Schwinger bosons and cold atom systems

Antônio Sérgio Teixeira Pires

Valentin Kasper

In this thesis we theoretically investigate the quantum simulation of lattice gauge theories for cold atom experiments. We give an explicit proposal to study a (1+1) - \ndimensional U(1) lattice gauge theory. Starting with a bosonic and a fermionic atomic gas we tune the geometry and engineer the interactions such that we end up with a \none-dimensional system obeying the principle of local gauge invariance. A further important aspect of this proposal is the explicit use of highly occupied bosonic states in \norder to make the investigation of strong field quantum electrodynamics feasible. In addition, we present an approach based on the functional integral in order to theoretically treat U(1) and SU(N) gauge fields interacting with matter out of equilibrium. We show that under specific conditions the quantum theory can be accurately mapped \nonto a classical statistical ensemble. Further, exploiting this possibility, we study the prospect to observe intricate high energy phenomena like Schwinger pair-production and string breaking in such future cold atom experiments.

Nakano, Yuki, Takumi Ishima, Naohiro Kobayashi +3 more

We study the three-dimensional bosonic t-J model, i.e., the t-J model of "bosonic electrons" at finite temperatures. This model describes a system of cold bosonic atoms with two species in an optical lattice. The model is derived from the Hubbard model for very large on-site repulsive interaction between bosons of same species (hard-core nature) and also strong correlations between different species. The operator B_{xσ} for an atom at the site x with a two-component (pseudo-) spin σ(=1,2) is treated as a hard-core boson operator, and represented by a composite of two slave particles; a spinon described by a CP^1 field (Schwinger boson) z_{xσ} and a holon described by a hard-core-boson field ϕ_x as B_{xσ}=ϕ^†_x z_{xσ}. ϕ_x is then expressed by a pseudo-spin, which is, in turn, represented by another CP^1 (pseudo) spinon w_{xη} as ϕ_x = w_{x2}^†w_{x1}. We then have a double-CP^1 representation of the model by z_{xσ} and w_{xη}. By means of Monte Carlo simulations of this bosonic t-J model, we study its phase structure and the possible phenomena like appearance of antiferromagnetic long-range order, Bose-Einstein condensation, phase separation, etc. They should be compared with the possible experimental results of a recently studied boson-boson mixture like ^87Rb and ^41K in an optical lattice.

Dietrich E. Wolf, J. Zittartz

Fan Hong-Yi, Li Yong-ping

In terms of the Schwinger boson representation of angular momentum We introduce suitable phase operators which exhibit similar properties to those of the phase operators in radiation field into atomic system. With the help of them angular momentum's third component phase uncertainty relation are discussed. Also, the eigenstates of the Hermitian phase operator are derived.

Fei-Jie Huang, Qihui Chen, Wu-Ming Liu