State diagrams for harmonically trapped bosons in optical lattices

Abstract

We use quantum Monte Carlo simulations to obtain zero-temperature state diagrams for strongly correlated lattice bosons in one and two dimensions under the influence of a harmonic confining potential. Since harmonic traps generate a coexistence of superfluid and Mott insulating domains, we use local quantities such as the quantum fluctuations of the density and a local compressibility to identify the phases present in the inhomogeneous density profiles. We emphasize the use of the "characteristic density" to produce a state diagram that is relevant to experimental optical lattice systems, regardless of the number of bosons or trap curvature and of the validity of the local-density approximation. We show that the critical value of U/t at which Mott insulating domains appear in the trap depends on the filling in the system, and it is in general greater than the value in the homogeneous system. Recent experimental results by Spielman et al. [Phys. Rev. Lett. 100, 120402 (2008)] are analyzed in the context of our two-dimensional state diagram, and shown to exhibit a value for the critical point in good agreement with simulations. We also study the effects of finite, but low (T<t/2), temperatures. We find that in two dimensions they have little influence on our zero-temperature results, while their effect is more pronounced in one dimension.

10 pages, 11 figures, published version

References in corpus (25)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• A Mott insulator of fermionic atoms in an optical lattice
• The Mott insulator transition in two dimensions
• Monte Carlo study of two-dimensional Bose-Hubbard model
• Quantum Monte Carlo simulations of confined bosonic atoms in optical lattices
• Local quantum criticality in confined fermions on optical lattices
• Condensate fraction in a 2D Bose gas measured across the Mott-insulator transition
• Measuring the one-particle excitations of ultracold fermionic atoms by stimulated Raman spectroscopy
• Spatial correlations of trapped 1d bosons in an optical lattice
• Spectroscopy of ultracold atoms by periodic lattice modulations
• Boson Mott insulators at finite temperatures
• Quantum Monte Carlo study of confined fermions in one-dimensional optical lattices
• Bethe-Ansatz density-functional theory of ultracold repulsive fermions in one-dimensional optical lattices
• Intrinsic Heating and Cooling in Adiabatic Processes for Bosons in Optical Lattices
• The Stochastic Green Function (SGF) algorithm
• Directed update for the Stochastic Green Function algorithm
• Signature of Mott-insulator transition with ultra-cold fermions in a one-dimensional optical lattice
• Trapping and cooling fermionic atoms into the Mott and Néel states
• Numerical simulations of strongly correlated fermions confined in 1D optical lattices
• Compression as a tool to detect Bose glass in cold atoms experiments
• Canonical Trajectories and Critical Coupling of the Bose-Hubbard Hamiltonian in a Harmonic Trap
• Probing correlated phases of bosons in optical lattices via trap squeezing
• Time of flight observables and the formation of Mott domains of fermions and bosons on optical lattices
• Phases of Bosons or Fermions in confined optical lattices

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• Superfluid to normal phase transition in strongly correlated bosons in two and three dimensions
• Pairing in a two-dimensional Fermi gas with population imbalance
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• Expansion of Bose-Hubbard Mott insulators in optical lattices
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• Thermal bosons in 3d optical lattices via tensor networks
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• Spectral moment sum rules for the retarded Green's function and self-energy of the inhomogeneous Bose-Hubbard model in equilibrium and nonequilibrium
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• Counterflow of lattice polarons in harmonically confined optical lattices
• Small quench dynamics as a probe for trapped ultracold atoms
• Half-integer Mott-insulator phases in the imbalanced honeycomb lattice
• The Bose-Hubbard polaron from weak to strong coupling
• Interaction-Induced Gradients Across a Confined Fermion Lattice