Erich Mueller

Research Statement

Like many academics, I am attracted to puzzles. I like coming face-to-face with apparent paradoxes, and explaining counterintuitive phenomena. Reflecting these interests, I have made a career out of studying quantum mechanics: the physics on the scale of single atoms, where classical mechanics fails. My research is focused on understanding how the theory of quantum mechanics manifest itself. I am particularly interested in the cases where simple interactions between a collection of particles leads to complicated behavior. Much of our technology is based on such emergent phenomena (electronics, lasers...), and I am always alert to possible applications of my work to areas such as metrology. My motivation, however, is closer to that of an explorer than that of an inventor. I want to see new things.

Much of my efforts are directed at understanding the behaviors of alkali gases cooled to nano-Kelvin temperatures. One cools these gases in order to eliminate the random thermal motion which dominates at room-temperature. One is then able to see the underlying quantum behavior of the atoms. As a simple example, consider one of the central tenents of quantum mechanics: the Heisenberg uncertainty principle. This principle states that one cannot simultaneously know where an object is and how fast it is moving (or more precisely that the product of the uncertaintly in position and momentum is bounded below by a fundamental constant). As one cools a gas, one is reducing the uncertainty in the speed of the particles, and hence their positions become less certain. In other words, quantum mechanics predicts that at low temperatures atoms become fuzzy, and that the colder they are the fuzzier and more spread-out they become. When the atoms are so cold that they begin to overlap, a qualitative change occurs to the gas: one no longer can tell where one atom ends and the next one begins. Effectively each atom becomes delocalized over the entire cloud, forming what is known as a condensate. For a typical cold atom experiment, this means atoms are in quantum superpositions of being in locations whose separations exceed 1 mm. I have been studying the consequences of such non-classical phenomena.

Some of my research is driven by asking fundamental questions. For example, the scenario described above applies to a gas of featureless atoms with no internal degrees of freedom. In sufficiently low fields most atoms have nuclear and electronic spins which can point in any direction. For such spinor gases, should one find a single condensate upon cooling? As was pointed out in the early 1980's, it is in principle possible to simultaneously have several condensates, each with the spins pointing in different directions. The answer to how many condensates are formed depends on an interplay of the atomic interactions and magnetic field gradients. With my collaborators, I have investigated this issue, relating the fragmentation of a single condensate to the more general issue of how the degeneracies of single-particle states manifest themselves in the many-body problem.

I also carry out more experimentally driven research. For example, In 2006 I helped resolved a major conflict between experimental observations at MIT and Rice. These groups found qualitatively different density profiles for two-component clouds of Lithium atoms. I showed that the experimental observations could be traced to surface tension: at Rice they were working with long skinny clouds with a much larger surface area to volume ratio. The large surface tension distorted their clouds, causing the observed discrepancies.

In addition to my research aimed at producing independent publications, I enjoy performing small calculations to help out my experimental colleagues. For example, John Reppy introduced me to some experiments that Moses Chan at Penn State was performing on solid helium. Moses was seeing behavior which was reminiscent of superfluidity. I performed some calculations of potential flow in their geometry which lent extra weight to their observations [see E. Kim and M. H. W. Chan, ``Observation of Superflow in Solid Helium," Science 305, 1941 (2004)]. Similarly, I wrote a computer program which Randy Hulet from Rice routinely uses to analyze the data from his experiments. [When I last talked with Debbie Jin, she told me that she was also using a version of the program.]

I have connections with experimentalists at Cornell. I have performed studies of electrons in thin wires, which were informed by discussions with Paul McEuen and his group. Similarly, one of my students, Stefan Baur, spent some time calculating spin-orbit coupling effects in carbon structures -- a study which was motivated by discussions with McEuen's group. [Stefan's work on this was independent of me, but I like to flatter myself and think that some of my interest in collaboration rubbed off on him.] I regularly discuss Cornell's experimental efforts in solid helium with John Reppy and Seamus Davis. I have been modelling systems related to Seamus Davis and Kyle Shen's experiments in cuprate superconductors. I have invested time into thinking about Alex Gaeta's optics experiments, and Keith Schwab's nanomechanical analogs of cavity QED experiments. I am actively involved in understanding David Lee's experiments on solid hydrogen, and another of my students, Kaden Hazzard, is in the process of writing a theory paper which constrains the possible explanations for some of David's observations. Finally, I am very excited to have the opportunity to collaborate with our latest assistant professor, Mukund Vengalattore, who performs experiments involving cold atoms. I anticipate collaborating closely with him. [Again, one of my students, Stefan Natu, is leading that collaboration.]

My research group generally consists of three-four graduate students. Roughly every other semester I also hire an undergraduate researcher. Additionally, I have directed the research of one postdoctoral fellow.

In the near future I will continue working in these areas, with a similarly sized group. I have ongoing projects involving atoms on lattices, strongly interacting Fermi gases, spin-orbit coupling, dimensional crossovers in cold atoms, solid hydrogen, two dimensional gases, and radio frequency spectroscopy. I have a clear global picture of the cold atom field, and I am directing my resources towards making the largest possible impact. I am especially interested in finding ways for cold atom experiments to become more relevant for understanding other areas of physics.

Teaching Statement

I have a strong commitment to teaching, both at the graduate and undergraduate level. I have been involved in teaching 3 graduate and 2 undergraduate courses at Cornell, and have helped with several major educational initiatives. I see teaching as a team effort, involving everyone in the Cornell community. I believe learning should be student-centered, and strive to empower my students. One should not be content with the status quo, but should always be improving the teaching environment.

Roughly half of my teaching efforts at Cornell have focussed on introductory mechanics -- predominantly P112, a required course for freshman engineering students. For a number of reasons this is an exciting course to be involved in: (1) of all courses taught by the physics department, it is the one where I believe an instructor has the best opportunity to impact students and their educational trajectory; (2) the incoming freshman engineers posses an ernest enthusiasm which makes teaching and interacting with them a unique and valuable experience; and (3) this course provides unparalleled opportunities to innovate and grow as an instructor. In each of the past 3 semesters I have been head instructor for this class of ~300 freshman. I have directed a staff of roughly 9 graduate student TA's, and 3 instructors/faculty members. In a typical semester, I lectured 6 hours each week, facilitated a 1.5 h/week staff meeting, facilitated lab instructor meetings, performed administrative duties, prepared course material, and directed others in preparing course material. I try to have students actively participate in my lectures: answering questions, discussing with one another, and helping with demonstrations.

Continuing in the Cornell physics department's strong history of innovations in introductory teaching, I have been involved in two initiatives aimed at improving P112, and undergraduate physics education. The most dramatic and far reaching has been in Spring 2008, where we introduced an ``undergraduate learning assistants (ULA) program", in which we hired eight undergraduate students to help facilitate group-work activities in P112 recitation sections. This program, which has similarities with the Academic Excellence Workshop (AEW) program instituted by the engineering school, mirrors developments in Math 191. All such initiatives are motivated by education research which shows that when compared with traditional lectures and recitations, students learn more from cooperative group-work activities. These engage and motivate students, while leveraging the abilities of the top cohort. A key role is played by the facilitators: in our case a graduate student teaching assistant working with a ULA. The facilitators circulate among the groups asking probing questions which keep students on-task, and drive true critical thinking. Having two facilitators in the classroom makes the process more responsive, reducing one of the most common student concerns about these sorts of activities -- namely that they have to wait too long to get feedback from an instructor.

Modeled on a similar program at the University of Colorado, our ULA program has a second goal: encouraging students (the ULA's) to consider a career in teaching. Our efforts are funded through a grant from the National Science Foundation supported ``Physics Teacher Education Coalition" (PTEC) program, and are being directed by Robert Thorne. The PTEC program is designed to solve the problem of a lack of physics teachers in America's highschools and middle schools. According to the National Center for Education Statistics, in 1999-2000, 41\% of middle school students and 16\% of high school students were taught physical science by an instructor with no certification in the field. The need for more physics teachers has been recognized by the American Association of Employment in Education which ranks Physics as a ``field with considerable shortage" of high school teachers. Only special education teachers are in higher demand. In addition to hiring the ULA's, we have been able to hire a teacher-in-residence, Martin Alderman. Among his many tasks, Alderman taught the P112 TA's and ULA's a short course on pedagogy. Covering topics such as Bloom's taxonomy, epistemology, and metacognition, this weekly 90 minute seminar gave the recitation instructors (both TA's and ULA's) a practical foundation on how students learn. Training our teaching staff in this area will pay many dividends over their career at Cornell.

A unique aspect of our implementation of the ULA program was an organizational structure where the TA's and ULA's would have the opportunity to participate in developing course material. Every week I would produce a number of suggested recitation activities. The ULA's and TA's would then be encouraged to either fine-tune these activities to better connect with their students or to produce related activities. The teaching staff would trade these activities, and discuss amongst themselves how well each of them worked. This communication was facilitated by using a ``WIKI" -- a group editable web-site set up for exchange teaching material and comments. As such we have a complete record of all of the activities used throughout the spring 2008 semester, and these will be the basis for activities in future years.

With the help of Phil Krasicky, I have introduced a second innovation into P112. Most of the actual development was done by Phil, but I played a role in the implementation. In Spring 2007 Cornell awarded us an Innovation in Teaching grant. This project was aimed at a comprehensive overhaul of the laboratory component of P112. We have introduced 5 labs in which students use digital video cameras to produce strobe diagrams of two-dimensional motion. These labs have been an overwhelming success -- we have found measurable gains in conceptual knowledge between students in Fall 2007 (pre-innovation) and students in Spring 2008 (post-innovation). I would like to modify these laboratory exercises so that they could be used in a K-12 setting.

In addition to these formal innovations, I have put a large amount of effort into ``institutionalizing" and expanding some of lecture-hall techniques which have been used by P112 instructors in recent years. I have produced a CD which contains a summary of P112 teaching resources. In addition to collating resources introduced by previous instructors, I have worked with Julia Thom to produce a set of powerpoint slides which can be used by P112 instructors. An important aspect of these slides is that they naturally incorporate lecture-demonstrations, and contain a large number of short multiple-choice questions which are used to engage the class. Both of these approaches are well supported by the physics education literature, and make the typically impersonal lecture experience more student-centered. Voting on these questions can be done either using an electronic response system (clickers) or by a show-of-hands.

I have also been strongly involved in graduate education. I have taught a course on cold atom physics, and have spent 3 semesters teaching an advanced graduate course on statistical physics. Additionally I have been involved with the other condensed matter theorists at Cornell on revamping our graduate curriculum. As a group, we have been concerned that our PhD students are graduating as experts on very specific topics, but lack sufficient breadth. We decided to team-teach a modular course where each theorist teaches for one month. The topics continually rotate, so that students can take the course in several consecutive years, developing knowledge of all aspects of condensed matter physics. Since we have introduced this course, I have taught two modules: one on fermion superfluidity, and one on quantum optics.

For my latest module, I used a number of well-established pedagogical techniques which are not traditionally used in graduate physics courses. For example, almost every lecture I would devote some time to group activities, where students solve relevant problems which get to the conceptual core of the topic being discussed.

One of the joys of being at Cornell is that there is a strong community which is enthusiastic about improving the education of students. I appreciate being part of this community and having the opportunity to excel in all of my professional activities.