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New Journal of Physics

Creation of matter wave Bessel beams and observation of quantized circulation in a Bose–Einstein condensate

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

Published Jan 23, 2014• 44 citations
Publisher

Abstract

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.

DOI
10.1088/1367-2630/16/1/013046

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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.
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.
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.
We report on the realization of a novel rotating beam trap to investigate the superfluidity properties of Bose-Einstein condensates with different quanta of angular momentum. This has been achieved by scanning a red detuned focused beam trap using a 2-axis AOM while compensating for varying diffraction efficiencies using a synchronized AM modulation. Using this set up allows the creation of different ring diameters as well as adding different amounts of angular momentum to the Bose-Einstein condensate.
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 reveal that Hopf solitons can be stabilized in rotating atomic Bose-Einstein condensates. The Hopfion is a matter-wave vortex complex which carries two independent winding numbers. Such a topological solitonic structure results from a superfluid flow of atoms simultaneously quantized in poloidal and toroidal directions. In the framework of a dissipative mean-field model we observe different unstable evolution scenarios of the Hopfions. We demonstrate energetic and dynamical stability of the Hopf solitons under experimentally feasible conditions.