State diagram and the phase transition of $p$-bosons in a square bi-partite optical lattice

Details State diagram and the phase transition of $p$-bosons in a square bi-partite optical lattice State diagram and the phase transition of $p$-bosons in a square bi-partite optical lattice

2012-02-05

arxiv.org/abs/1202.0955v1

Physics

Condensed Matter

Quantum Gases

15 pages; 5 figures, some in color

Scientific paper

10.1103/PhysRevA.85.013614

It is shown that, in a reasonable approximation, the quantum state of $p$-bosons in a bi-partite square two-dimensional optical lattice is governed by the nonlinear boson model describing tunneling of \textit{boson pairs} between two orthogonal degenerate quasi momenta on the edge of the first Brillouin zone. The interplay between the lattice anisotropy and the atomic interactions leads to the second-order phase transition between the number-squeezed and coherent phase states of the $p$-bosons. In the isotropic case of the recent experiment, Nature Physicis 7, 147 (2011), the $p$-bosons are in the coherent phase state, where the relative global phase between the two quasi momenta is defined only up to mod($\pi$): $\phi=\pm\pi/2$. The quantum phase diagram of the nonlinear boson model is given.

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