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

• Published in: Computer physics communications 2015-10, Vol.195, p.117-128
• Main Authors: Kumar, R. Kishor, Young-S., Luis E., Vudragović, Dušan, Balaž, Antun, Muruganandam, Paulsamy, Adhikari, S.K.
• Format: Article
• Language: English
• Subjects: Atomic interactions; Bose–Einstein condensate; C (programming language); Dipolar atoms; FORTRAN; Fortran and C programs; Gross–Pitaevskii equation; Mathematical analysis; Mathematical models; Real- and imaginary-time propagation; Split-step Crank–Nicolson scheme; Summaries; Three dimensional; Two dimensional
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/j.cpc.2015.03.024

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. Program title: (i) imag1dZ, (ii) imag1dX, (iii) imag2dXY, (iv) imag2dXZ, (v) imag3d, (vi) real1dZ, (vii) real1dX, (viii) real2dXY, (ix) real2dXZ, (x) real3d Catalogue identifier: AEWL_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEWL_v1_0.html Program obtainable from: CPC Program Library, Queens University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 111384 No. of bytes in distributed program, including test data, etc.: 604013 Distribution format: tar.gz