Mesoscopic effects in quantum phases of ultracold quantum gases in optical lattices

Journal Article · Fri Jan 15 00:00:00 EST 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.013613· OSTI ID:21388776

Carr, L D; Schirmer, D G ^[1]; Wall, M L ^[1]; Brown, R C; Williams, J E; Clark, Charles W ^[2]

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1. Department of Physics, Colorado School of Mines, Golden, Colorado 80401 (United States)
2. Joint Quantum Institute, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 (United States)

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.

• OSTI ID: 21388776
• Journal Information: Physical Review. A, Vol. 81, Issue 1; Other Information: DOI: 10.1103/PhysRevA.81.013613; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANTIFERROMAGNETISM
APPROXIMATIONS
BOSONS
BOUNDARY CONDITIONS
CHARGE DENSITY
COMPARATIVE EVALUATIONS
CORRELATIONS
ENTROPY
HAMILTONIANS
MAGNETIZATION
NUMERICAL SOLUTION
ONE-DIMENSIONAL CALCULATIONS
QUANTUM ENTANGLEMENT
SIMULATION
STRUCTURE FACTORS
CALCULATION METHODS
DIMENSIONLESS NUMBERS
EVALUATION
MAGNETISM
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
PHYSICAL PROPERTIES
QUANTUM OPERATORS
THERMODYNAMIC PROPERTIES