# Finite-temperature study of bosons in a two-dimensional optical lattice

## Abstract

We use quantum Monte Carlo (QMC) simulations to study the combined effects of harmonic confinement and temperature for bosons in a two-dimensional(2D) optical lattice. The scale-invariant, finite temperature state diagram is presented for the Bose-Hubbard model in terms of experimental parameters - the particle number, confining potential and interaction strength. To distinguish the nature of the spatially separated superfluid, Mott insulator, and normal Bose liquid phases, we examine the local density, compressibility, superfluid density, and Green's function. In the annular superfluid rings, as the width of the ring decreases, the long-range superfluid correlations start to deviate from an equivalent homogeneous 2D system. At zero temperature, the correlation decay is intermediate between one-dimension and two-dimensions, while at a finite temperature, the decay is similar to that in one-dimension at a much lower temperature. The calculations reveal shortcomings of the local density approximation in describing superfluid properties of trapped bosons. We also present the finite-temperature phase diagram for the homogeneous two dimensional Bose-Hubbard model. We compare our state diagram with the results of a recent experiment at NIST on a harmonically trapped 2D lattice [Phys. Rev. Lett. 105, 110401 (2010)], and identify a finite-temperature effect in the experiment.

- Authors:

- Department of Physics, University of California, Davis, California 95616 (United States)
- Department of Physics, Ohio State University, Columbus, Ohio 43210 (United States)
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581 (Japan)

- Publication Date:

- OSTI Identifier:
- 21596836

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. B, Condensed Matter and Materials Physics

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevB.84.054302; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1098-0121

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; BOSONS; COMPARATIVE EVALUATIONS; COMPRESSIBILITY; CORRELATIONS; GREEN FUNCTION; HUBBARD MODEL; INTERACTIONS; INTERFERENCE; LASER RADIATION; MONTE CARLO METHOD; PHASE DIAGRAMS; SIMULATION; STARK EFFECT; SUPERFLUIDITY; TEMPERATURE DEPENDENCE; TRAPPING; TWO-DIMENSIONAL CALCULATIONS; CALCULATION METHODS; CRYSTAL MODELS; DIAGRAMS; ELECTROMAGNETIC RADIATION; EVALUATION; FUNCTIONS; INFORMATION; MATHEMATICAL MODELS; MECHANICAL PROPERTIES; RADIATIONS

### Citation Formats

```
Mahmud, K. W., Scalettar, R. T., Duchon, E. N., Trivedi, N., Kato, Y., and Kawashima, N..
```*Finite-temperature study of bosons in a two-dimensional optical lattice*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVB.84.054302.

```
Mahmud, K. W., Scalettar, R. T., Duchon, E. N., Trivedi, N., Kato, Y., & Kawashima, N..
```*Finite-temperature study of bosons in a two-dimensional optical lattice*. United States. doi:10.1103/PHYSREVB.84.054302.

```
Mahmud, K. W., Scalettar, R. T., Duchon, E. N., Trivedi, N., Kato, Y., and Kawashima, N.. Mon .
"Finite-temperature study of bosons in a two-dimensional optical lattice". United States. doi:10.1103/PHYSREVB.84.054302.
```

```
@article{osti_21596836,
```

title = {Finite-temperature study of bosons in a two-dimensional optical lattice},

author = {Mahmud, K. W. and Scalettar, R. T. and Duchon, E. N. and Trivedi, N. and Kato, Y. and Kawashima, N.},

abstractNote = {We use quantum Monte Carlo (QMC) simulations to study the combined effects of harmonic confinement and temperature for bosons in a two-dimensional(2D) optical lattice. The scale-invariant, finite temperature state diagram is presented for the Bose-Hubbard model in terms of experimental parameters - the particle number, confining potential and interaction strength. To distinguish the nature of the spatially separated superfluid, Mott insulator, and normal Bose liquid phases, we examine the local density, compressibility, superfluid density, and Green's function. In the annular superfluid rings, as the width of the ring decreases, the long-range superfluid correlations start to deviate from an equivalent homogeneous 2D system. At zero temperature, the correlation decay is intermediate between one-dimension and two-dimensions, while at a finite temperature, the decay is similar to that in one-dimension at a much lower temperature. The calculations reveal shortcomings of the local density approximation in describing superfluid properties of trapped bosons. We also present the finite-temperature phase diagram for the homogeneous two dimensional Bose-Hubbard model. We compare our state diagram with the results of a recent experiment at NIST on a harmonically trapped 2D lattice [Phys. Rev. Lett. 105, 110401 (2010)], and identify a finite-temperature effect in the experiment.},

doi = {10.1103/PHYSREVB.84.054302},

journal = {Physical Review. B, Condensed Matter and Materials Physics},

issn = {1098-0121},

number = 5,

volume = 84,

place = {United States},

year = {2011},

month = {8}

}