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Detection of quantum orders of ultracold atoms in optical lattices by off-resonant scattering of cavity photons

Jinwu Ye, Jiangming Zhang, Wu‐Ming Liu, Keye Zhang, Yan Li, Z. Y. Ou, Weiping Zhang

Published Dec 22, 2008• 0 citations
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We study the effect of defects in the Mott insulator phase of ultracold atoms in an optical lattice on the dynamics of resonant electronic excitations. These excitations can be described analogous to Frenkel excitons in solids and form polaritons, when coupled to an optical resonator. Defects, which are empty sites in a singly occupied Mott insulator state or singly occupied sites for a filling factor two, change the exciton dynamics. We show that vacancies behave like hard sphere scatterers, while singly occupied sites in a doubly filled region generate either attractive or repulsive interaction potentials. We suggest cavity polaritons as tools which detect such defects and show how the scattering can be controlled by changing the exciton–photon detuning. In the case of aspherical individual lattice sites, we calculate the effective scattering potential as a function of the cavity photon polarization direction which exhibits a crossover from a repulsive into an attractive potential and should give a clearly observable signal.
We study off-resonant collective light scattering from ultracold atoms trapped in an optical lattice. Scattering from different atomic quantum states creates different quantum states of the scattered light, which can be distinguished by measurements of the spatial intensity distribution, quadrature variances, photon statistics, or spectral measurements. In particular, angle-resolved intensity measurements reflect global statistics of atoms (total number of radiating atoms) as well as local statistical quantities (single-site statistics even without optical access to a single site) and pair correlations between different sites. As a striking example we consider scattering from transversally illuminated atoms into an optical cavity mode. For the Mott-insulator state, similar to classical diffraction, the number of photons scattered into a cavity is zero due to destructive interference, while for the superfluid state it is nonzero and proportional to the number of atoms. Moreover, we demonstrate that light scattering into a standing-wave cavity has a nontrivial angle dependence, including the appearance of narrow features at angles, where classical diffraction predicts zero. The measurement procedure corresponds to the quantum nondemolition measurement of various atomic variables by observing light.