Vortices as quantum objects in the lowest Landau level

We provide a quantum description of the vortex degrees of freedom for Bose gases in the lowest Landau level. The results can be used to interpret correlated many-particle wave functions in terms of superpositions of vortex configurations. These effects may be visible in the next generation of mesoscopic trap experiments. We expose the important role of nonorthogonality in using simple vortex descriptions, and formulate a basis set which does not experience these difficulties. We show that in general any correlated ground state (even completely fragmented) can be represented as a superposition of completely condensed states. We provide simple illustrations of these methods: a vortex interpretation of the exact, many-body, eigenstates for L <= N, the determination of the energy levels of the single-vortex subspace and finally mention a more speculative description of the Laughlin state in vortex variables.