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

TL;DR

This paper models $p$-bosons in a bi-partite optical lattice using a nonlinear boson model, revealing a phase transition between number-squeezed and coherent states influenced by lattice anisotropy and interactions.

Contribution

It introduces a nonlinear boson model for $p$-bosons in a square optical lattice and analyzes the phase transition between different quantum states.

Findings

Identification of a second-order phase transition between quantum states.

In the isotropic case, $p$-bosons are in a coherent phase state.

Quantum phase diagram of the nonlinear boson model is provided.

Abstract

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.