A sampling of everything that is possible

It is spine tingling to view a two-dimensional representation of everything that is possible given the laws of physics. I had previously written about our work, where Shoresh used Monte Carlo simulations to let the computer randomly sample all possible quantum systems that are compatible with the Schrodinger equation. In my recent report to the National Science Foundation, my awe in Physics and its ability to make such grand and sweeping statements was rekindled. Above is a summary of our work in graphical form. It is aesthetically pleasing in its visual appeal, but more so in its intellectual content.

I cannot explain in the small amount of space here the beauty of these results, nor what they mean in terms of the basic science. Nature is clearly hinting at some deep structure of the quantum world when we probe molecules with light. My summary to NSF states it best:

"The uniqueness of our work is that it provides a new way of thinking, which in the words of a Spotlight on Optics article describes our approach as "reminiscent of the cutting of the Gordian knot by Alexander the Great. (see article)" Rather than focusing on one application, our work provides a new paradigm for understanding the critical material properties that need to be controlled for making better materials for any application that is based upon the interaction of light with matter.

"Technologies that may benefit from this work include high-contrast medical imaging, laser-based cancer therapies that target malignant cells without damaging surrounding cells, all-optical computers that are ultrafast by virtue of new architectures enabled by light, high-speed telecommunications through technologies that eliminate the electronics bottleneck, and high-density reconfigurable optical information storage."

Now I need to get back to the painfully boring task of updating my CV and preparing my annual review materials. I can't wait to finish these inane tasks so that I can get back to thinking about the things that I find most meaningful in life.

Monte Carlo simulation appears on the Spotlight on Optics section of OpticsInfoBase.org

Our paper on Monte Carlo simulations of the second hyperpolarizability has just appeared in the Journal of the Optical Society of America B. The paper was selected to be highlighted on Spotlight on Optics. An excerpt from the summary follows:

Spotlight summary: The paper of Shafei et al. belongs to a series of papers initiated a decade ago by M.G. Kuzyk, oriented toward a theoretical analysis of fundamental limits and the optimization of attainable first- and second-order off-resonant electronic nonlinear hyperpolarizabilities, which describe a molecule’s response—its nonlinear polarization—to optical fields. Nonlinear hyperpolarizabilities are expressed in terms of infinite series. In the absence of a small parameter, the optimization of hyperpolarizabilities and the search for universal features constitute a challenge, which requires, first of all, a deep physical intuition.

In earlier papers, Kuzyk et al. calculated the fundamental limits for nonlinear hyperpolarizabilities using the three-state ansatz, which states that when a hyperpolarizability is near the fundamental limit, the system can be described by a three-level model. To this end they have used sum rules—one of standard approaches in quantum theories—that put constraints on infinite sets of energy levels and transition moments.

Surprisingly, experimental studies and earlier theoretical approaches have revealed a large gap between attainable values of the first and second hyperpolarizabilities and predicted fundamental limits. This casted doubt on the validity of the three-state ansatz...see more