Optical Lattice Effects on Shannon Information Entropy in Rotating Bose–Einstein Condensates

Abstract

We investigate the formation of Shannon information entropy in a rotating Bose–Einstein condensates confined in a harmonic potential combined with an optical lattice (OL) using the mean field Gross–Pitaevskii equation. With the increase of OL depth $$V_0$$ , at the same rotational frequency $$\Omega $$ , we show that the information entropy increases in momentum space $$S_r$$ and total entropy S and it decreases in position space $$S_k$$ . We also calculate the Landsberg order parameter $$\delta $$ and its dependence on $$\Omega $$ . We find that the critical points between the case of OL and non-OL move along the direction of decreasing $$\Omega $$ with the increase of $$V_0$$ . In particular, the dynamics behaviors indicate that the periodicity of S and $$S_{\text{ max }}$$ loses due to the broken symmetry when OL is added.