Regular Article

On the information entropy of matter-waves in quasi-periodic lattice potentials

¹ Department of Physics, Banwarilal Bhalotia College, Asansol 713303, India
² Department of Physics, Kazi Nazrul University, Asansol 713340, India
³ Department of Physics, Government General Degree College, Chapra Shikra, Nadia 741123, India

^a e-mail: skgolamali@gmail.com

Received: 1 June 2018
Received in final form: 13 August 2018
Published online: 17 January 2019

Abstract

We consider spatial localization of matter waves in quasi-periodic potentials within the framework of mean-field approach. The system can support bound states localized either in single lattice site or extended over many lattice sites. Localization of the state is quantified by means of Shannon information entropy in co-ordinate (S_ρ) and momentum (S_γ) spaces for both attractive and repulsive interaction. It is seen that the difference in entropies (S_n) between coordinate and momentum spaces becomes negative for attractive interaction while it becomes positive for repulsive interaction. The value of |S_n| decreases with the increase of localization. The highest value of localization is, however, limited by the entropic uncertainty relation. The quasi-bound state is found to hold lowest entropic uncertainty (maximally localized) in the zero interaction limit.