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

  • Qiang Zhao
  • Jingxiang Zhao


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.


Shannon information entropy Bose–Einstein condensate Vortex Optical lattice 



The authors would like to thank Professor Weizhu Bao for his help on the numerical calculation. Q.Z. is supported by the Applied Basic Research Programs of Tangshan (Grant No. 18130219a). Innovation Fund (Grant No. X2017287) and Ph.D. Start-up Fund (Grant No. BS2017096) of North China University of Science and Technology.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of ScienceNorth China University of Science and TechnologyTangshanChina
  2. 2.School of Applied ScienceBeijing Information Science & Technology UniversityBeijingChina

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