Classical aspects of ultracold atom wave packet motion through microstructured waveguide bends

Abstract

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.

Manifestations of vortices during ultracold-atom propagation through waveguides

“…As the specific details of the present method follow from those outlined in Ref. [17], the interested reader is directed there.…”

“…An implementation on a uniform Cartesian grid (equally spaced in both the x and z directions) was adopted here instead of the hybrid nonuniform Cartesian and polar grid approach used in [17]. The computational overhead in including grid points that have large V͑x , z͒ is not an impediment for the 0 = 10, 180°bend considered here.…”

“…[16,17]. That is, we assume a multiple wire configuration that does not require external bias fields applied in the plane of the microchip surface [23], so that the curved waveguide reduces to an effective 2D problem (assuming densities such that atom-atom interactions can be neglected).…”

“…Second, time-dependent wave-packet calculations were performed using a split-operator Crank-Nicolson method with finite differences [17]. An implementation on a uniform Cartesian grid (equally spaced in both the x and z directions) was adopted here instead of the hybrid nonuniform Cartesian and polar grid approach used in [17].…”

“…We chose to revisit [16,17] the circular bend geometry as it is a simple geometry that can easily be explored using both time-independent and wave-packet calculations. Furthermore, similar studies of ballistic electron transport have yielded intriguing vortex physics.…”