Dynamics in many-body quantum systems with long-range interactions

The ability to realise quantum simulation experimentally at extremely low temperature provides the capability to microscopically control macroscopic quantum phenomena. The control over cold atoms in optical lattices offers an excellent platform to study the out-of-equilibrium behaviour of strongly correlated systems, especially spin physics that can be realised with multicomponent gases. In this field a major ambition is to observe sensitive many-body phenomena such as quantum magnetism. This thesis contains theoretical and numerical studies of many-body dynamical phenomena of spin models with two-component bosonic atoms in optical lattices. Firstly, beginning from a state with all effective magnetic spins in the same direction, we investigate dynamics of spin-spin correlations, and how they behave for different spin models.;Most of the results explored in this thesis use reduced Hilbert space techniques, basedon the Density Matrix Renormalisation Group, and the representation of Matrix Product States and Matrix Product Operators. Using numerical methods in 1D we compute non-equilibrium dynamics, ground states, and thermal states for these systems. We also study and compare their behaviour in terms of spin correlation functions and induced currents. We find in some cases, where the current is non-decaying for the ground state, a decay for the rotated state with time, since the decay of the long-range correlations becomes important. Furthermore, we explore changes that occur when we add long range interactions to the models, and analyse how the correlations can be affected by the presence of disorder. We found that in the regime of short and intermediate range interactions, the correlations are affected by the disorder, whereas these effects were suppressed for long-range interactions. One of the challenges in ongoing experiments remains reaching the low temperatures/entropies necessary for some particularly sensitive interacting states.;We investigate the magnetically ordered quantum states that can be engineered in these two-species bosonic models, studying techniques to prepare states with a very low entropy using a diabatic and near-adiabatic protocols. We compute the corresponding dynamics, modelling these techniques for realistic experimental parameters. We also show how the same models can give rise to entanglement that is potentially useful for quantum enhanced metrology, and characterise the states we can prepare in terms of their Quantum Fisher Information. Lastly, we analyse the effect of dissipation in these models. Our results provide an interesting experimental perspective to probe the difference between mean-field spin states and the true ground states for effective spin models. In summary, our studies offer innovative new results to study spin models in optical lattices, which should be feasible with current experimental techniques.The ability to realise quantum simulation experimentally at extremely low temperature provides the capability to microscopically control macroscopic quantum phenomena. The control over cold atoms in optical lattices offers an excellent platform to study the out-of-equilibrium behaviour of strongly correlated systems, especially spin physics that can be realised with multicomponent gases. In this field a major ambition is to observe sensitive many-body phenomena such as quantum magnetism. This thesis contains theoretical and numerical studies of many-body dynamical phenomena of spin models with two-component bosonic atoms in optical lattices. Firstly, beginning from a state with all effective magnetic spins in the same direction, we investigate dynamics of spin-spin correlations, and how they behave for different spin models.;Most of the results explored in this thesis use reduced Hilbert space techniques, basedon the Density Matrix Renormalisation Group, and the representation of Matrix Product States and Matrix Product Operators. Using numerical methods in 1D we compute non-equilibrium dynamics, ground states, and thermal states for these systems. We also study and compare their behaviour in terms of spin correlation functions and induced currents. We find in some cases, where the current is non-decaying for the ground state, a decay for the rotated state with time, since the decay of the long-range correlations becomes important. Furthermore, we explore changes that occur when we add long range interactions to the models, and analyse how the correlations can be affected by the presence of disorder. We found that in the regime of short and intermediate range interactions, the correlations are affected by the disorder, whereas these effects were suppressed for long-range interactions. One of the challenges in ongoing experiments remains reaching the low temperatures/entropies necessary for some particularly sensitive interacting states.;We investigate the magnetically ordered quantum states that can be engineered in these two-species bosonic models, studying techniques to prepare states with a very low entropy using a diabatic and near-adiabatic protocols. We compute the corresponding dynamics, modelling these techniques for realistic experimental parameters. We also show how the same models can give rise to entanglement that is potentially useful for quantum enhanced metrology, and characterise the states we can prepare in terms of their Quantum Fisher Information. Lastly, we analyse the effect of dissipation in these models. Our results provide an interesting experimental perspective to probe the difference between mean-field spin states and the true ground states for effective spin models. In summary, our studies offer innovative new results to study spin models in optical lattices, which should be feasible with current experimental techniques