It's been three years since Juefei Zhou finished his Ph.D. research that culminated in a nice piece of collaborative work with the group of Koen Clays of the University of Leuven in Belgium. The research used a combination of theory and experiments to determine all the parameters needed to predict the full wavelength dependence of the two-photon absorption cross section. The beauty of the approach is that the theory uses the Thomas Kuhn sum rules to significantly reduce the number of parameters required to describe a molecule. This reduced set of parameters was determined from two experiments - a linear absorption spectrum and the measurement of the hyperpolarizability at just one wavelength.
Given that nonlinear-optical quantum calculations are notoriously inaccurate; and, independent measurements (such as first and second hyperpolarizability measurements) often disagree, we were elated that our approach led to a global agreement between all quantities using just one small set of parameters. The only problem was that our theory was wrong. We had made a false assumption. Thus, our manuscript was placed on the back burner.
A year later, in 2009, I spent a summer in Belgium, and used a combination of symmetry arguments and sum rules to show that our equations turned out to be correct, but for very different reasons. As we were applying the final touches to the manuscript when I returned back to Pullman, Xavi found an error. After days of intense debate, we found a way to correct the mistake and submitted a revised manuscript to Physical Review A.
A very sharp reviewer caught what appeared to be a fatal error. Our symmetry arguments were correct, but they implied an additional condition that rendered our approach untenable. For the next 12 months, we were haunted by a model that was wrong yet seemed to fit the data perfectly well.
At the beginning of the summer of 2010, Shengting was getting frustrated with a laser that refused to work properly, and asked for a theoretical project as a diversion. I suggested that he learn group theory and apply it to fixing the model. While Shengting was making good progress in both learning group theory and developing a plan of attack to address our problems, Xavi arrived from Belgium for a six-week stay. During my trip to Budapest, they had found a solution, albeit with a few holes.
A day before I returned, Koen Clays arrived in Pullman, and spent some time discussing the problem with Xavi and Shengting. As a result, they got closer to a solution. When I got back to Pullman (a day late because of a missed connection in Amsterdam), the four of us met to discus the problem and the proposed fix. Xavi acted as the spokesperson and very animatedly described the approach on the blackboard. Within an hour, everything fell into place. Not only did the original mathematical form of the theory turn out to be true, the underlying physics was even more beautiful than we had imagined. This project has led to new ideas that will take us into novel areas of research that we hope will make a closer connection between our theory, which is a bit esoteric, and real molecules.
It was worth the wait. This paper will add a significant new paradigm to the body of knowledge that seeks to more deeply understand the nonlinear-optical response of complex molecules. The path of our research took us through exhilarating highs and unbearable lows. Hopefully, our models are finally right. If not, the self-correcting process of the scientific method will eventually lead us, or someone else, closer to the truth.