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Physica D Nonlinear Phenomena

Rotating matter waves in Bose–Einstein condensates

Todd Kapitula, P. G. Kevrekidis, R. Carretero-González

Published Jun 28, 2007• 31 citations
Publisher
DOI
10.1016/j.physd.2007.06.012

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Matter–wave interferometers are, in principle, orders of magnitude more sensitive than their optical counterparts. Nevertheless, creation of matter–wave currents to achieve such a sensitivity is a continuing challenge. Here, we propose the use of Optical-Angular-Momentum (OAM) induced vortex superpositions in Bose–Einstein condensates (BECs) as an alternative to other atom interferometers for gyroscopy. The coherent superposition of two counter-rotating vortex states of a trapped condensate leads to an interference pattern that rotates by an angle proportional to the angular velocity of the rotating trap – in accordance with the Sagnac effect. We show that the rotation rate can be easily read out, and that the device is highly stable. The signal-to-noise ratio and sensitivity of the scheme are also estimated.
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 report new matter-wave solutions of the one-dimensional spin-1 Bose-Einstein condensate system by combining global spin-rotation states and similarity transformation. Dynamical behaviors of non-stationary global spin-rotation states derived from the SU(2) spin-rotation symmetry are discussed, which exhibit temporal periodicity. We derive generalized bright-dark mixed solitons and new rogue wave solutions and reveal the relations between Euler angles in spin-rotation symmetry and parameters in ferromagnetic and polar solitons. In the modulated spin-1 Bose-Einstein condensate system, new solutions are derived and graphically illustrated for different types of modulations. Moreover, numerical simulations are performed to investigate the stability of some obtained solutions for chosen parameters.