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).

Multicore computing: now and future

Moore's Law has been the golden rule in predicting the increasing of personal computing power for more than a decade, but change has arrived. A couple of years ago, Amdahl's Law became the governing law (without an inauguration). Multicore computing is now the critical driven force of computer performance. As of October 2008, the 7400-series "Dunnington" of Intel's Xeon offers hexa-core capacity.

The trend is, knowing it or not, computers will have more cores and your personal computer will rival the computing power of a supercomputer defined by the government only a decade ago. There are, of course, some debates going on among CPU designers whether to make a personal computer something like a shiny iPhone box, or to make it a little machine that can easily crack the current military code (http://www.eetimes.com/showArticle.jhtml?articleID=206105179). This is a critical decision that will affect the architecture of future computers: will the future generation of CPUs be a bundle of different special-purpose cores, or will they will be made of homogeneous, generic cores that can be assigned any task? (Or, maybe they should be the combination of the special-purpose cores such as GPUs and generic cores, as that seems to be the way our brains work.)

As a software developer, I clearly want to have more generic cores, as they are apparently my power base. One could suggest that a developer can try to access the power of things like a GPU (as folding@home seems to be doing well with), but the real questions are: (1) Do we really want to learn those lower-level libraries for each type of the special-purpose cores, in order to use them? (2) Do we really want our applications to be bound to special-purpose cores, which raises the cross-platform issues?

On the one hand, if a CPU comes with a lot of power that cannot be easily harnessed by an average programmer, then it will become only a few elite developers' privilege. On the other hand, if average programmers like me cannot come up with a convincing argument that we can develop killer applications if we are given more generic power, then the industry has the right reason to doubt that generic power will be useful to the vast majority of people out there.

So, can we come up with some cool ideas how multicore computing may be good to average people like Joe and Jane (not just offering dream machines to evil hackers --- for them to break into our bank accounts)?

I feel it is not easy to present a clear example of how I would use a 128-core CPU predicted to be available on a single notebook machine in less than 10 years (note that each core will surely run faster than the ones currently in your dual-core CPU --- just imagine the power we will have at our fingers). It is hard for me to imagine an application that will invoke 128 processes simultaneously at any time. But I recognize that I am probably in a mind block. The fact that I cannot see the big picture now simply does not mean it does not exist.

My background as a computational physicist gave me some hints of how things might develop. Parallel computing is essential in solving many scientific problems that involve huge calculations. Computational scientists are used to think in the language of parallelism. So a 128-core computer is nothing new for them. It is just a shared-memory supercomputer condensed to a laptop box.

Molecular dynamics is a "lab rat" for parallel computing research, because it is relatively simple to implement and study. Given the fact that the Molecular Workbench does molecular dynamics on a personal computer, it may be a wonderful candidate for us to make a highly relevant case.

The Molecular Workbench currently benefits from multicore computing in two ways. First, there exists embarrassingly parallel problems that automatically utilize this power. For example, one can do multiple simulations at the same time. If there are enough cores available, each will run on a core independently. This needs no extra work from the programmer, because a simulation runs on a thread that is assigned by the JVM and OS to a core. It is interesting to note that the model containers in the Molecular Workbench could provide a way to decompose a larger system, if the simulations are synchronized by communication among them through scripts.

Second, the graphics part of a simulation is handled in a different thread than the calculation thread. Therefore, a single simulation can have its molecular dynamics calculations running on one core, and the graphics running asynchronously on another. This is most helpful when the refreshing rate needs to be high to render the motion smoothly.

The Java molecular dynamics code of the Molecular Workbench, however, has not been parallelized. I have been playing with java.util.concurrent to parallelize it, but at this point, it seems the gain won't be measurable (if positive at all!) if we only have two cores, as is the case of most personal computers as of today. The overhead cost of task coordination may be higher than what it worths.

But suppose I had a 128-core CPU to back my pool of simulation threads, the story I am writing could be quite different.

Besides scientific simulations, 3D navigation environments such as SecondLife would also benefit enormously from multicore computing. The process of landscape download and construction can be easily decomposed into chunks and assigned to different cores.

Can photonics simulations be useful to advanced technical education?

Photonics is a difficult subject because it involves electromagnetism that is basically an invisible and unintuitive world to many students. Yet this is a promising and thriving technical field where many jobs are being created.

Computer simulation of light propagation in medium has become an important part in the design of optical waveguides, photonic circuits and optical fiber communication units. Commercial tools such as those developed by Optiwave have been widely used in industry. These tools and methods may also be very useful in helping students develop intuition ans sense about photonics.

Theoretical photonics is largely based on the numerical solution of the Maxwell equation, which governs light propagation. Solving the Maxwell equation for different system configurations is by no mean a trivial task. Many approximations have been developed. Each is good at solving a particular type of problem. Most of them are based on either the finite element method (FEM) or the finite difference method (FDM). Among them, the beam propagation method (BPM) is one that was specifically developed to simulate light propagation in waveguides. It gives reasonably accurate results that can provide useful guidance to designing optimal photonic circuits.

BPM seems to be an attractive candidate of teaching tool in that it can be used to build salient (that is, interactive and dynamic) simulations that show h0w things work in photonic devices. A playful environment that allows students to build circuits and run simulations to see how light travels through them may be very instructive and attractive to students.

The following pictures show a BPM 2D simulation of a photonic parallel circuit (many real engineering problems can be reduced to 2D based on the effective index method). Note that there are some loss due to the twist of the two branches where they split and join.

Integrating simulations in SecondLife/Wonderland?

SecondLife has drawn extensive interest among educators. It is an attractive immersive environment for multiple users to interact with each other through navigating in an interesting 3D landscape. SecondLife represents the latest effort of developing 3D Internet, which, as opposed to the conventional page-by-page Internet, provides a novel mechanism to display information in a more interesting way beyond text, images, animations and applets interspersed in a 2D layout.

Although SecondLife is very interesting, it currently does not allow an author to embed an existing simulation in its environment. The media support is currently limited to text (animated or not), images and movies. Considering the fact that there exists a vast number of simulations on the Internet written in Java and C++, including those offered by the Molecular Workbench (http://mw.concord.org), it would be nice if one day we can see the user interacts with a simulation hung on a whiteboard inside SecondLife. We can imagine that there will be a virtual math and science musuem. Students will "walk" into rooms that have different exhibits, explore the wonderful models by pushing various buttons and observing what happens, and discuss with people in the same room about it --- pretty much like their real experience when they go to a real museum.

I think it is unlikely that SecondLife itself would offer simulations that are content-specific, such as those offfered by the Molecular Workbench. The SecondLife community will have to rely on the domain experts to fill in the real stuff. So it seems to me that the best strategy is to make Java work in SecondLife and provide a plugin service for C++ applications.

Wonderland (https://lg3d-wonderland.dev.java.net/) is a toolkit developed by Sun Microsystem that rivals SecondLife. Wonderland is particularly interesting because Open Office works within it. As a result, multiple users can work on the same Open Office document projected onto a whiteboard in Wonderland. If an application as complex as Open Office can work within Wonderland, there is every reason that we should believe Java should just work without a problem in Wonderland. Wonderland, therefore, may seem a very attractive option for developing a virtual museum as described above.

There are many technical issues about integrating a compute-intensive simulation with a compute-intensive immersive environment. Some of the problems will automatically go away as multicore computers become more powerful and more available. Some won't without substantial work in figuring out better ways of synchronizing a simulation for multiple users and synthesizing their inputs.