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APS

Propagation of ultracold atoms through bends in waveguides

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

Published May 1, 2003• 0 citations
OpenAlex

Abstract

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.

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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 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 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.
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 gases in ring geometries hold promise for significant improvements of gyroscopic sensitivity. Recent experiments have realized atomic and molecular storage rings with radii in the centimeter range, sizes whose practical use in inertial sensors requires velocities significantly in excess of typical recoil velocities. We use a combination of analytical and numerical techniques to study the coherent acceleration of matter waves in circular waveguides, with particular emphasis on its impact on single-mode propagation. In the simplest case we find that single-mode propagation is best maintained by the application of time-dependent acceleration force with the temporal profile of a Blackmann pulse. We also assess the impact of classical noise on the acceleration process.
A detailed analysis of the wave-mode structure in a bend and its incorporation into a stable algorithm for calculation of the scattering matrix of the bend is presented. The calculations are based on the modal approach. The stability and precision of the algorithm is numerically and analytically analysed. The algorithm enables precise numerical calculations of scattering across the bend. The reflection is a purely quantum phenomenon and is discussed in more detail over a larger energy interval. The behaviour of the reflection is explained partially by a one-dimensional scattering model and heuristic calculations of the scattering matrix for narrow bends. In the same spirit, we explain the numerical results for the Wigner–Smith delay time in the bend.