Fortran and C programs for the time-dependent dipolar Gross-Pitaevskii equation in an anisotropic trap

• Autor(a) principal: Kumar, R. Kishor
• Data de Publicação: 2015
• Outros Autores: Young-S., Luis E. [UNESP], Vudragović, Dušan, Balaž, Antun, Muruganandam, Paulsamy, Adhikari, S. K. [UNESP]
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1016/j.cpc.2015.03.024; http://hdl.handle.net/11449/171896
• topic: Bose-Einstein condensate; Dipolar atoms; Fortran and C programs; Gross-Pitaevskii equation; Real- and imaginary-time propagation; Split-step Crank-Nicolson scheme

Many of the static and dynamic properties of an atomic Bose-Einstein condensate (BEC) are usually studied by solving the mean-field Gross-Pitaevskii (GP) equation, which is a nonlinear partial differential equation for short-range atomic interaction. More recently, BEC of atoms with long-range dipolar atomic interaction are used in theoretical and experimental studies. For dipolar atomic interaction, the GP equation is a partial integro-differential equation, requiring complex algorithm for its numerical solution. Here we present numerical algorithms for both stationary and non-stationary solutions of the full three-dimensional (3D) GP equation for a dipolar BEC, including the contact interaction. We also consider the simplified one- (1D) and two-dimensional (2D) GP equations satisfied by cigar- and disk-shaped dipolar BECs. We employ the split-step Crank-Nicolson method with real- and imaginary-time propagations, respectively, for the numerical solution of the GP equation for dynamic and static properties of a dipolar BEC. The atoms are considered to be polarized along the z axis and we consider ten different cases, e.g., stationary and non-stationary solutions of the GP equation for a dipolar BEC in 1D (along x and z axes), 2D (in x-y and x-z planes), and 3D, and we provide working codes in Fortran 90/95 and C for these ten cases (twenty programs in all). We present numerical results for energy, chemical potential, root-mean-square sizes and density of the dipolar BECs and, where available, compare them with results of other authors and of variational and Thomas-Fermi approximations.