Typical atoms and molecules in a gas are compact and nearly impervious to all but the strongest electric and magnetic fields that can be applied in a laboratory, and they hardly interact with each other except for the rare cases when they pass within tiny distances of each other. Using simple lasers, one of the electrons in an atom or molecule can acquire so much energy that it is only barely bound to the atom or molecule. An atom with such a weakly bound electron is called a Rydberg atom after Johannes Rydberg who gave a mathematical description of the allowed energies. Because the electron is weakly attached to the atom or molecule, its properties can be controlled using modest fields that are easily accessible. Also, the interaction between two or more Rydberg atoms is millions of times larger than is usual which gives interesting atom-atom effects even for a dilute gas.
The main technical goal of this project is to calculate the properties of a single Rydberg atom in static electric or magnetic fields or in laser fields and to calculate the properties of many interacting Rydberg atoms. Within the past decade, there have been an increasing number of experimental groups investigating different arrangements of Rydberg atoms or molecules and fields. One of the general goals of this project is to provide understanding of the experimental results and/or to propose new arrangements worth studying. The reason for investigating a Rydberg atom in different fields is that there is nearly full external control of this quantum system so that it is possible to learn what properties of the interaction control how energy and/or particles move within a closed system. There is a similar reason for studying many interacting Rydberg atoms: the flow of energy through a purely quantum is a fundamental question and is worth studying in different situations. Lastly, there have been several proposals to use Rydberg atoms as components in quantum computers and/or as non-linear optical devices. Thus, studies which use state-of-the-art computational techniques could aid in the understanding of the feasibility of these proposals.
This project will investigate several situations where the exaggerated electronic properties of Rydberg atoms are the main common feature. Calculations for systems that consist of a single Rydberg atom exposed to strong fields as well as many Rydberg atoms that interact through their large electric dipole moments will be performed. For all of the systems, the group will use either fully quantum or a mixture of quantum and classical methods in the calculations. The main long term goal of this project is to develop theoretical and computational tools that allow the quantitative description of complex quantum phenomena. The calculations proposed involve highly excited states where the many nodes of the wave function allow for complex phenomena or involve many body systems where the correlations between particles lead to nontrivial dynamics. At a basic level, this goal is a fundamental goal of nearly all atomic theory proposals. Thus, the lessons learned in these studies could be of wide interest. Also, understanding these systems could allow for experimental control of complex states and many body systems.
There are a couple of projects that investigate how a single Rydberg atom behaves when exposed to strong fields. The first situation is when an atom is exposed to the structured potential that arises in a bottle-beam trap; when the nucleus is off-center, this potential has little symmetry with respect to the nucleus so that nearly all states are mixed together. The second situation is to understand the role that quantum friction (in the form of spontaneous emission) plays in a driven quantum system; this system is interesting because the classical dynamics leads to the oscillator locking to the drive. The classical motion does not decay out of the O-point and, thus, can remain forever with high energy even though 'friction' is present. The projects involving two or more interacting Rydberg atoms focus on separate aspects of this system but invoke similar computational tools and theoretical ideas. One project is to study the kick an atom receives due to Rydberg-Rydberg interactions, especially for blockaded systems. This kick arises due to the finite interaction energy between the atoms and could have implications for quantum computation schemes. Another project is to study Anderson localization in a Rydberg gas: the randomness in the placement of atoms translates into a randomness in the hopping amplitude of an excitation. A goal is to understand how the 1/R3 dependence in the hopping amplitude affects the basic properties of Anderson localization. Another project is to understand the role that near-field versus far-field dipole-dipole interactions play within a Rydberg gas. By systematically varying the types of states participating in the dipole-dipole interaction, one can tune the system from predominantly near-field (states with large principle quantum number) to far-field (states with small principle quantum number). Lastly, calculations of the interaction between two Rydberg atoms with large electric dipole moments aligned along an external electric field and how it affects the relative motion of the atoms will be performed. This will investigate whether it is possible to vary the direction of the electric field in a rapid, time dependent manner so that the atoms form a dynamically stable molecule.
