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arXiv:1309.3225

Creation of matter wave Bessel beams

Changhyun Ryu, Kevin C. Henderson, M. G. Boshier

Published Sep 12, 2013• 0 citations
arXivHTMLPDF

Abstract

Bessel beams are plane waves with amplitude profiles described by Bessel functions. They are important because of their property of limited diffraction and their capacity to carry orbital angular momentum. Here we report the creation of a Bessel beam of de Broglie matter waves. The Bessel beam is produced by the free evolution of a thin toroidal atomic Bose-Einstein condensate (BEC) which has been set into rotational motion. By attempting to stir it at different rotation rates, we show that the toroidal BEC can only be made to rotate at discrete, equally-spaced frequencies, demonstrating that circulation is quantized in atomic BECs. The method used here to generate matter wave Bessel beams with a Painted Potential can be viewed as a form of wavefunction engineering which might be extended to implement arbitrary cold atom matter wave holography.

DOI
10.48550/arxiv.1309.3225

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Bessel beams are plane waves with amplitude profiles described by Bessel functions. They are important because of their property of limited diffraction and their capacity to carry orbital angular momentum. Here we report the creation of a Bessel beam of de Broglie matter waves. The Bessel beam is produced by the free evolution of a thin toroidal atomic Bose-Einstein condensate (BEC) which has been set into rotational motion. By attempting to stir it at different rotation rates, we show that the toroidal BEC can only be made to rotate at discrete, equally-spaced frequencies, demonstrating that circulation is quantized in atomic BECs. The method used here to generate matter wave Bessel beams with a Painted Potential can be viewed as a form of wavefunction engineering which might be extended to implement arbitrary cold atom matter wave holography.
Bessel beams are plane waves with amplitude profiles described by Bessel functions. They are important because they propagate 'diffraction-free' and because they can carry orbital angular momentum. Here we report the creation of a Bessel beam of de Broglie matter waves. The Bessel beam is produced by the free evolution of a thin toroidal atomic Bose–Einstein condensate (BEC) which has been set into rotational motion. By attempting to stir it at different rotation rates, we show that the toroidal BEC can only be made to rotate at discrete, equally spaced frequencies, demonstrating that circulation is quantized in atomic BECs. The method used here can be viewed as a form of wavefunction engineering which might be developed to implement cold atom matter wave holography.
We present experiments investigating different aspects concerning the coherent manipulation of a Bose-Einstein condensate wavefunction with far blue detuned dipole potentials. In a first set of experiments we study a waveguide for matter waves as an important atom optical element allowing to hold and guide the atoms for long observation times. We present a flexible realization of this waveguide based on a tube shaped Laguerre Gaussian laser beam and investigate the dynamics of a Bose condensed ensemble transferred into this guide. In a second set of experiments we study the dynamics of dark solitons created by the manipulation of the phase of the condensate wave function by temporally applied dipole potentials. This method of phase imprinting represents a powerful tool for the design of matter waves and the controlled creation of various excitations. The dynamics of dark solitons in matter waves is investigated in detail by experimentally and numerically studying the temporal evolution of the condensate density as well as by mapping the velocity field of the excited condensate wavefunction. In these measurements we directly detect the flux of the wave function associated with the dark soliton using spatially resolved Bragg scattering. Experiments investigating the creation and interaction of several dark solitons conclude this chapter.
An integrated coherent matter wave circuit is a single device, analogous to an integrated optical circuit, in which coherent de Broglie waves are created and then launched into waveguides where they can be switched, divided, recombined, and detected as they propagate. Applications of such circuits include guided atom interferometers, atomtronic circuits, and precisely controlled delivery of atoms. Here we report experiments demonstrating integrated circuits for guided coherent matter waves. The circuit elements are created with the painted potential technique, a form of time-averaged optical dipole potential in which a rapidly moving, tightly focused laser beam exerts forces on atoms through their electric polarizability. The source of coherent matter waves is a Bose–Einstein condensate (BEC). We launch BECs into painted waveguides that guide them around bends and form switches, phase coherent beamsplitters, and closed circuits. These are the basic elements that are needed to engineer arbitrarily complex matter wave circuitry.
The atom laser has long been a holy grail within atom physics and with the creation of an atom laser we hope to bring a similar revolution in to the field of atom optics. With the creation of the Bose-Einstein Condensate (BEC) in 1995 the path to an atom laser was initiated. An atom laser is continues source of BEC. In a Bose condensate all the atoms occupy the same quantum state and can be described by the same wave function and phase. With an atom laser the De Broglie wavelength of atoms can be much smaller than the wavelength of light. Due to the ultimate control over the atoms the atom laser is very interesting for atom optics, lithography, metrology, etching and deposition of atoms on a surface. All previous atom lasers have been created from atoms coupled out from an existing Bose-Einstein Condensate. There are different approaches but common to them all is that the duration of the output of the atom laser is limited by the size of the initial BEC and they all have a low flux. This leaves the quest to build a continuous high flux atom laser. An alternative approach to a continuous BEC beam is to channel a continuous ultra cold atomic beam into a magnetic guide and then cool this beam down to degeneracy. Cooling down a continuous beam of atoms faces three large problems: The collision rate has to be large enough for effective rethermalization, since evaporative cooling in 2D is not as effective as in 3D and a large thermal conductivity due to atoms with a high angular momentum causes heating downstream in the guide. We have built a 4 meter magnetic guide that is placed on a downward slope with a magnetic barrier in the end. In the guide we load packets of ultra cold rubidium atoms with a frequency rate large enough for the packets to merge together to form a continuous atomic beam. The atomic beam is supersonic and when the beam reaches the end barrier it will return and collide with itself. The collisions lowers the velocity of the beam into subsonic velocities and a shock wave is created between the two velocity regions. In order to conserve number of particle, momentum and enthalpy the density of the atomic beam passing through the shock wave must increase. We have build such a shock wave in an atomic beam and observed the density increase due to this. As an extra feature having a subsonic beam on a downward slope adds an extra density increase due to gravitational compression. Loading ultra cold atoms into a 3D trap from the dense subsonic beam overcomes the problem with 2D cooling and thermal conductivity. This was done and evaporative cooling was applied creating an unprecedented large number rubidium BEC.
We predict that classes of coherent matter waves can self-accelerate without the presence of an external potential. Such Bose-Einstein condensates can follow arbitrary power-law trajectories and can also take the form of diffraction-free Airy waves. We also show that suitably engineered radially symmetric matter waves can abruptly autofocus in space and time. We suggest different schemes for the preparation of the condensate using laser beams to imprint an amplitude or a phase pattern onto the matter wave. Direct and Fourier space generation of such waves is discussed using continuous and binary masks as well as magnetic mirrors and lenses. We study the effect of interactions and find that independently of the type and strength of the nonlinearity, the dynamics are associated with the generation of accelerating matter waves. In the case of strong attractive interactions, the acceleration is increased while the radiation reorganizes itself in the form of soliton(s).
The concept that all de Broglie particles can form vortex beams is analyzed for neutral atoms. It is shown how atoms diffracted from a suitably constructed optical mask configuration employing light of lll units of orbital angular momentum and at far-off resonance with an atomic transition can lead to the generation of a discrete set of atom vortex beams each endowed with the property of quantized orbital angular momentum about the beam axis in units of $\ensuremath{\hbar}l$. Selection criteria of atom vortex beams are derived and the functioning of the mask configuration for angular dispersion of beams in terms of de Broglie wavelength is analyzed. Prospects of applications in the areas of atom interferometry and dispersion, and quantum information processing via atom vortices are pointed out.