Optical bistability in cold atom cavity systems

Coupled cold atom-cavity/BEC-cavity systems have attracted significant attention owing to their appeal as optomechanical systems [1] and as probes of atomic many body quantum effects in a novel setting [2]. We investigate the non-linear nature of the effective Hamiltonian that describes the cavity-atom system. We analyse the energy dispersion derived from the effective Hamiltonian in regions where the atom-cavity system exhibits bistability. \\[4pt] [1] F. Brennecke et.al., Science \textbf{322}, 235 (2008)\\[0pt] [2] J.Larson et.al., Phys. Rev. Lett. \textbf{100}, 050401 (2008)