Cold atoms

                                             Lecture 4.

                                        1^st  November, 2006

                                   Interacting bosons in the trap

                                  Are the interactions important?

                              Fortunate properties of the interactions

                              Fortunate properties of the interactions

                                      Interatomic interactions

                                      Interatomic interactions

                                      Interatomic interactions

                                 Scattering length, pseudopotential

                                         Experimental data

                                       Many-body Hamiltonian

                           Gross-Pitaevskii equation at zero temperature

                                     Gross-Pitaevskii equation

                                     Gross-Pitaevskii equation

                                     Gross-Pitaevskii equation

                       Gross-Pitaevskii equation – variational interpretation

                       Gross-Pitaevskii equation – variational interpretation

                       Gross-Pitaevskii equation – variational interpretation

                       Gross-Pitaevskii equation – variational interpretation

                               Interacting atoms in a parabolic trap

                                   Importance of the interaction

                                   Importance of the interaction

                                   Importance of the interaction

                                   Importance of the interaction

                                   Importance of the interaction

                                              The end

                              On the way to the mean-field Hamiltonian

                              On the way to the mean-field Hamiltonian

                              On the way to the mean-field Hamiltonian

                              On the way to the mean-field Hamiltonian

Variational approach                                                  to the condensate ground state

                         Variational estimate of the condensate properties

                         Variational estimate of the condensate properties

                         Variational estimate of the condensate properties

                         Variational estimate of the condensate properties

                         Variational estimate of the condensate properties

                         Variational estimate of the condensate properties

                         Variational estimate of the condensate properties