Many-Body Dipole Interactions

Abstract

This dissertation presents the study of controllable but strong long-range interaction between dipoles. In particular, we investigate the excitation and interaction between atoms in a cold gas where the collisional time is much greater than the interaction time between neighboring Rydberg atoms. In addition to quantum systems, we also examine the excitation properties of a collection of classical electric dipoles created by optically driving metallic nanospheres. We use various theoretical techniques to simulate these systems, including the direct numerical solutions to Schr\""odinger's equation, a Monte Carlo method, and a simple coupled point-dipole model.

We first perform simulations involving the excitation of a collection of cold atoms to Rydberg states. When the interaction energy between excited atoms is large enough to shift multiply-excited states out of resonance with the tightly tuned excitation laser, the number of atoms able to be excited is suppressed, creating a dipole blockade effect. The blockade effect offers exciting possibilities in the control of quantum bits, which is crucial for the development of quantum computing. We also examined the effects of density variation with respect to the the dipole blockade with three different models.

We then simulate the coherent interactions between Rydberg atoms. If the atoms are excited into states where the dipole-dipole interaction between them allows for resonant energy transfer to occur, then one state can freely hop from one atom to the next via the dipole-dipole interaction. We generated band structures for one, two, and three dimensional lattices and characterized the nature of the coherent hopping. This hopping is also studied in both a perfect and non-perfect lattice case which should be possible to examine experimentally.

Next, we simulate the effect of special excitation pulses on a cold gas of atoms. First a rotary echo sequence is used to examine the coherent nature of a frozen Rydberg gas. If collective excitation and de-excitation is present with little or no source of dephasing, after these pulses the system should be returned to a state with few excitations, and a strong echo signal should occur. We investigate systems that should display a perfect echo and systems where the interaction between atoms reduces the echo signal. A spin echo sequence is also used on a system of coherent hopping excitations, and we simulate how the strength of a spin echo signal is affected by thermal motion.

Finally, we describe the dipole-dipole interactions between a linear array of optically driven metallic nanospheres. These classical model calculations incorporate the full electric field generated by an oscillating electric dipole. The effects due to retardation of the generated electric field must be taken into account and several interesting effects are explored such as the ability to preferentially excite specific nanospheres.