Abstract
We study the system that two-component atoms, which are confined in an off-resonance optical lattice, interact with two cavity modes. It has a rich phase diagram composed of many phases, such as anti-ferromagnetic, ferromagnetic, and the XY phases in Mott-insulating (MI) region with odd filling factor. These phases could be distinguished by analyzing the photon numbers with two methods, i.e. the semiclassical approximation and the quantized approach, depending on the intensity of the probe light.
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