Superfluid vortex with Mott insulating core

Transcription

1 Superfluid vortex with Mott insulating core Congjun Wu, Han-dong Chen, Jiang-ping Hu, and Shou-cheng Zhang (cond-mat/ ) Department of Physics, Stanford University Department of Applied Physics, Stanford University Department of Physics and Astronomy, University of California, Los Angels Stanford University

2 Outline Introduction. Vortex configuration in in the strongly correlated bosonic system. Suggested experiments. Conclusions.

3 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.

4 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.

5 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.

6 Mean field approximation Decouple to single site problems: The MF ground state wavefunction: The SF order: CDW order: Valid at the small t/u.

7 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.

8 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.

9 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.

10 Vortex evolution at <N>=2.05 and W=0 with varying t/u

11 Evolution of the vortex particle density distribution

12 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.

13 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.

14 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.

15 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.