• cold atoms
• correlation
• kinetic monte carlo
• rubidium
• runge-kutta
• Rydberg
• van der Waals

The understanding of the strongly correlated dynamics of many-body quantum systems out of equilibrium is one of the most challenging tasks in modern physics. Rydberg atoms, which are atoms excited to states with high principal quantum number, have proved to be a very successful platform for the study of these systems. The detailed understanding of the excitation dynamics will be helpful for the implementation of various quantum simulation and quantum computation protocols.

In the present thesis the emergent properties of a many-body system are studied in conditions where the dynamics of the internal and external degrees of freedom can be partially decoupled. The study is done by means of Monte Carlo simulations upon a simple toy model.

Internally the system is modelled as an Ising-like spin system coupled to an external field and with long range interactions among the spins. Dissipation is also included in the model, and a master equation approach is used to derive the time evolution of the system. Different Kinetic Monte Carlo methods are discussed in order to solve that master equation.

We used the model and the methods developed to study emergent phenomena in the excitation dynamics of a cold gas of Rydberg atoms. In the resonant regime we observed the effects of the blockade where the presence of an excited atom inhibits the excitation of his neighbors. In the off resonant regime we observed facilitated excitation, whereby an excitation in the system shifts a ground state atom at a well-defined distance into resonance. We also performed simulations of the excitation process with quenches of the detuning finding interesting and unexpected results in the dynamics approaching the equilibrium.

The dynamics of the external (translational) degrees of freedom is modelled as as that of classical particles which interact by means of a potential C_α/r^α. The features of different algorithms to solve the classical equations of motion are discussed focusing on the requirement that the Hamiltonian must be conserved while integrating the Hamilton equations for such systems.

We performed simulations on the external dynamics of a cluster of Rydberg atoms replicating the features of an experiment performed in the laboratory. Our experiment aims to measure directly the effect of van der Waals forces between atoms of Rubidium excited to Rydberg states. We used the simulations to analyze the outcome to the experiment and found good agreement between the experimental data and the simulation.