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Physical Review A

Atomic de Broglie waves in multiple optical standing waves

Chang Jae Lee

Published Jun 1, 1996• 2 citations
Publisher

Abstract

In this work the dynamical behavior of the center of mass of a two-level atom in sequences of multiple optical standing waves is explored. In a standing wave the atomic momentum distribution fans out. But with a suitably designed sequence of standing waves it is possible to refocus the momentum-space wave packet and bring the momentum distribution to the initial value, which may be regarded as an atom optical analog to spin or photon echo. If the total interaction time is fixed, the refocusing performance gets better as the number of standing waves in a sequence increases. Also the atomic wave packet in position space evolves as if in free space. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.4238

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In this work the dynamical behavior of the center of mass of a two-level atom in sequences of multiple optical standing waves is explored. In a standing wave the atomic momentum distribution fans out. But with a suitably designed sequence of standing waves it is possible to refocus the momentum-space wave packet and bring the momentum distribution to the initial value, which may be regarded as an atom optical analog to spin or photon echo. If the total interaction time is fixed, the refocusing performance gets better as the number of standing waves in a sequence increases. Also the atomic wave packet in position space evolves as if in free space. \textcopyright{} 1996 The American Physical Society.
The quantized center-of-mass dynamics of two-level atoms in a periodically modulated standing-wave laser field is analyzed, including the decohering effect of spontaneous emission. Under conditions appropriate for the occurrence of dynamical localization as determined in previous work, we predict a random diffusive motion of dynamically localized de Broglie waves due to spontaneous emission and calculate the diffusion constant and the diffusing distribution of wave packets. \textcopyright{} 1996 The American Physical Society.
Atoms interacting with a standing wave are diffracted into even multiples of photon momentum. We argue that the spreading of the atomic momentum is analogous to the fanning out of Bloch vectors of an ensemble of two-level systems in coherent optics. It is shown that a continuous, time-proportional phase increment of the standing wave reverses the dynamics of the atoms and generates momentum echoes. Monte Carlo wave-function simulations are performed to see how the scheme works for realistic atomic models, taking spontaneous emission into account. Application of the echo formation to lifetime measurements of atoms is proposed.
We consider the scattering of an atom by a sequence of two near-resonant standing light waves, each formed by two running waves with slightly different wave vectors. Due to opposite detunings of the two standing waves, within the rotating wave approximation, the adiabatic approximation applied to the atomic center-of-mass motion, and a smooth turning on and off of the interaction, the dynamical phase cancels out and the final state of the atom differs from the initial one only by the sum of the two Berry phases accumulated in the two interaction regions. This phase depends on the position of the atom in a way such that the wave packet emerging from the scattering region will focus, which constitutes a method to observe the Berry phase without resorting to interferometric methods.
The propagation of a two-level atomic wave packet across a laser beam is considered. For small incident kinetic energies of the atom, the wave nature of the center-of-mass motion becomes apparent, giving reflections and refractions in the case of a square profile of the laser beam. When the incident momentum is low enough, we show that one of the dressed states cannot propagate inside the laser beam, giving rise to an evanescent atomic wave packet. Also a stopped excited component is found when the incident momentum equals in modulus---not in direction---the one-photon recoil. \textcopyright{} 1996 The American Physical Society.
We present numerical calculations of the evolution of an atomic wave packet in the optical potential created by a laser standing wave. These calculations do not rely on the Raman-Nath approximation, and fully account for transverse atomic motion within the standing wave. Our results show that atomic dynamics is important even for very brief interactions, and that the wave packet can become well localized during and shortly after the interaction. We propose several atomic beam splitters and deflectors which make use of this effect. This effect may also have repercussions for recent proposals to measure the position of an atom in a standing wave by monitoring the phase shift of the optical field; these schemes require that the field does not act back on the atom to alter its position wave function. A standing wave can also localize the wave packet in momentum space, which we show can be used to cool an atomic beam in one transverse dimension.
Atom optical analoga exist for many light-optical elements like mirrors, lenses and beam splitters. Light - or generally electromagnetic fields - and matter virtually exchange roles: Optical elements correspond to electromagnetic fields and light fields to matter waves. The goal of this thesis was to realize a de Broglie waveguide: A standing wave was generated by reflecting a laser beam on a gold coated prism surface. Near the resonance frequency of an atomic transition in metastable argon the light field exercises a dipole force, which can be described by a potential proportional to the intensity distribution of the interferece patterns of the light field. Atoms with small enough kinetic energy can be stored in the potential minima. In longitudinal direction to the standing wave the center of mass motion of these atoms is strongly confined. It is characterised by a discreet quantum mechanical mode structure where the energy distance of the indivdual motional states is big compared to their uncertainty. Transversally the atoms can virtually move freely, i.e. their mode spectrum is continual. Therefore one single potential minimum can be considered a resonator for atomic de Broglie waves and can be regarded as the atom optical analogon of a two-dimensial waveguide in light optics. A de Broglie waveguide provides a possiblity of examining a nearly two-dimensional gas of ultracold atoms in front of a surface. Moreover a continuous laser-like source of atoms may be realized on this basis.