Rydberg atoms, in which the outermost electron has been excited to a very high energy level, can interact strongly by exchanging energy with each other. When they are slowed to ultracold temperatures, a few hundred millionths of a degree above absolute zero, it becomes possible to study and control these dipole-dipole interactions. In our work, a collaboration between the small liberal arts institutions Bryn Mawr College and Ursinus College, we use a combination of experimental and computational techniques to explore the quantum dynamics of Rydberg atom systems.

We achieved two primary goals with the work funded by this grant. First, we developed a genetic algorithm to control the ionization of the Rydberg electron which allows for the measurement of previously difficult-to-resolve atomic states. Second, we used this technique to make the first measurement of the time evolution of three- and four-body interactions among Rydberg atoms.

Selective field ionization is an important laboratory technique in atomic physics used to measure the distribution of energy states that a Rydberg electron occupies. A ramped electric field is used to sequentially ionize states from low to high binding energy. The arrival time of the ionized electron at a detector is then correlated with its original energy. While this simple picture provides a basic understanding of selective field ionization, it neglects complications introduced by shifts and interactions among energy states during ionization. The complicated details, as hundreds of energy levels converge and nearly cross on the way to ionization, are shown in Fig. 1. Unfortunately, some energy states overlap in their paths to ionization, making it difficult or impossible to tell them apart in arrival time.

We have developed a technique to control the electron's path to ionization by adding small wiggles to the linearly increasing electric field ramp. These perturbations can cause the electron to simultaneously take different paths, leading to quantum interference. By selectively enhancing some paths while suppressing others, a particular set of wiggles can make large adjustments to the arrival time of the electron.

The complexity of the ionization process makes it impossible to directly calculate the optimal perturbation to the field ionization ramp. We therefore developed a "genetic algorithm" that evolves the wiggles in an effort to best achieve the desired state separation. A genetic algorithm is an artificial intelligence technique, inspired by Darwinian evolution, in which the software attempts to achieve an outcome by trying many different solutions. Each solution is scored by how well it achieved the target goal and the most successful members are mated together to create a new generation of possible solutions. After a few dozen generations, the algorithm can evolve near optimal solutions to the problem. 

We are interested in studying these particular energy levels because Rydberg atoms excited to these states can exchange energy with each other in rarely seen triplets or quadruplets. These three- and four-body interactions can be used for quantum gates or for studies of quantum dynamics. In particular, these interactions can model the behavior of more difficult to study solid state materials. Our new genetic algorithm technique allowed us to quantitatively measure the rate at which the atoms interacted with each other.

We measured and directly compared these rates for the two-, three-, and four-body cases as shown in Fig. 2. We built a computational model of the experiment and simulated it on a supercomputer. Our data revealed interesting features in the dynamics. For example, since each type of interaction depends differently on the density of the atomic sample, comparison of simulation to data could allow for an indirect measurement of the density. We also observed interesting thermodynamic behavior. Quantum systems that do not come to equilibrium, or thermalize, in the expected way could have much to teach us about quantum dynamics. We see hints in our data of such a failure to thermalize.

Our work trained many undergraduate students at our institutions, who participated in all aspects of this research: computational, experimental, presenting at conferences, and writing journal articles. More than half of our student researchers are from populations under-represented in the physical sciences. Most of them have gone on to careers or graduate school in STEM fields or are planning to upon graduation.

Last Modified: 11/16/2020
Modified by: Thomas Carroll