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Measuring spatial entanglement in an optical lattice

Fabbri N., Cramer M, Bernard A, Caruso F., Rosi S., L. Fallani, M. C. FORT, Martin Bodo Plenio, Inguscio M.

Published Jan 1, 2014• 0 citations
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In this work we study the entangled states that can be created in bipartite two-dimensional optical lattices loaded with ultracold atoms. We show that, by using only two sets of measurements, it is possible to compute a set of entanglement witness operators distributed over arbitrarily large regions of the lattice, and use these witnesses to produce two-dimensional plots of the entanglement content of these states. We also discuss the influence of noise on the states and on the witnesses, as well as the relation to ongoing experiments.
We show that the effect of measurement backaction results in the generation of multiple many-body spatial modes of ultracold atoms trapped in an optical lattice, when scattered light is detected. The multipartite mode entanglement properties and their nontrivial spatial overlap can be varied by tuning the optical geometry in a single setup. This can be used to engineer quantum states and dynamics of matter fields. We provide examples of multimode generalizations of parametric down-conversion, Dicke, and other states; investigate the entanglement properties of such states; and show how they can be transformed into a class of generalized squeezed states. Furthermore, we propose how these modes can be used to detect and measure entanglement in quantum gases.