Making sense of quantum phenomena through simulations

"We have become quantum mechanics -- engineering and exploring the properties of quantum states. We're paving the way for the future nanotechnicians." --- Donald M. Eigler, IBM Fellow

Understanding how things work in the microscopic world is fundamentally important to science and engineering education in this century. The micro world is essentially operated by quantum mechanics, which is traditionally very difficult to learn--even for a physics student--because it is so unintuitive. Nevertheless, a large number of phenomena can only be understood with the quantum picture. Understanding these phenomena is becoming imperative. Many important technologies such as microelectronics and nanophotonics are built upon the science of electrons. These technologies are now spearheading new innovations that will lead to revolutionary changes in manufacturing, computing, communication, health care, and medicine.

This poses an interesting challenge to educators: how do we teach quantum reasoning to students without getting them bogged down in the complex field of quantum mechanics (and possibly the philosophical issues associated with its weird interpretations that are still at issues among some scientists and philosophers)? Is there a pathway for students to develop a quantum sense without resorting to the formalism of quantum mechanics?

Funded by the National Science Foundation, we are currently exploring effective ways through simulations to teach the science of electrons and the related technologies. Unlike many existing interactives on the web, our simulation program will provide students a tool with which they can familiarize themselves with the strange quantum world, without having to learn any equation at all. They will learn through playing with existing systems set up by curriculum developers or customized by their instructors (learning by interacting), or through designing new virtual devices of their own (learning by designing), such as a multigate field effect transistor, a quantum dot, a nanowire, or a molecular switch.

Unlike the common approach in which knowledge is told, these quantum simulations allow students to discover how tiny things behave through exploring the emergent behaviors of the microelectronic systems. For example, photon absorption and stimulate emission emerge from a quantum dynamics simulation of a bound electron and a laser. It also allows students to discover that it is the frequency of the laser, not the intensity, that determines these important processes. Another example is related to the core of chemistry. Our quantum dynamics simulator can be used to model how electron cloud changes when an atom is polarized (see the left part of the image on the left). When the user moves the nucleus closer, there is a dramatic change of the electron cloud--it now covers both nuclei. This causes a strong binding of two nuclei through the electron cloud, which is called the covalent bonding. When the user applies an external electric field (other than that of a point charge), it will also cause polarization. When the intensity of the field increases to a certain extent, the electron cloud will be stripped away from the nucleus--a phenomenon that we call ionization. It is fascinating to see that these fundamental concepts in chemistry just emerge from our quantum dynamics simulations! (see this page for more information.) These seemingly disparate concepts can be learned with a single, coherent picture of moving electron cloud in our simulations. The technology provides us a fresh opportunity to look at the reductionist approach, which advocates teaching fewer but more fundamental scientific principles and deriving other knowledge based on them (also see a recent article "How less can be more" by Bob Tinker).

In addition to the quantum dynamics simulator, we are also building a user interface that students can use to design systems such as a chemical reaction or a nanoscale circuit board.

These virtual experiments and virtual designs provide an accessible way to learning quantum phenomena. After all, a large part of the difficulty in understanding quantum phenomena stems from trying to explain microscopic things using our everyday experience, among some other philosophical issues that technical and engineering students may not care. If this obstacle is removed, understanding quantum phenomena should not be much more difficult than understanding water waves and optics. Computer models just streamline this learning process, as if students had a powerful, ultrafast microscope that can be used to look into the micro world. The visualization of how a nanoelectronic device works will help students understand the mechanism, just like a video that shows how air flows in a wind tunnel. Creating virtual devices and observing their properties will allow students to apply their knowledge and further enhance their learning, just like designing a stream table and then running water through it. Through this intimate interaction with a salient simulated micro world, students will learn more deeply than the traditional treatment through the standard teaching approach used in a textbook of solid state physics or chemistry, which either attempts to teach quantum concepts through daunting formalism or static illustrations, or completely avoids them.

It is important to point out that, although we do not try to teach the formalism of quantum mechanics, we use the theory to create the simulation tool. Our quantum dynamics simulation engine behind the user interface is based on numerically solving the time-dependent Schrodinger equation, and our computational method is based on cutting-edge research in computational physics (e.g., a speedy finite-difference time-domain method and novel boundary conditions). Because of this, our tool delivers accurate simulations that correctly depict the spatial distribution and the time evolution of electrons. This is very important, because it ensures the quality and scientific integrity of our simulations.

Image captions: 1) A quantum corral (click here to launch the model). 2) The probability wave just in the middle of a quantum tunneling event (click here to launch the model). 3) The electron clouds in the polarization of an atom and the formation of a covalent bond (click here to launch the model). 4) A nano star coupler that splits an input signal into three output signals (click here to launch the model).