We analyze the finite temperature phase diagram of fermion mixtures in one-dimensional optical lattices as a function of interaction strength. At low temperatures, the system evolves from an anisotropic three-dimensional Bardeen-Cooper-Schrieffer (BCS) superfluid to an effectively two-dimensional Berezinskii-Kosterlitz-Thouless (BKT) superfluid as the interaction strength increases. We calculate the critical temperature as a function of interaction strength, and identify the region where the dimensional crossover occurs for a specified optical lattice potential. Finally, we show that the dominant vortex excitations near the critical temperature evolve from multiplane elliptical vortex loops in the three-dimensional regime to planar vortex-antivortex pairs in the two-dimensional regime, and we propose a detection scheme for these excitations.We analyze the finite temperature phase diagram of fermion mixtures in one-dimensional optical lattices as a function of interaction strength. At low temperatures, the system evolves from an anisotropic three-dimensional Bardeen-Cooper-Schrieffer (BCS) superfluid to an effectively two-dimensional Berezinskii-Kosterlitz-Thouless (BKT) superfluid as the interaction strength increases. We calculate the critical temperature as a function of interaction strength, and identify the region where the dimensional crossover occurs for a specified optical lattice potential. Finally, we show that the dominant vortex excitations near the critical temperature evolve from multiplane elliptical vortex loops in the three-dimensional regime to planar vortex-antivortex pairs in the two-dimensional regime, and we propose a detection scheme for these excitations.

arXiv:0803.1498Physical Review LettersOct 12, 200928 citations

Orbital physics in one dimensional optical lattices

Xiaopeng Li

Bulletin of the American Physical SocietyMar 18, 20130 citations

Phase transitions of S=1 spinor condensates in an optical lattice

Daniel K. Podolsky, Shailesh Chandrasekharan A, Ashvin Vishwanath

We study the phase diagram of spin-one polar condensates in a two-dimensional optical lattice with magnetic anisotropy. We show that the topological binding of vorticity to nematic disclinations allows for a rich variety of phase transitions. These include Kosterlitz-Thouless-like transitions with a superfluid stiffness jump that can be experimentally tuned to take a continuous set of values, and a cascaded Kosterlitz-Thouless transition, characterized by two divergent length scales. For higher integer spin bosons $S$ , the thermal phase transition out of the planar polar phase is strongly affected by the parity of $S$ .We study the phase diagram of spin-one polar condensates in a two-dimensional optical lattice with magnetic anisotropy. We show that the topological binding of vorticity to nematic disclinations allows for a rich variety of phase transitions. These include Kosterlitz-Thouless-like transitions with a superfluid stiffness jump that can be experimentally tuned to take a continuous set of values, and a cascaded Kosterlitz-Thouless transition, characterized by two divergent length scales. For higher integer spin bosons $S$, the thermal phase transition out of the planar polar phase is strongly affected by the parity of $S$.

arXiv:0707.0695Physical Review BDec 9, 200936 citations

Berezinskii-Kosterlitz-Thouless transition of two-dimensional Bose gases in a synthetic magnetic field

Junjun Xu, Qiang Gu

We study the field dependency of the Berezinskii-Kosterlitz-Thouless transition temperature ${T}_{c}(H)$ of Bose gases in a two-dimensional optical lattice in the synthetic magnetic field using the Metropolis Monte Carlo method. The system is described by the frustrated $XY$ model and the critical temperature is determined through observing the disappearance of the central peak of the momentum distribution of the gas, which can be directly measured by the time-of-flight absorbing imaging in cold-atom experiments. ${T}_{c}(H)$ is found to exhibit a largest peak at the fraction of a flux quantum $f=\ensuremath{\varphi}/{\ensuremath{\varphi}}_{0}=1/2$ and a second-largest one at $f=1/3$ , in agreement with former studies on superconducting Josephson arrays. We also indicate that the synthetic magnetic field experiment can produce strong enough frustration for exploring the physics of the frustrated $XY$ model.We study the field dependency of the Berezinskii-Kosterlitz-Thouless transition temperature ${T}_{c}(H)$ of Bose gases in a two-dimensional optical lattice in the synthetic magnetic field using the Metropolis Monte Carlo method. The system is described by the frustrated $XY$ model and the critical temperature is determined through observing the disappearance of the central peak of the momentum distribution of the gas, which can be directly measured by the time-of-flight absorbing imaging in cold-atom experiments. ${T}_{c}(H)$ is found to exhibit a largest peak at the fraction of a flux quantum $f=\ensuremath{\varphi}/{\ensuremath{\varphi}}_{0}=1/2$ and a second-largest one at $f=1/3$, in agreement with former studies on superconducting Josephson arrays. We also indicate that the synthetic magnetic field experiment can produce strong enough frustration for exploring the physics of the frustrated $XY$ model.

arXiv:1112.1264Physical Review AApr 11, 20123 citations

Berezinskii-Kosterlitz-Thouless quantum transition in two dimensions

Anonymous

Physical review. B./Physical review. BOct 21, 20250 citations

S

, the thermal phase transition out of the planar polar phase is strongly affected by the parity of

S

We study the field dependency of the Berezinskii-Kosterlitz-Thouless transition temperature

{T}_{c}(H)

of Bose gases in a two-dimensional optical lattice in the synthetic magnetic field using the Metropolis Monte Carlo method. The system is described by the frustrated

XY

model and the critical temperature is determined through observing the disappearance of the central peak of the momentum distribution of the gas, which can be directly measured by the time-of-flight absorbing imaging in cold-atom experiments.

{T}_{c}(H)

is found to exhibit a largest peak at the fraction of a flux quantum $f=\ensuremath{\varphi}/{\ensuremath{\varphi}}_{0}=1/2$ and a second-largest one at

f=1/3

, in agreement with former studies on superconducting Josephson arrays. We also indicate that the synthetic magnetic field experiment can produce strong enough frustration for exploring the physics of the frustrated

XY

model.