## Research

- Research Areas
- Astrophysics & Cosmology (Observ.)
- Astrophysics & Cosmology (Theo.)
- Atomic Physics (Expt.)
- Atomic Physics (Theo.)
- Beam Physics
- Biological Physics
- Condensed Matter Physics (Expt.)
- Condensed Matter Physics (Theo.)
- General Relativity
- Microscopy
- Nuclear Physics
- Particle Physics (Expt.)
- Particle Physics (Theo.)

- Institutes & Centers
- Undergrad Research
- Graduate Research

# Graduate Student Research

Research opportunities for graduate students abound. In addition to working directly with a Physics Department faculty member, graduate students also conduct research with faculty in Astronomy & Astrophysics, Chemistry, Geophysical Sciences, Biological Sciences, Molecular Engineering, as well as at Fermilab, Argonne, CERN, and many other facilities.

In many cases, graduate students can get involved in research immediately upon, and sometime before, beginning their first quarter in the program. The best way for graduate students to get involved in the research of his or her choice is to communicate with the faculty members working in their area(s) of interest to find out how to best proceed based on their specific situations. A great way to explore an experimental research group early-on is to satisfy the experimental physics requirement by doing a year-long project with that group.

Below, you will find a sampling of some of the fore-front-level research being done by our graduate students. You may also view the graduate research archive for previous profiles. Enjoy…

- Michael Geracie

(theoretical physics) - Li-Chung Ha

(expt atomic physics) - Jennifer Lin

(string theory)

- Jeremy Neuman

(theoretical neuroscience) - Kartik Prabhu

(relativity theory) - Martin Scheeler

(expt soft matter physics)

## Michael Geracie

**Degrees:**

- B.S., UW-Milwaukee, 2010 (Physics)

- B.S., UW-Milwaukee, 2010 (Mathematics)

- M.S., University of Chicago, 2011 (Physics)

**Graduate Student** (2010-pres), Dept. of Physics, Kadanoff Center for Theoretical Physics

**Research**: *Condensed Matter and High-energy Physics*

**Awards**: Robert A. Millikan Fellowship, Gregor Wentzel Teaching Prize, Gregor Wentzel Research Prize (Dept. of Physics)

**Research Advisor**: Dam Thanh Son

My interests lie on the interface between condensed matter and high energy physics. Though often treated separately, these subjects have a rich shared history. This is possible because of the power of geometry and quantum field theory, which can describe diverse phenomena within a unified way of thinking. I hope to further this program by applying techniques familiar to high energy physicists in new condensed matter settings.

My initial research focused on novel applications of geometry to the quantum Hall effect. Since its discovery, the quantum Hall effect has proven a fruitful playground for both theorists and experimentalists. The first known example of a topological phase, its discovery precipitated a revolution in our understanding of quantum matter that continues to this day. My work in this field involved studying these systems in a new regime, the lowest Landau level (LLL) fluid, in which the system is cold enough to be effectively constrained to the LLL, but is otherwise hydrodynamic. We demonstrated that such flows are highly constrained, characterized by only the equation of state and a thermal Hall conductivity. In addition, we were able to extract a number of new Streda-type formulas for both charge and energy transport.

To be as constraining as possible required the full implementation of spacetime symmetries. Since these samples are typically non-relativistic in nature, this required a number of formal developments in non-relativistic, or Newton-Cartan (NC) geometry. In several papers, myself and collaborators made the necessary advances, writing the first fully diffeomorphism covariant Ward identities for an NC geometry and constructing the first Galilean covariant description of torsionful NC backgrounds, which is necessary to study non-relativistic energy transport.

My current work is concerned with certain strongly coupled field theories at finite density. Large N Chern-Simons theories have attracted much attention among high energy circles in recent years. These systems are unique in that they exhibit a great deal of interesting physics, including anyonic excitations, as well as conjectured holographic and Bosonization dualities, yet also permit exact computations of many relevant quantities at strong coupling. Myself and collaborators use this setting as a playground to investigate the properties of condensed Fermion systems at strong coupling and low temperatures. We have also found a number of novel phenomena, including an enhancement of quantum degeneracy that leads to a breakdown of the classical regime at strong coupling. By examining linear response in this system, we have also learned that Fermi liquid theory, long a pillar of condensed matter phenomenology, needs to be augmented to completely characterize zero temperature transport. Going forward, we seek to continue this program in the hopes of gaining new insights into strongly coupled condensed phases of matter.

### Publications

*Spacetime Symmetries of the Quantum Hall effect*, M. Geracie, C. Wu, S. Wu and D. T. Son,*Phys. Rev.***D91**(2015) 045030; arXiv:1407.1252 [cond-mat.mes-hall].*Hydrodynamics on the lowest Landau Level*, M. Geracie and D. T. Son,*JHEP*1506 (2015) 044, arXiv:1408.643 [cond-mat.mes-hall].*Fields and fluids on curved non-relativistic spacetimes*, M. Geracie, K. Prabhu and M. Roberts,*JHEP*1508 (2015) 042, arXiv:1503.02680 [hep-th].*Cold, dense Chern-Simons with Fermions at Large N*, M. Geracie, M. Goykhman and D. T. Son.

## Li-Chung Ha

**Degrees:**

- B.S., National Taiwan University, 2006 (Chemistry)

- M.S., National Taiwan University, 2009 (Physics)

**Graduate Student** (2010-pres), Dept. of Physics, James Franck Inst.

**Research**: *Atomic Physics*

**Awards**: Grainger Graduate Fellowship (Dept. of Physics), Government Scholarships for Study Abroad (Taiwan)

**Research Advisor**: Cheng Chin

Modern computers, based on silicon transistors, have experienced exponential year-on-year growth in computation power. Soon, this technology will reach the limitation defined by the tunneling effect of electrons in the semiconductor material. To respond to the increasing demand for faster data processing, a new type of computation technology is required. For data processing involving physical systems, the concept of quantum simulation was proposed by Richard Feynman. It involves the study of a complex system with a different system governed by the same equations, but which is relatively clean and controllable.

Ultracold atomic systems have been demonstrated as excellent candidates for doing quantum simulation. With the advantage of its cleanness and tunability, researchers are able to probe physical phenomena which are difficult to study in a complicated condensed matter system. Over the past decade, there have been numerous scientific results verifying the models shown in the textbook, e.g. realization of the Bose-Einstein condensate (BEC) and degenerate Fermi gas, demonstration of the Bose-Hubbard model, quantum magnetism, and quantum criticality.

The primary research direction of my thesis resides on engineering the band structure of a BEC in an optical lattice which is an optical potential created by interfering two laser beams. We load the condensate in a one dimensional optical lattice and phase modulate the lattice potential. The ground and the first excited bands from the lattice are coupled through the modulation, and the dispersion of the new admixed ground band evolves from having one single minimum to having two minima. This system exhibits effective ferromagnetism, and we directly observe the formation of domain and extract the correlation function.

Based on this new type of quantum phase, we are also able to simulate the roton which is a quasi-particle previously only observed in superfluid helium. The existence of roton in superfluid helium was speculated by Lev Landau to explain many experiments on the suppression of the superfluid critical velocity. In our system, the roton originates from the double-well dispersion in the shaken lattice, and can be controlled by both the atomic interaction and the amplitude of the modulation. We determine the excitation spectrum using Bragg spectroscopy and measure the critical velocity by dragging a weak speckle potential through the condensate. We observe good agreement between our measurement and the modified Bogoliubov model.

A future research direction is to study the scaling of the domain size versus the speed used to cross the phase transition in order to understand and simulate the early universe. As was predicted by Tom Kibble, the density of frozen-out cosmological defects, such as cosmic domains and strings, is set by the cooling rate of the universe after the Big Bang. Wojciech Zurek later extended the idea to condensed matter systems, which is the formation of vortices (an excitation with quantized angular momentum) in liquid helium after being quenched to the superfluid phase. The Kibble-Zurek mechanism is of particular interest in grand unified theories of symmetry-breaking phase transitions in the early universe, 10^{-35} s after the Big Bang. While it is infeasible to perform an experiment or classical computer simulation on a cosmological scale, a quantum simulator would be readily applicable to the question.

### Publications

- Roton-maxon excitation spectrum of Bose condensates in a shaken optical lattice, arXiv:1407.7157 (2014). L.-C. Ha, L. W. Clark, C. V. Parker, B. M. Anderson, C. Chin.
- Anomalous thermoelectric transport in two-dimensional Bose gas, arXiv:1306.4018 (2013). E. L. Hazlett, L.-C. Ha, and C. Chin.
- Direct observation of effective ferromagnetic domains of cold atoms in a shaken lattice, Nature Phys. 9, 769 (2013). C. V. Parker, L.-C. Ha, and C. Chin
- Strongly interacting two-dimensional Bose gases, Phys. Rev. Lett. 110, 145302 (2013). L.-C. Ha, C.-L. Hung, X. Zhang, U. Eismann, S.-K. Tung, and C. Chin
- Extracting density-density correlations from in situ images of atomic quantum gases, New Journal of Physics 13, 075019 (2011). C.-L. Hung, X. Zhang, L.-C. Ha, S.-K. Tung, N. Gemelke, and C. Chin.

** Jennifer Lin**

**Degrees**:

- B.A., Princeton University, 2010 (Physics)

- Ph.D., University of Chicago, 2015 (Physics)**Graduate Student** (2010-2015), Dept. of Physics, Enrico Fermi Inst.

**Research**:* String Theory*

**Awards**: National Science Foundation Graduate Fellowship (NSF), Sidney Bloomenthal Fellowship (Dept. of Physics)

**Research Advisor**: David Kutasov

Quantum field theory (QFT) is the framework which underlies our present-day understanding of elementary particles and their interactions. In its early history, QFT was formulated in a perturbative expansion around a non-interacting free theory. However many physical phenomena, such as color confinement of quarks (i.e. why no isolated quarks are observed) and mass generation for bound states (i.e. why nucleons are much heavier than their constituent quarks) lie outside this regime. Developing a better understanding of non-perturbative and strong coupling features of QFT's is thus of obvious interest.

One strategy is to study theories that share qualitative features with real world physics, yet are in some way simpler, allowing us to understand their strong coupling dynamics. Examples include the study of QFT's in lower dimensions, QFT's with extra symmetry (such as conformal symmetry and supersymmetry), or QFT's that exhibit strong-weak coupling duality, a general phenomenon where the same physics has both a strongly coupled description and an alternative, weakly coupled one.

My PhD work has revolved around deepening our understanding of field theory in this way. An example of a problem that I worked on recently is in supersymmetric QFT's in four spacetime dimensions. In 1994 N. Seiberg showed that N=1 SQCD, the supersymmetric generalization of the theory of quantum chromodynamics (QCD) that describes the strong force in nuclei, can be analyzed via a duality where it exhibits the same non-trivial physics at large distances as a different field theory. Extensions of his work have led to insights into the strong coupling dynamics of other supersymmetric QFT's, that exhibit qualitatively new features.

In one such extension, we can add extra matter fields to SQCD along with interactions for them. In 2003, K. Intriligator and B. Wecht classified all IR fixed points that can be obtained by deforming SQCD with adjoint matter. They found that the non-trivial fixed points corresponded to interaction terms that coincide with a mathematical structure called an ADE classification. The A and D theories in the classification were studied in the 1990's, where they were found to exhibit Seiberg-like duality, but there remained three models in the classification called E6, E7 and E8 which were not previously understood.

With my advisor David Kutasov, I analyzed the physics of the E7 theory by conjecturing a Seiberg dual description that passes many non-trivial checks. I also ruled out the existence of a qualitatively similar duality for the E6 and E8 cases. What happens for them remains an open problem. It is surprising that these two cases appear not to work like all the other ones, and suggests an opportunity for new insights into the structure of 4d QFT's.

Other topics that I have worked on while at Chicago include the dynamics of field theories in lower dimensions (2d theories with N= (0,2) supersymmetry and 3d non-SUSY Chern-Simons theory coupled to vector matter) as well as aspects of gauge/gravity duality, a strong-weak duality connecting field theories to higher-dimensional theories with gravity.

### Publications:

- D. Kutasov and J. Lin. N=1 Duality and the Superconformal Index. arXiv:1402.5411.
- D. Kutasov and J. Lin. Exceptional N=1 Duality. arXiv:1401.4168.
- D. Kutasov and J. Lin. (0,2) ADE Models From Four Dimensions. arXiv:1401.5558.
- D. Kutasov and J. Lin. (0,2) Dynamics From Four Dimensions. Phys. Rev. D89, 085025 (2014). arXiv:1310.6032.
- D. Kutasov, J. Lin, and A. Parnachev. Holographic Walking from Tachyon DBI. Nucl.Phys.B863:361-397 (2012). arXiv:1201.4123.
- D. Kutasov, J. Lin, and A. Parnachev. Conformal Phase Transitions at Weak and Strong Coupling. Nucl. Phys. B858:155-195 (2012). arXiv:1107.2324.

** Jeremy Neuman**

**Degrees**:

- B.S., UCLA, 2010 (Physics with Honors)

- B.S., UCLA, 2010 (Mathematics)

- M.S., University of Chicago, 2011 (Physics)

**Graduate Student** (2010-pres) Dept. of Physics

**Research**:* Theoretical Neuroscience, Nonequilibrium Statistical Mechanics*

**Awards**: GAANN Fellowship (Dept. of Education), GSA Travel Award (Univ. of Chicago)

**Research Advisors**: Jack Cowan (Mathematics), Wim van Drongelen (Pediatric Neurology)

Generally in physics, model systems are close to equilibrium. In biology, however, this is almost never the case. Take for example the human brain, a structure as complicated as there is in the living world. It contains tens of billions of neurons, each with roughly one thousand connections. Yet many of its attributes lend it nicely to the study of non-equilibrium statistical mechanics and many body theory. Because of this, physicists can make large contributions to the field of theoretical neuroscience. My research seeks to use mean field and statistical field theories to explain a wide variety of neuronal dynamics, most of which we investigate with aggregate or "population" models. Primarily, we utilize the Wilson-Cowan equations, a set of nonlinear integro-differential equations designed to describe interactions at the mean-field level between the two general types of neurons, excitatory and inhibitory. These neurons connect in one of four ways: excitatory-excitatory, excitatory-inhibitory, inhibitory-excitatory, and inhibitory-inhibitory. From here, we can build an effective lattice or continuum model of the brain with only these assumptions.

One important question in neuroscience I've investigated is whether the resting state of the brain is critical and, if so, how it might organize itself into such a state. The idea behind this study is Self-Organized Criticality (SOC), a property of certain statistical systems which have their own mechanism for attraction to a critical point. The concept was developed to describe a wide array of phenomena across various fields of science, including physics, chemistry, economics, biology, and even sociology. In neuroscience, one manifestation of this self-tuning process is called synaptic plasticity, the ability of neurons to strengthen or weaken their connection strength over time. Previously, my advisors and I developed a model of plasticity, which, when coupled to a simple neural network with only an excitatory population, exhibits SOC. However, when we expanded our model to include inhibitory neurons, we found that the brain operates slightly below criticality, which we termed "self-organized near criticality." There is a large amount of data suggesting that this regime is optimal over being right at the critical point.

Recently, my advisors and I have been interested in the connection between localized and spreading neural activity. In the brain, experiments have shown that small inputs generate transient wave propagation while large inputs keep activity confined. One of our main efforts is to deterministically and stochastically simulate this effect because it could have implications, among other things, on our understanding of noise and consciousness, which at the neural network level is just the outgrowth of communication between brain regions. When activity cannot spread, the subject loses consciousness. On the other hand, spreading activity in an uncontrolled matter is the basis for a seizure, another topic of interest. Thus, it's clear that certain parameters in the brain must be met in order for us to be conscious but not constantly seizing. So far, we've found at the mean-field level that a slight redefinition in how clusters of neurons fire can answer this problem. As part of the remaining research for my Ph.D., I will further investigate the conditions on which neurons are able to communicate in a controlled fashion. This could lead to profound changes in the way we view a wide variety of neurological phenomena at the network level.

### Selected Publications:

- H. Meijer, T. Eissa, B. Kiewiet, C. Schevon, J. Neuman, A. Tryba, C. Marcuccilli, S. van Gils, W. van Drongelen, "Modeling Focal Epileptic Activity in the Wilson-Cowan model with Depolarization Block" Manuscript in preparation (2014).
- J. D. Cowan, J. Neuman, and W. van Drongelen, "Self‐Organized Criticality and Near‐Criticality in Neural Networks" Criticality in Neural Systems, 465-484 (2014).
- J. D. Cowan, J. Neuman, B. Kiewiet, & W. van Drongelen, "Self-organized criticality in a network of interacting neurons" Journal of Statistical Mechanics: Theory and Experiment, 2013(04), P04030 (2013).

** Kartik Prabhu**

**Degrees**:

M.Sc. and B.Sc., Indian Inst. of Tech., Kharagpur, 2010 (Physics)**Graduate Student** (2010-pres) Dept. of Physics, Enrico Fermi Institute

**Research**:* General Relativity and black holes*

**Awards**: Jerry Rao (Dept. of Physics)

**Research Advisors**: Robert M. Wald

General Relativity is the best description of gravity that we have presently. Some of the most exotic predictions of this theory include spacetime singularities and black holes. Even though the theory is a 100 years old, there are many aspects of black holes at remain unresolved. One such problem is whether black holes (specially in higher dimensions) are stable. The problem essentially is: If we perturb a black hole by a small amount, does the perturbation "settle down" to some other configuration (stability), or does it become larger and larger without any bound (instability)?

With Prof. Robert M. Wald, I investigated the instabilities of stationary and axisymmetric black holes in General Relativity in vacuum. The key idea is to investigate an energy-like quantity for small axisymmetric perturbations of the black hole. In an earlier work Hollands and Wald had already shown that if this energy is negative then the black hole is unstable in the sense that it does not settle down to any other stationary black hole. Expanding on this work, using a reflection symmetry of such black holes, we proved that the kinetic energy part of the total energy is always positive. Further, if the remaining potential energy part is negative then the small perturbation will grow exponentially in time i.e. we have an unstable perturbation. We also found a variational formula that give the rate of this exponential growth. At present, along with former UChicago student Josh Schiffrin, we are extending this result to black holes with matter fields and also to perfect fluid stars in General Relativity.

Along with this, I am working on generalising the first law of black holes mechanics and the formula for black hole entropy to situations where matter fields like magnetic monopoles or fermions are present around the black hole.

Another topic that I have worked on along with Michael Geracie and Matthew M. Roberts, is to formulate non-relativistic spacetimes and matter fields in a geometric way in a manner that is very close to General Relativity. Such a geometric viewpoint on non-relativistic systems was already shown to be very fruitful in condensed matter systems like the Quantum Hall Effect by Prof. Dam T. Son. We are continuing to work on further applications of this non-relativistic geometry to look at other applications that might give some insight into other condensed matter systems.

### Selected Publications:

*Curved non‑relativistic spacetimes, Newtonian gravitation and massive matter*, (with M. Geracie, M. M. Roberts)*J. Math. Phys.***56**, 103505 (2015), arXiv:1503.02682.*Fields and fluids on curved non‑relativistic spacetimes*, (with M. Geracie, M. M. Roberts)*JHEP***08**, 042 (2015), arXiv:1503.02680.*Black Hole Instabilities and Exponential Growth*, (with R. M. Wald)*Commun. Math. Phys.***340**, 253‑290 (2015), arXiv:1501.02522.

** Martin Scheeler**

**Degrees**:

A.B., Princeton University, 2011 (Physics)**Graduate Student** (2011-pres) Dept. of Physics

**Research**:* Experimental Soft Matter - Topological Vortex Dynamics*

**Awards**: McCormick Fellow, Sachs Fellow, Wentzel Teaching Prize, Yodh Research Prize (Dept. of Physics), GAANN Fellowship (Dept. of Education)

**Research Advisors**: William Irvine

Vortices lie at the heart of fluid flow, driving all fluid motion in the absence of boundaries. Naturally this vorticity can organize into vortex loops—thin, closed loops which house compact arrangements of vortex lines—resulting structures akin to a smoke ring. Since these compact, geometric objects provide enough information to reconstruct the flow everywhere in space, they can be thought of as building blocks of a flow, with more complex flows corresponding to more complicated tangles of these loops. In the absence of viscosity, the dynamics of these elemental structures are bound to a simple rule: they are not allowed to cross. What would happen then if you took one of these vortex loops, like a smoke ring, and tied it into a knot?

Once a vortex loop is knotted, the only way to remove the knot is to pass one segment of the loop through another, but in an ideal flow, it is exactly this sort of filament crossing that is forbidden, and thus, vortex knots should stay knotted for all time. This topological stability manifests mathematically as the conservation of a quantity known as the fluid helicity, which measures the degree of vortex line linking and knotting in a flow. Like energy or momentum conservation, this topological conservation provides a strong constraint on the evolution of the fluid throughout all of space, and in doing so, provides a powerful framework for understanding the messy vortex tangles that produce complicated flows.

But in a real flow, one which has even the slightest amount of viscosity, vortex tube dynamics acquire a feature which seems to jeopardize this conservation law: the ability to reconnect. Rather than crossing, two small sections of vortex tube can align anti-parallel to each other, becoming so close that their separation approaches the viscous length scale, allowing the small regions to diffuse into each other and annihilate. The removal of these sections and the subsequent reconnecting of the tubes swaps the connectivity of the branches of the loop, providing knots a chance to reconfigure their topology and eventually unknot.

Working with Prof. William Irvine, I study the dynamics of these topological vortices experimentally. To generate these vortex knots and links in water, we take advantage of a phenomenon known as a "starting vortex", in which an airplane wing, when suddenly accelerated from rest, sheds a vortex along its trailing edge. Leveraging advances in 3D printing technology, we design and fabricate hydrofoils – airplane wings extruded along closed, curved paths in space – which when impulsively accelerated, produce vortex loops that match their geometry. This method allows us to produce isolated vortex links and knots for the first time in experiment.

How does the behavior of these experimental knots compare to our theoretical expectations? Recall that in an ideal flow, once we generate a knotted vortex, we expect it to remain knotted. Surprisingly, what we observe in a viscous fluid is instead the rapid unknotting of these vortices via topology-removing reconnections. At first glance, this result could indicate that helicity is a very poorly conserved quantity, discontinuously dropping to zero as the divergent reconnection process undoes the knotting. But what if instead of being lost, this knotting was flowing into a different form?

This potential discrepancy can be resolved by thinking a little more carefully about what helicity is measuring: it is not a measure of the knotting of the vortex tube containing the field lines, but rather of the knotting of the field lines themselves. Clearly, by knotting the tube containing the field lines, we've also knotted the lines themselves, but we could also wind the vortex lines around the center-line of a tube which is unknotted in a way that links or knots them (visually similar to the fibers wound together into rope). This linking inside a tube is generated in two independent ways: by coiling the center-line of the tube into a helix, and by twisting the field lines about the center-line.

With this knowledge, we can return to the experimental evolutions, where we observe that whenever there is a reconnection that changes the tube topology, it also introduces a helical coil in the post-reconnection geometry. Measurements of the helicity before and after the reconnection show that the formation of this coil is enough to exactly compensate for the tube unknotting, conserving helicity throughout the process. These results suggest that vortex field line topology might provide a useful interpretive key in understanding real fluid flows, and inspire future work intended on understanding how helicity can be cascaded towards dissipation and its role in vortex stability.

### Selected Publications:

- M.W. Scheeler, D. Kleckner, D. Proment, G.L. Kindlmann, W. T. M. Irvine, "Helicity conservation by flow across scales in reconnecting vortex links and knots"
*PNAS*111 (43) 15350 (2014).