Quantum information and many body physics with cold atoms

Xiaofei Zhang,Wuming Liu,Yaohua Chen,Wei Wu,Guocai Liu,Lin Wen

doi:10.1007/s11434-012-5095-1

Abstract

We review our recent theoretical advances in quantum information and many body physics with cold atoms in various external potential, such as harmonic potential, kagome optical lattice, triangular optical lattice, and honeycomb lattice. The many body physics of cold atom in harmonic potential is investigated in the frame of mean-field Gross-Pitaevskii equation. Then the quantum phase transition and strongly correlated effect of cold atoms in triangular optical lattice, and the interacting Dirac fermions on honeycomb lattice, are investigated by using cluster dynamical mean-field theory and continuous time quantum Monte Carlo method. We also study the quantum spin Hall effect in the kagome optical lattice.

Highlights

Observation of Bose-Einstein condensates (BECs) in gases of weakly interacting alkali-metal atoms has stimulated intensive studies of the nonlinear matter waves, where both bright and dark solitons have been observed [1,2,3] and the gap solitons are realized in a optical lattice experimentally [4, 5]
We investigate the formation of various types of vector solitons in two-species Bose-Einstein condensates with arbitrary scattering lengths, and find that by tuning the interaction parameter via Feshbach resonance, transformation between different types of vector solitons is possible
We investigate the quantum phase transition and strongly correlated effect of cold atoms in triangular optical lattice, and the interacting Dirac fermions on honeycomb lattice

Summary

Quantum information and many body physics with cold atoms

We review our recent theoretical advances in quantum information and many body physics with cold atoms in various external potential, such as harmonic potential, kagome optical lattice, triangular optical lattice, and honeycomb lattice. To obtain the exact soliton solutions of eq (1), we take advantage of the method of similar transformation, which is widely used to solve the general nonlinear Schrodinger equation with timeand space-modulated coefficients. To this end, we first assume the order parameter is written in terms of amplitude and phases as ψ = φ exp(iα), with φ positively defined as real function. We investigate the quantum phase transition and strongly correlated effect of cold atoms in triangular optical lattice, and the interacting Dirac fermions on honeycomb lattice. See [26] for a detailed discussion

Mott insulator

Aαeff α

Conclusions