Quantum monte carlo simulations of confined bosonic atoms in optical lattices

We study static properties of ultra-cold bosonic atoms in two-dimensional optical lattices by quantum Monte Carlo simulations of the bosonic Hubbard model in parabolic confinement potentials. Our focus is on local probes identifying Mott-insulating and superfluid regions, which can coexist in the inhomogenous environment of the trap. By proposing an effective ladder model for the boundary region between the two phases we can show clear evidence for the absence of true quantum critical behavior and explain the absence of critical slowing down at the quantum phase transition in a harmonic trap.

[1]  Oliva.  Density profile of the weakly interacting Fermi gas confined in a potential well: Nonzero temperature. , 1989, Physical review. B, Condensed matter.

[2]  Local-density approximation for confined bosons in an optical lattice (7 pages) , 2004, cond-mat/0404395.

[3]  Phase diagram of the Bose-Hubbard Model , 1993, cond-mat/9307011.

[4]  R. Scalettar,et al.  Local quantum criticality in confined fermions on optical lattices. , 2003, Physical review letters.

[5]  U. Schollwock,et al.  Spatial correlations of trapped one-dimensional bosons in an optical lattice , 2003, cond-mat/0310388.

[6]  T. Esslinger,et al.  Transition from a strongly interacting 1d superfluid to a Mott insulator. , 2003, Physical review letters.

[7]  A. Sandvik,et al.  Quantum Monte Carlo simulation method for spin systems. , 1991, Physical review. B, Condensed matter.

[8]  Erik S. Sørensen,et al.  Generic incommensurate transition in the two-dimensional boson Hubbard model , 2004, cond-mat/0401236.

[9]  Fisher,et al.  Boson localization and the superfluid-insulator transition. , 1989, Physical review. B, Condensed matter.

[10]  C. Gardiner,et al.  Cold Bosonic Atoms in Optical Lattices , 1998, cond-mat/9805329.

[11]  A. Michel,et al.  Directional effects of heavy-ion irradiation in Tb/Fe multilayers , 2000 .

[12]  A. Sandvik,et al.  Quantum Monte Carlo with directed loops. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  R. Scalettar,et al.  Mott domains of bosons confined on optical lattices. , 2002, Physical review letters.

[14]  A. Sandvik.  A generalization of Handscomb's quantum Monte Carlo scheme-application to the 1D Hubbard model , 1992 .

[15]  T. Hänsch,et al.  Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms , 2002, Nature.

[16]  Pollock,et al.  Path-integral computation of superfluid densities. , 1987, Physical review. B, Condensed matter.

[17]  Batrouni,et al.  Quantum critical phenomena in one-dimensional Bose systems. , 1990, Physical review letters.

[18]  B. Svistunov,et al.  Revealing the superfluid–Mott-insulator transition in an optical lattice , 2002, cond-mat/0202510.

[19]  J. Cirac,et al.  High-temperature superfluidity of fermionic atoms in optical lattices. , 2002, Physical review letters.

[20]  Olav F Syljuåsen.  Directed loop updates for quantum lattice models. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  A. Sandvik.  Stochastic series expansion method with operator-loop update , 1999, cond-mat/9902226.

[22]  Phase transition of a Bose gas in a harmonic potential , 1996, cond-mat/9604037.

[23]  Matthias Troyer,et al.  Parallel Object Oriented Monte Carlo Simulations , 1998, ISCOPE.