (2) guide atoms coherently in atom waveguides. Our group is working on these issues using optical techniques with cold atoms derived from a magneto-optical trap that contains roughly 108 rubidium atoms at a temperature of 10 muK and density of 10(11) atoms/cm(3).
The transition of atoms from the disorder of the gaseous phase into the “disciplined” behavior of the condensate can be compared with the transformation of chaotic incoherent light into a laser light beam. This analogy leads directly to the definition of the atom laser: a device that produces a beam of boson atoms that have “escaped” from a trapped Bose–Einstein condensate. The operation of our well-known optical laser requires essentially three things: an optical cavity, an active medium, and a mechanism that allows light to escape from the cavity. Within the cavity, a huge number of atoms of the active medium interact with photons. The cavity consists essentially of two mirrors with very high reflectivity onto which the photons are reflected many times. Multiple reflections cause photons to interact continuously with atoms in the cavity, leading to a continuous generation of new photons by stimulated emission. The result is an increase in the number of photons, i.e., amplification of the beam traveling within the cavity. All of the photons have the same frequency and phase (i.e., they oscillate synchronously). Since one of the mirrors is not perfectly reflective, the photons manage to escape from the cavity, resulting in the well-known, monochromatic, and directional laser beam.