Weakly Coupled Bose-Einstein Condensates In Three Dimensions : Numerical Solution of Non linear Gross-Pitaevskii Equation and TFA in Three Dimensions

In the present work the ground state energy of two weakly coupled Bose Einstein condensates separated by double well potential is estimated in three dimensions. By solving three dimensional time independent Gross Pitaevskii equation wave function, density, kinetic energy, potential energy, self energy and total energy of the Bose-Einstein condensates in double well potential have been studied. All these various quantities are also numerically calculated by using Thomas-Fermi Approximation (TFA). It is found that at small number of condensate atoms (N) in the trap, the results obtained from these two methods are quite different but when number of condensate atoms in the trap goes on increasing, the values calculated by using TFA is closer and closer to that obtained from the numerical calculation method. When the value of N is increased, tunneling current in TFA begins to appear and coherent splitting of matter waves starts to be affected. Hence for sufficiently larger value of N, there is "Spontaneous Symmetry Breaking". Further we have numerically calculated the first excited state wave function, density, kinetic energy, potential energy, self energy and total energy.