Title:

Ultracold gases of Rydbergdressed atoms in multiwell traps

Rydbergdressed ground state atoms are atoms with an electron offresonantly excited to a very high energy state, i.e., a state of high principal quantum number n ≫ 1. This thesis investigates the quantum dynamics of interacting Rydbergdressed ground state atoms trapped in several multiwell potential traps. Rydberg atoms are atoms with exaggerated properties. One of their most interesting properties is that they exhibit a strong and longranged interaction that can be tuned leading to a variety of different quantum behaviours. My work focuses on studying the effects of these interacting atoms when loaded in multiwell potential traps. Generally, multiwell systems are considered as the simplest example of a finite optical lattice structure. For this reason, this thesis covers three research topics that examine the effects of longrange interaction on Rydbergdressed atoms trapped in several potential confinements. I begin, in the introduction, by discussing the theoretical background of relevance to this work. It starts with presenting the physics of BoseEinstein condensate. Then, the fundamentals of the interaction between twolevel atom and light are analytically studied. This study has the purpose of understanding both; the dressed interacting atoms and optical lattices. The definition, characteristics, and the nature of the interaction between Rydberg atoms are analysed afterwards. The second chapter examines the dynamics of an ensemble of interacting Rydberg dressed atoms trapped in static, i.e., timeindependent, multiwell potentials using a meanfield theoretical approach. I choose onedimensional double and triplewell in addition to a twodimensional quadruplewell potentials. The timedependent nonlinear GrossPitaevskii equation is used to numerically explore the ensemble's quantum dynamics. Solving the dynamical differential equations along with tuning the strength of the applied longrange interaction shows that the behaviour of noninteracting Rydbergdressed atoms does not differ conceptually according to the geometry of the trapping potential. However, this changes when the interactions are switched on where the shape of the confinement leads to interesting outcomes especially in the nonlinear interacting limit, such as macroscopic quantum selftrapping. After investigating an ensemble of interacting Rydbergdressed atoms in static multiwell potential traps, the second research topic examines the dynamical evolution of these atoms when loaded in a finite optical lattice using the extended BoseHubbard model. In this chapter, the atoms ensemble is assumed to be in a superfluid state where I investigate both, the order parameter when the Rydberg excitation laser is applied and the interference pattern of the condensates in different dimensions. The study shows the emerging longrange interactions lead to a rapid collapse of the superfluid order parameter and in general allow only for partial revivals. In addition, the interference experiments can directly reveal the interaction between Rydbergdressed atoms. In the fourth chapter, the dynamics of Rydbergdressed atoms trapped in a dynamical, i.e., timedependent, potential confinement is presented. The dynamical trap is constructed such that it begins as a harmonic oscillator and ends as a double well potential. The analysis investigates an ensemble of contactinteracting atoms via the timedependent nonlinear GP equation.
