Characteristics of information entropy in spin-orbit coupled spin-1 Bose-Einstein condensates

In this paper, we study the properties of information entropy in spin-orbit coupled spin-1 Bose-Einstein condensates. Our discussion is divided into two parts, stationary state and dynamics. For the former, we find that the coordinate component S-r and total entropy S increase with the strength of the spin-orbit coupling kappa. The momentum component S-k shows a discontinuity behavior, it increases with kappa when kappa is lesser than a critical value kappa(c), while it decreases with kappa when kappa is greater than kappa(c). In order to characterize the disorder-to-order transition, we introduce an order parameter eta. Numerical results display that eta gradually increases with increasing kappa and reaches its saturation, which implies that the system becomes more and more ordered. For the latter, the S-r increases and S-k decreases with increasing kappa at the same time. The entropic uncertainty relation is well obeyed at fixed kappa. Moreover, eta decreases as a function of t. The strength effect of spin-orbit coupling on order-to-disorder transition becomes weak.