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 phrase transition in the ground state of BoseEinstein condensates (BECs) trapped in a double square well and in an optical lattice well, respectively. By usingstanding-wave expansion method, we present symmetric and asymmetric ground state solutions of nonlinear Schrodingerequation (NLSE) with a symmetric double square well potential for attractive nonlinearity. In particular, we study theground state wave function’s properties by changing the depth of potential and atomic interactions (here we restrictourselves to the attractive regime). By using the Fourier grid Hamiltonian method, we also reveal a phase transition ofBECs trapped in one-dimensional optical lattice potential.