Vortex matter and ultracold superstrings in optical lattices

Abstract

The combination of a rotating cigar-shaped Bose-Einstein condensate with a one-dimensional optical lattice gives rise to very interesting physics. The one-dimensional optical lattice splits the Bose-Einstein condensate into two-dimensional pancake-condensates, each containing a small number of particles and coupled by tunneling processes. The rotation gives rise to the appearance of quantized vortices. The quantum fluctuations of these vortex lines are strongly enhanced because of the small number of particles in each pancake-condensate. For slow rotation the system contains a single vortex-line. The transverse fluctuations of this vortex-line are bosonic modes and obey the same equations as a non-relativistic bosonic string in four dimensions. When fermionic atoms are bound to the vortex-core, it is possible to tune the system parameters such that the dispersions of the fermionic and bosonic modes are identical and the system is supersymmetric. This is called the ultracold superstring and it corresponds to the non-relativistic limit of a four-dimensional superstring. The supersymmetry is experimentally observable by performing density measurements. Moreover, it stabilizes the vortex-line from dissipation. Dissipation means that the vortex-line moves out of the center of the condensate. Since this is directly visible experimentally, this system allows for the investigation of the dynamics of sypersymmetry breaking. For fast rotation a vortex lattice appears. Because of the optical lattice, the modes of the optical lattice get a dispersion in the axial direction of the condensate. When the ratio of the number of particles to the number of vortices is small enough, the vortex lattice melts. Because of the small number of particles in each pancake-condensate, the particle density is inhomogeneous. Therefore also the vortex-lattice melting occurs homogeneous and phase coexistence between a vortex crystal and a vortex liquid occurs. By looking into the correlation functions between the vortex positions, it is possible to distinguish different phases within the vortex crystal and within the vortex liquid.