In ultracold atoms settings, inelastic light scattering is a preeminent technique to reveal static and dynamic properties at nonzero momentum. In this work, we investigate an array of one-dimensional trapped Bose gases, by measuring both the energy and the momentum imparted to the system via light scattering experiments. The measurements are performed in the weak perturbation regime, where these two quantities — the energy and momentum transferred — are expected to be related to the dynamic structure factor of the system. We discuss this relation, with special attention to the role of in-trap dynamics on the transferred momentum.

N. Fabbri et al.,
Energy and momentum transfer in one-dimensional trapped gases by stimulated light scattering
New J. Phys. 17, 063012 (2015)

Entanglement is a fundamental resource for quantum information processing, occurring naturally in many-body systems at low temperatures. The presence of entanglement and, in particular, its scaling with the size of system partitions underlies the complexity of quantum many-body states. The quantitative estimation of entanglement in many-body systems represents a major challenge, as it requires either full-state tomography, scaling exponentially in the system size, or the assumption of unverified system characteristics such as its Hamiltonian or temperature. Here we adopt recently developed approaches for the determination of rigorous lower entanglement bounds from readily accessible measurements and apply them in an experiment of ultracold interacting bosons in optical lattices of 10⁵ sites. We then study the behaviour of spatial entanglement between the sites when crossing the superfluid-Mott insulator transition and when varying temperature. This constitutes the first rigorous experimental large-scale entanglement quantification in a scalable quantum simulator.

M. Cramer et al.,
Spatial entanglement of bosons in optical lattices
Nat. Commun. 4, 2161 (2013)

We report the Bragg spectroscopy of interacting one-dimensional Bose gases loaded in an optical lattice across the superfluid to the Mott-insulator phase transition. Elementary excitations are created with a nonzero momentum and the response of the correlated 1D gases is in the linear regime. The complexity of the strongly correlated quantum phases is directly displayed in the spectra which exhibit novel features. This work paves the way for a precise characterization of the state of correlated gases in optical lattices.

D. Clément et al.,
Spatial entanglement of bosons in optical lattices
Phys. Rev. Lett. 102, 105301 (2009)

See also the Physics Viewpoint by D. Jaksch:

D. Jaksch
A stimulated atomic response
Physics 2, 29 (2009)

We use a two-color lattice to break the homogeneous site occupation of an atomic Mott insulator of bosonic 87Rb. We detect the disruption of the ordered Mott domains via noise correlation analysis of the atomic density distribution after time of flight. The appearance of additional correlation peaks evidences the redistribution of the atoms into a strongly inhomogeneous insulating state, in quantitative agreement with the predictions.

V. Guarrera et al.
Noise Correlation Spectroscopy of the Broken Order of a Mott Insulating Phase
Phys. Rev. Lett. 100, 250403 (2008)

We use a bichromatic optical lattice to experimentally realize a disordered system of ultracold strongly interacting 87Rb bosons. In the absence of disorder, the atoms are pinned by repulsive interactions in the sites of an ideal optical crystal, forming one-dimensional Mott-insulator states. We measure the excitation spectrum of the system as a function of disorder strength and characterize its phase-coherence properties with a time-of-flight technique. Increasing disorder, we observe a broadening of the Mott-insulator resonances and the transition to a state with vanishing long-range phase coherence and a flat density of excitations, which suggest the formation of a Bose-glass phase.

L. Fallani et al.
Ultracold Atoms in a Disordered Crystal of Light: Towards a Bose Glass
Phys. Rev. Lett. 98, 130404 (2007)