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Ultracold atoms loaded on optical lattices can provide unprecedentedexperimental systems for the quantum simulations and manipulations of manyquantum phases and quantum phase transitions between these phases. However, sofar, how to detect these quantum phases and phase transitions effectivelyremains an outstanding challenge. In this paper, we will develop a systematicand unified theory of using the optical Bragg scattering, atomic Braggscattering or cavity QED to detect the ground state and the excitation spectrumof many quantum phases of interacting bosons loaded in bipartite and frustratedoptical lattices.  We show that the two photon Raman transition processes in the three detectionmethods not only couple to the density order parameter, but also the {\slvalence bond order} parameter due to the hopping of the bosons on the lattice.This valence bond order coupling is very sensitive to any superfluid order orany Valence bond (VB) order in the quantum phases to be probed. These quantumphases include not only the well known superfluid and Mott insulating phases,but also other important phases such as various kinds of charge density waves(CDW), valence bond solids (VBS), CDW-VBS phases with both CDW and VBS ordersunique to frustrated lattices, and also various kinds of supersolids.  The physical measurable quantities of the three experiments are the lightscattering cross sections, the atom scattered clouds and the cavity leakingphotons respectively. We analyze respectively the experimental conditions ofthe three detection methods to probe these various quantum phases and theircorresponding excitation spectra. We also address the effects of a finitetemperature and a harmonic trap.

annals of physics

Optical Bragg, atom Bragg and cavity QED detections of quantum phases  and excitation spectra of ultracold atoms in bipartite and frustrated optical  lattices