Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2016, Tutora: Montserrat Guilleumas Morell
We have studied the internal Josephson effect between two hyperfine components of a Bose-Einstein condensate within the non-linear Gross-Pitaevskii equation framework. We have derived the sine-Gordon equation for the relative phase between the two components under the assumption of small variations of the density. In order to check the validity of this approximation, we have performed numerical simulations of the 1D Gross-Pitaevskii equation and we have found a good agreement with the theoretical predictions