Investigating the excitation spectrum of a spin-orbit coupled Bose-Einstein condensate
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- Institutt for fysikk 
The excitation spectrum of a spin-orbit coupled Bose-Einstein condensate is investigated by the use of the Bose-Hubbard model and a mean-field approach. The undiagonalized Hamiltonian matrix for a general inversion-symmetric Bravais lattice is found. Analytical expressions for the excitation spectrum is then found in the limiting case of on-site interactions and nearest-neighbor hopping on a one-dimensional chain and a two-dimensional quadratic lattice. The densities of particles in the ground state acting as mean-field parameters are found self-consistently by minimization of the free energy, and they are seen to be in agreement with published literature.