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Ultracold atoms loaded on optical lattices can provide unprecedented experimental systems for the quantum simulations and manipulations of many quantum phases and quantum phase transitions between these phases. However, so far, how to detect these quantum phases and phase transitions effectively and non-destructively remain an outstanding challenge. We show that cavity enhanced off-resonant light scattering from ultra-cold atoms loaded on optical lattices can provide such a method. It can be used to detect not only the well known superfluid and Mott insulating phases and the superfluid to Mott transition, but also other important phases such as charge density wave, valence bond solid and several kinds of supersolids in one, two and three dimensional optical lattices and quantum phases transitions between these phases. Host: Jian-Xin Zhu |