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arXiv:1205.6272 · Physical Review A

Dynamical properties of hard-core anyons in one-dimensional optical lattices

Yajiang Hao, Shu Chen

Published Oct 31, 2012• 50 citations
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Abstract

We investigate the dynamical properties of anyons confined in one-dimensional optical lattices combined with a weak harmonic trap using the exact numerical method based on a generalized Jordan-Wigner transformation. The evolving density profiles, momentum distributions, occupation distributions, and occupations of the lowest natural orbital after quench of the harmonic trap are obtained for different statistical parameters. The density profiles of anyons display the same behaviors irrespective of statistical parameter in the full evolving period, while the behaviors dependent on statistical property are shown in the momentum distributions and occupations of natural orbitals.

DOI
10.1103/physreva.86.043631

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We investigate the dynamical properties of anyons confined in one-dimensional optical lattices combined with a weak harmonic trap using the exact numerical method based on a generalized Jordan-Wigner transformation. The evolving density profiles, momentum distributions, occupation distributions, and occupations of the lowest natural orbital after quench of the harmonic trap are obtained for different statistical parameters. The density profiles of anyons display the same behaviors irrespective of statistical parameter in the full evolving period, while the behaviors dependent on statistical property are shown in the momentum distributions and occupations of natural orbitals.
We investigate the ground-state properties of anyons confined in one-dimensional optical lattices with a weak harmonic trap using the exact numerical method based on Jordan-Wigner transformation. It is shown that in the Bose limit $(\ensuremath{\chi}=1)$ and Fermi limit $(\ensuremath{\chi}=0)$ the momentum distributions are symmetric but in between they are asymmetric. It turns out that the origin of asymmetry comes from the fractional statistics that anyons obey. The occupation distribution and the modulus of natural orbitals show crossover behaviors from the Bose limit to the Fermi limit.
Using an anyon-fermion mapping method, we investigate the ground-state properties of hard-core anyons confined in a one-dimensional harmonic trap. The concise analytical formula of the reduced one-body density matrix is obtained. Based on this formula, we evaluated the momentum distribution, the natural orbitals, and their occupation distributions for different statistical parameters. The occupation and occupation fraction of the lowest natural orbital versus anyon number are also displayed. It is shown that the ground-state properties of anyons interplay between bosons and fermions continuously. We can expect that the hard-core anyons of larger statistical parameters exhibit similar properties to the hard-core bosons although anyon systems satisfy specific fractional statistics.
We study the ground-state properties of hard-core bosons trapped by arbitrary confining potentials on one-dimensional optical lattices. A recently developed exact approach based on the Jordan-Wigner transformation is used. We analyze the large distance behavior of the one-particle density matrix, the momentum distribution function, and the lowest natural orbitals. In addition, the low-density limit in the lattice is studied systematically, and the results obtained compared with the ones known for the hard-core boson gas without the lattice.
We study properties of the strongly repulsive Bose gas on one-dimensional incommensurate optical lattices with a harmonic trap, which can be dealt with by use of an exact numerical method through Bose-Fermi mapping. We first exploit the phase transition of hard-core bosons in optical lattices from the superfluid to the Bose-glass phase as the strength of the incommensurate potential increases. Then we study the dynamical properties of the system after suddenly switching off the harmonic trap. We calculate the one-particle density matrices, the momentum distributions, and the natural orbitals and their occupations for both the static and dynamic systems. Our results indicate that the Bose-glass and superfluid phases display quite different properties and expansion dynamics.
We present an exact study of the finite-temperature properties of hard-core bosons (HCB's) confined on one-dimensional optical lattices. Our solution of the HCB problem is based on the Jordan-Wigner transformation and properties of Slater determinants. We analyze the effects of the temperature on the behavior of the one-particle correlations, the momentum distribution function, and the lowest natural orbitals. In addition, we compare results obtained using the grand-canonical and canonical descriptions for systems like the ones recently achieved experimentally. We show that even for such small systems, as small as 10 HCB's in 50 lattice sites, there are only minor differences between the energies and momentum distributions obtained within both ensembles.
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