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arXiv:physics/0411176 · Physical Review A

Transverse excitations of ultracold matter waves upon propagation past abrupt waveguide changes

M. Koehler, M. W. J. Bromley, Brett D. Esry

Published Aug 3, 2005• 5 citations
arXivHTMLPDF

Abstract

The propagation of ultracold atomic gases through abruptly changing waveguide potentials is examined in the limit of noninteracting atoms. Time-independent scattering calculations of microstructured waveguides with discontinuous changes in the transverse harmonic binding potentials are used to mimic waveguide perturbations and imperfections. Three basic configurations are examined: steplike, barrierlike, and well-like with waves incident in the ground mode. At low energies, the spectra rapidly depart from single moded, with significant transmission and reflection of excited modes. The high-energy limit sees 100% transmission, with the distribution of the transmitted modes determined simply by the overlap of the mode wave functions and interference.

DOI
10.1103/physreva.72.023603

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The propagation of ultracold atomic gases through abruptly changing waveguide potentials is examined in the limit of noninteracting atoms. Time-independent scattering calculations of microstructured waveguides with discontinuous changes in the transverse harmonic binding potentials are used to mimic waveguide perturbations and imperfections. Three basic configurations are examined: steplike, barrierlike, and well-like with waves incident in the ground mode. At low energies, the spectra rapidly depart from single moded, with significant transmission and reflection of excited modes. The high-energy limit sees 100% transmission, with the distribution of the transmitted modes determined simply by the overlap of the mode wave functions and interference.
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The properties of noninteracting, low-energy atom waves propagating through circular bends are investigated. Time-independent quantum mechanical calculations using various simple harmonic oscillator based confining potentials explore the transmission, reflection, and mode-transfer probabilities over a range of energies. It is shown that at low energies single-mode wave propagation dominates. At higher energies, however, excitation and transmission of other modes become significant. Notably, reflections generally remain negligible even for sharply curved bends. The behavior near the mode thresholds and their associated resonances is emphasized.
The properties of low-density, low-energy matter wave packets propagating through waveguide bends are investigated. Time-dependent quantum-mechanical calculations using simple harmonic oscillator confining potentials are performed for a range of parameters close to those accessible by recent ``atom chip''-based experiments. We compare classical calculations based on Ehrenfest's theorem to these results to determine whether classical mechanics can predict the amount of transverse excitation as measured by the transverse heating. The present results thus elucidate some of the limits for which matter wave propagation through microstructures can be reliably considered using classical particle motion.
The possibility of generating vortices during matter-wave propagation through microstructures is examined. Vortices can arise solely due to wave interference in low-density ultracold atom clouds, and do not require any atom--atom (nonlinear) interactions. The properties of these ``interference vortices'' are understood from a simple two-mode model in a straight waveguide. This model is then applied to vortex creation in a circular bend since a circular waveguide bend is one of the simplest atom optical elements that can induce mode excitations. Time-independent and time-dependent analyses are used to investigate vortex creation and dynamics in these systems.
Ultracold atoms whose de Broglie wavelength is of the same order as an extended confining potential can experience waveguiding along the potential. When the transverse kinetic energy of the atoms is sufficiently low, they can be guided in the lowest order mode of the confining potential by analogy with light guided by a single mode optical fiber. We have obtained the first images of the transverse mode structure of guided matter waves in a confining potential with up to 6565%65 of atoms in the lowest order mode. The coherence of the guided atomic de Broglie waves is demonstrated by the diffraction pattern produced when incident upon a two dimensional periodic structure. Such coherent waveguides will be important atom optic components in devices with applications such as atom holography and atom interferometry.
We present a time-dependent quantum calculation of the scattering of a few-photon pulse on a single atom. The photon wave packet is assumed to propagate in a transversely strongly confined geometry, which ensures strong atom-light coupling and allows a quasi-one-dimensional treatment. The amplitude and phase of the transmitted, reflected, and transversely scattered part of the wave packet strongly depend on the pulse length (bandwidth) and energy. For a transverse mode size of the order of ${\ensuremath{\lambda}}^{2},$ we find nonlinear behavior for a few photons already, or even for a single photon. In a second step we study the collision of two such wave packets at the atomic site and find striking differences between the Fock state and coherent state wave packets of the same photon number.