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In this paper we reveal the rich ground-state properties induced by thestrong nonlinear atom-photon interaction, which has been found in the recentexperiment about a Bose-Einstein condensate coupling with a high-finesse cavity[Nature (London) 464, 1301 (2010)]. Two detuning-dependent phase diagrams arerevealed by investigating the experimentally-measurable atomic population. Inparticular, two new quantum phase transitions from the superradiant phase orthe normal phase to a dynamically-unstable phase are predicted in the bluedetuning, and moreover, the three-phase coexistence points are found. It isalso demonstrated that these predicted quantum phase transitions are theintrinsic transitions governed only by the second-order derivative of theground-state energy. Finally, we also point out that the region involvingcoexistence of the superradiant phase and the normal phase predicted before cannot happen in the ground state.

Light-shift-induced quantum phase transitions of a Bose-Einstein condensate in the optical cavities