Fernanda Pinheiro, A. F. R. de Toledo Piza
Properties of bosonic atoms in a small system with a periodic quasi one-dimensional ring lattice potential subjected to rotation are examined by performing exact diagonalization in a truncated many body space. The expansion of the many-body Hamiltonian is considered in terms of the first band Bloch functions. No assumption regarding restriction to nearest-neighbor hopping (tight-binding approximation) is involved. Plots which correspond to the zero-temperature phase diagrams are obtained and their salient features, in remarkable quantitative correspondence with the results available for much larger systems, are discussed. The parameter domain associated with the "Mott insulator to superfluid" transition in the ground state corresponds to progressive hopping induced boson delocalization. This is studied in terms of the spectral representation of one-body reduced density matrices and thereby linked to essentially complete dominance of a single eigenstate. Ground state properties relating to superfluidity are examined in the context of two-fluid phenomenology. The basic tool, consisting of the intrinsic inertia associated with small rotation angular velocities in the lab frame, is used to obtain ground state "superfluid fractions" numerically. They are analytically associated with one-body, uniform solenoidal currents in the case of the adopted geometry. These currents are in general incoherent superpositions of contributions from each eigenstate of the associated reduced one-body densities, with the corresponding occupation numbers as weights. Full coherence occurs therefore only when only one eigenstate is occupied by all bosons. The obtained numerical values for the superfluid fractions remain small throughout the parameter region corresponding to the "Mott insulator to superfluid" transition, and saturate at unity only as the lattice is completely smoothed out.
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http://arxiv.org/abs/1301.4672
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