Superfluid vortex with Mott insulating core Congjun Wu, Han-dong Chen, Jiang-ping Hu, and Shou-cheng Zhang (cond-mat/0211457) Department of Physics, Stanford University Department of Applied Physics, Stanford University Department of Physics and Astronomy, University of California, Los Angels Stanford University
Outline Introduction. Vortex configuration in in the strongly correlated bosonic system. Suggested experiments. Conclusions.
Introduction Vortex in in the ultra-cold atomic system. topological defect of of the the SF SF order, core core of of size size ξ (healing length); Gross-Pitaevskii-Bogoliubov approximation (weak coupling); both both the the minimal particle density and and SF SF order are are located at at the the core. core. The superfluid-mott insulator (SF-MI) transition on on optical lattices. MI MI phases with with commensurate (integer) fillings at at small t/u; t/u; the the SF SF phase with with incommensurate fillings or or commensurate fillings at at large large t/u. t/u.
Introduction Vortex core as as a probe to to competing orders. the the antiferromagnetic vortex core core in in underdoped cuprates; SO(5) theory, the the topological meron defect of of the the 5-d 5-d superspin. Vortex near the SF-MI and SF-CDW transitions. vortex with with the the nearly MI MI or or CDW core; core; the the core core particle density distribution; evolution from from the the strong to to weak coupling region.
Bose-Hubbard model M. P. A. Fisher et al, PRB 40, 546 (1989) Also valid for charged bosonic systems in the magnetic field. t: the hopping amplitude, U: on-site repulsion, W: nearest neighbor repulsion, µ: the chemical potential, m: the boson mass, Ω: rotating angular velocity, A: vector potential from the Coriolis force, Vex: the trap potential, Vcf: the centrifugal potential.
Mean field approximation Decouple to single site problems: The MF ground state wavefunction: The SF order: CDW order: Valid at the small t/u.
Phase diagram at W=0 and Ω =0 Lobes of commensurate MI phases, suppression of the SF order at small t/u. Approximate particle-hole symmetry around each commensurate filling.
d l A = 2 π, Ω= h êi2 m L 2 M Ω= h ê I2 m L 2 M Typical Vortex configurations at t/u=0.02, W=0 L=40 a0. circulation of A:2π. Ω=h/(2mL*L). Vex and Vcf are neglected, Hole-like: (a), (b) <N>=1.95; Particle-like: (c), (d) <N>=2.05.
Vortex evolution at <N>=1.95 and W=0 with varying t/u The path is cut from (10,20) and (30,20) in the 40*40 system. Evolution from the strong to weak coupling as increasing t/u~0.06. teff/u is reduced as approaching the vortex core.
Vortex evolution at <N>=2.05 and W=0 with varying t/u
Evolution of the vortex particle density distribution
Phase diagram with W/U=0.1 and Ω=0 CDW and Super-solid phases appear at the half-integer filling and small t/u. Map to the spin 1/2 Heisenberg model with the Ising anisotropy. Approximate SO(3) symmetry: <a> and CDW.
Vortex with the CDW core ( meron ) W/U=0.1, t/u=0.023 and <N>=1.5. Similar to the AF vortex in underdoped high Tc superconductors.
Suggested experiments Difficulty: small size of the vortex core for the optical imaging. Whether the strong coupling vortex structure can survive in the time-of-flight expansion is not clear. Put the two-component condensate Rb on the optical lattice. Follow Willams s method (Nature 401, 568) to verify the existence of the vortex non-destructively and then do the expansion to study relations between the density contrast and t/u. The Josephson array system in the magnetic field. From the electrical field distribution, it is possible to determine the vortex charge.
Conclusion The vortex core is a more strongly coupled region compared to the bulk area. Near the SF-MI transition, the vortex core is nearly Mott insulating and the core particle density approaches the nearest commensurate value. Near the SF-CDW transition, the meron like vortex is found. As t/u increases, the vortex evolves from the strong coupling configuration to weak coupling one.