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Bulletin of the American Physical Society

Finite-size effects and entanglement in ultracold atoms on optical lattices

Carr, Brown, Schirmer, Ryan V. Mishmash, Serge Santos, Ippei Danshita, Jamie Williams, Charles W. Clark

Published Mar 8, 2007• 0 citations
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arXiv:1211.7085•Physical Review A•Feb 8, 2013•22 citations
We present a wide array of quantum measures on numerical solutions of one-dimensional Bose- and Fermi-Hubbard Hamiltonians for finite-size systems with open boundary conditions. Finite-size effects are highly relevant to ultracold quantum gases in optical lattices, where an external trap creates smaller effective regions in the form of the celebrated ``wedding cake'' structure and the local density approximation is often not applicable. Specifically, for the Bose-Hubbard Hamiltonian we calculate number, quantum depletion, local von Neumann entropy, generalized entanglement or Q measure, fidelity, and fidelity susceptibility; for the Fermi-Hubbard Hamiltonian we also calculate the pairing correlations, magnetization, charge-density correlations, and antiferromagnetic structure factor. Our numerical method is imaginary time propagation via time-evolving block decimation. As part of our study we provide a careful comparison of canonical versus grand canonical ensembles and Gutzwiller versus entangled simulations. The most striking effect of finite size occurs for bosons: we observe a strong blurring of the tips of the Mott lobes accompanied by higher depletion, and show how the location of the first Mott lobe tip approaches the thermodynamic value as a function of system size.
We show that the recently developed optical lattices with Peierls substitution---which can be modeled as a lattice with a complex tunneling coefficient---may be used to induce controllable quantum transport of ultracold atoms. In particular, we show that by ramping up the phase of the complex tunneling coefficient in a spatially uniform fashion, a finite quasi-steady-state current (QSSC) ensues from the exact dynamics of noninteracting fermions. The direction and magnitude of the current can be controlled by the overall phase difference but not the details of the ramp. The entanglement entropy does not increase when the QSSC lasts. Due to different spin statistics, condensed noninteracting bosons do not support a finite QSSC under the same setup. We also find that an approximate form of the QSSC survives when perturbative effects from interactions, weak harmonic background traps, and finite temperature are present, which suggests that our findings should be observable with available experimental capabilities.