Symmetry Breaking Ground States of Bose-Einstein Condensates in 1D Double Square Well and Optical Lattice Well

We investigate the phenomena of symmetry breaking and phase transitionin the ground state of Bose-Einstein condensates (BECs) trapped ina double square well and in an optical lattice well, respectively.By using standing-wave expansion method, we present symmetric andasymmetric ground state solutions of nonlinear Schrödingerequation (NLSE) with a symmetric double square well potential forattractive nonlinearity. In particular, we study the ground statewave function's properties by changing the depth of potentialand atomic interactions (here we restrict ourselves to the attractiveregime). By using the Fourier grid Hamiltonian method, we alsoreveal a phase transition of BECs trapped in one-dimensionaloptical lattice potential.