H. Pino, E. Alba, J. Taron, J. J. Garcia-Ripoll, N. Barberan
Interacting bosonic atoms under strong gauge fields undergo a series of phase transitions that take the cloud from a simple Bose-Einstein condensate all the way to a family of fractional quantum Hall states [M. Popp et al, Phys. Rev. A 70, 053612 (2004)]. In this work we demonstrate that the Hall response of the atoms can be used to locate the phase transitions and characterize the ground state of the many-body state. Moreover, the same response function reveals within some regions of the parameter space, the structure of the spectrum and the allowed transitions to excited states. We verify numerically these ideas using exact diagonalization for a small number of atoms, and provide an experimental protocol to implement the gauge fields and probe the linear response using a periodically driven optical lattice. Finally, we discuss our theoretical results in relation to recent experiments with condensates in artificial magnetic fields [L. J. LeBlanc et al, Proc. Natl. Acad. Sci. USA 109,10811 (2012)] and in agreement to their results verify that the existence of vortex states decreases the Hall response.
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http://arxiv.org/abs/1303.0747
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