Excitation spectrum of correlated bosons in a trap

Subhasis Sinha

Max-Planck Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, 01187 Dresden, Germany

Bosons in a tight optical lattice can be described by Bose-Hubbard model which undergoes quantum phase-transition from superfluid to Mott insulator for strong on site repulsion. We study the zero temperature phase diagram within mean-field approximation. The small amplitude oscillations of the system are obtained within the time-dependent variational method. Particle(hole) excitation spectrum is also found analytically for Mott insulator. In superfluid it shows gapless linear excitation spectrum, which in deep superfluid regime corresponds to the collective excitations of discrete non-linear Schrodinger equation (DNLS). Next we generalise this method for non-uniform system of bosons in a trap. A few low lying excitations (like dipole, quadrupole etc.) are calculated for varying onsite interaction.