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Physical Review A

Manifestations of vortices during ultracold-atom propagation through waveguides

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

Published Jul 12, 2004• 6 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.70.013605

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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.
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.
We report on the observation of vortex formation in a Bose-Einstein condensate of 87Rb^{87}\text{R}\text{b}87Rb atoms. Vortices are generated by superimposing an oscillating excitation to the trapping potential introduced by an external magnetic field. For small amplitudes of the external excitation field we observe a bending of the cloud axis. Increasing the amplitude we observe formation of a growing number of vortices in the sample. Shot-to-shot variations in both vortex number and position within the condensed cloud are observed, probably due to the intrinsic vortex nucleation dynamics. We discuss the possible formation of vortices and antivortices in the sample as well as possible mechanisms for vortex nucleation.
We consider two-dimensional (2D) localized vortical modes in the three-wave system with the quadratic ( χ ( 2 ) ) nonlinearity, alias nondegenerate second-harmonic (SH)-generating system, guided by the isotropic harmonic-oscillator (alias parabolic) confining potential. In addition to the straightforward realization in optics, the system models mixed atomic-molecular Bose–Einstein condensates. The main issue is stability of the vortex modes, which is investigated through computation of instability growth rates for eigenmodes of small perturbations, and by means of direct simulations. The threshold of parametric instability for single-color beams, represented solely by the SH with zero vorticity, is found in an analytical form with the help of the variational approximation. Trapped states with vorticities ( + 1 , − 1 , 0 ) in the two fundamental-frequency components and the SH one (the so-called hidden-vorticity modes) are completely unstable. Also unstable are semi-vortices , with component vorticities ( 1 , 0 , 1 ) . However, full vortices, with charges ( 1 , 1 , 2 ) , have a well-defined stability region. Unstable full vortices feature regions of robust dynamical behavior, where they periodically split and recombine, keeping their vortical content.
We analyze numerically the process of dynamical generation of spatially localized vortices in Bose-Einstein condensates (BEC's) with repulsive atomic interactions confined by two-dimensional optical lattices. Akin to bright solitons in a repulsive condensate, these nonlinear localized states exist only within the gaps of the matter-wave band-gap spectrum imposed by the periodicity of the lattice potential. We discuss the complex structure of matter-wave phase singularities associated with different types of stationary gap vortices and suggest two different excitation methods. In one method, the condensate is adiabatically driven to the edge of the Brillouin zone where a vortex phase is subsequently imprinted onto the condensate wave packet. Alternatively, a vortex is created in a condensate confined in a harmonic trap and then is nonadiabatically released into the lattice potential. We find that only the latter method leads to robust and reliable generation of vortices within the gap of the matter-wave band-gap spectrum. Moreover, the nonadiabatic excitation can lead to the formation of broad gap vortices from the initial BEC wave packets with a large number of atoms. These broad vortices are intimately connected to self-trapped nonlinear states of the BEC recently demonstrated in experiments with a one-dimensional optical lattice. Our numerical simulations also confirm the feasibility of a homodyne interferometric detection of broad gap vortices.