This article gives an introduction to the realization of effective quantum magnetism with ultracold molecules in an optical lattice, reviews experimental and theoretical progress, and highlights future opportunities opened up by ongoing experiments. Ultracold molecules offer capabilities that are otherwise difficult or impossible to achieve in other effective spin systems, such as long-ranged spin-spin interactions with controllable degrees of spatial and spin anisotropy and favorable energy scales. Realizing quantum magnetism with ultracold molecules provides access to rich many-body behaviors, including many exotic phases of matter and interesting excitations and dynamics. Farfrom-equilibrium dynamics plays a key role in our exposition, just as it did in recent ultracold molecule experiments realizing effective quantum magnetism. In particular, we show that dynamical probes allow the observation of correlated many-body spin physics, even in polar molecule gases that are not quantum degenerate. After describing how quantum magnetism arises in ultracold molecules and discussing recent observations of quantum magnetism with polar molecules, we survey prospects for the future, ranging from immediate goals to long-term visions. Contents

Two novel control methods based on adiabatic passage are proposed to be implemented in coherent anti-Stokes Raman scattering (CARS) microscopy for noninvasive imaging of biological structure and dynamics. The first method provides optimal pulse-area control of the resonant vibrational transitions by using a pair of equally linear-chirped pulses. The second method, named the 'roof' method, utilizes the chirp sign variation at the central time and gives robust adiabatic excitation of the resonant vibrational mode. Both methods are robust with respect to suppression of the off-resonant transitions. The methods allow one to achieve chemical sensitivity with high resolution and can be used to obtain CARS spectra of biological molecules with efficiently suppressed background.

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Optimal control theory implementations for an efficient population transfer and creation of a maximum coherence in three-level system are considered. We demonstrate that the half-STIRAP (stimulated Raman adiabatic passage) scheme for creation of the maximum Raman coherence is the optimal solution according to the optimal control theory. We also present a comparative study of several implementations of optimal control theory applied to the complete population transfer and creation of the maximum coherence. Performance of the conjugate gradient method, the Zhu-Rabitz method and the Krotov method has been analyzed.

A semiclassical model is used to investigate the possibility of selectively exciting one of two closely spaced, uncoupled Raman transitions. The duration of the intense pump pulse that creates the Raman coherence is shorter than the vibrational period of a molecule (impulsive regime of interaction). Pulse shapes are found that provide either enhancement or suppression of particular vibrational excitations.

Optical properties of ensembles of three-level quantum emitters coupled to plasmonic systems are investigated employing a self-consistent model. It is shown that stimulated Raman adiabatic passage (STIRAP) technique can be successfully adopted to control optical properties of hybrid materials with collective effects present and playing an important role in light-matter interactions. We consider a core-shell nanowire comprised of a silver core and a shell of coupled quantum emitters and utilize STIRAP scheme to control scattering efficiency of such a system in a frequency and spatial dependent manner. After the STIRAP induced population transfer to the final state takes place, the core-shell nanowire exhibits two sets of Rabi splittings with Fano lineshapes indicating strong interactions between two different atomic transitions driven by plasmon near-fields.