- 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
- Nuclear Physics
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Experimental Condensed Matter Physics
Ph.D., California, Berkeley, 1987.
Prof., Depts. Chemistry and Physics, James Franck Inst., and the College
Experimental physics, surface physics, nonlinear optical spectroscopy.
Philippe Guyot-Sionnest's homepage
Quantum Confined Semiconductors. Delocalized electronic wavefunctions are readily achievable in semiconductor quantum dots, such as semiconductor nanocrystal colloids. This leads to extraordinary optical properties, which may lead to applications ranging from full-color displays, to photovoltaic cells. We synthesize semiconductor nanocrystals, and control their sizes and their surfaces. Microscopy and nonlinear spectroscopy are used to study the basic aspects of electron dynamics and interaction in strongly confined structures. We currently focus on the doping of nanocrystals and the infrared response, as well as the novel electrical transport properties in films made of these artificial atoms.
Optical Response of Metallic Nanostructures. Metallic structures much smaller than the wavelength of light allow to enhance locally the electromagnetic fields by several orders of magnitude. The enhancement is achieved by the plasmon resonance which is a collective excitation specific to the shape of the structure but involving all its free electrons. The enhancement is thus often limited by electron scattering process, in particular surface scattering which is increased in this small structures. Our research aims to synthesize metallic nanostructures, characterize their optical response, and optimize the materials combination to obtain much faster radiative emission of connected chromophores as well as giant optical nonlinearities.
- Superconductivity in films of Pb/PbSe nanocrystals, ACS Nano (ASAP) (2012)
- Mid-infrared HgTe colloidal quantum dot photodetectors, Nature Photonics 5 , 489 (2011)
- Meissner Effect in Colloidal Pb Nanoparticles, ACS Nano 4 , 5599-5608 (2010)
- Mott and Efros-Shklovskii Variable Range Hopping in CdSe Quantum Dots Films, ACS Nano 4, 5211-5216 (2010)
- Reduced damping of surface plasmons at low temperatures, Phys. Rev. B 79. 035418 (2009)
- Excitation of Dark Plasmons in Metal Nanoparticles by a Localized Emitter, Phys. Rev. Lett. 102, 107401 (2009)
- Magnetoresistance of CdSe/CdS quantum dot films, Appl. Phys. Lett. 95, 142105 (2009)
- Slow Electron Cooling in Colloidal Quantum Dots, Science 322 929-932 (2008)
- Conducting n-type CdSe Nanocrystal solids, Science 300, 1277 (2003)
- Electrochromic nanocrystal quantum dots, Science, 201, 2390 (2001)
- N-type colloidal semiconductor nanocrystals, Nature, 407, 981 (2000)
Ph.D., California, Santa Barbara, 2006.
Assistant Prof., Dept. of Physics, James Franck Inst., and the College
Experimental soft condensed matter, knotted fields.
William Irvine's homepage
My research interests are in the fields of experimental soft condensed matter and theoretical and experimental "knotted fields". A common theme in my research interests is the strong role played by geometry and advanced optical techniques.
"Soft" is used to describe a rich variety of classical many-body systems that have energetics accessible at room temperature and are large enough for their constituents to be imaged, providing an ideal playground for the study of many open questions in equilibrium and non-equilibrium many-body physics. Using colloidal particles, (both spherical and shaped, fluids and foams), we are investigating a variety of problems in ordered and disordered phases. A recent focus has been on the use of curvature as a tool to probe structure in two dimensions. In particular, we recently investigated the structure of two-dimensional colloidal crystals frustrated by the Gaussian curvature of the curved oil-water interface they are bound to. We are currently developing techniques to extend these ideas to far from equilibrium processes in curved space.
To tie a shoelace into a knot is a relatively simple affair. Tying a knot in a field is a different story, because the whole of space must be filled in a way that matches the knot being tied at the core. The possibility of such localized knottedness in a space-filling field has fascinated physicists and mathematicians ever since Kelvin’s 'vortex atom' hypothesis, in which the atoms of the periodic table were hypothesized to correspond to closed vortex loops of different knot types. Recently I investigated some remarkably intricate and stable topological structures that can exist in light fields whose evolution is governed entirely by the geometric structure of the field. Open questions remain about he the rules that govern the topological structure of field lines, the possible states that can be created and especially what happens when topologically nontrivial states are coupled to matter. I am currently interested in exploring such structures in both light and `softer' fields.
- Pleated crystals on curved surfaces, W.T.M. Irvine V.Vitelli and P.M. Chaikin, To appear in Nature (2010)
- Linked and knotted beams of light, W.T.M.Irvine and D. Bouwmeester, Nature Physics 4, 716–720 (2008)
- Robust Long-Distance Entanglement and a Loophole-Free Bell Test with Ions and Photons, C.Simon and W.T.M. Irvine, Phys. Rev. Lett. 91, 110405 (2003)
- Realisation of Hardy's thought experiment, W.T.M. Irvine, J.H. Hodelin, C. Simon and D. Bouwmeester, Phys. Rev. Lett. 95. 030401 (2005)
Eric D. Isaacs
Ph.D., M.I.T., 1988.
Provost, University of Chicago
Professor (part-time), Dept. of Physics and James
Experimental physics, condensed matter.
Studies of novel electronic and magnetic materials including strongly correlated condensed matter systems, quantum antiferromagnets and hydrogen bonding; development of synchrontron-based x-ray nanoprobe, magnetic and inelastic scattering techniques, applied especially to bridging electronic through macroscopic length and time scales; plasmonic "meta-materials" for RF and photonics; combinatorial approaches to new materials discovery.
Ph.D., Minnesota, 1987.
William J and Alicia Townsend Friedman Professor, Dept. Physics, James Franck Inst., and the College.
Experimental condensed matter physics, nanoscale systems, colloids and suspensions, granular materials.
Heinrich Jaeger's homepage
Nanoscale Particle Systems. Just as ordinary solids are composed of tightly packed atoms, nanoparticle solids consist of closely spaced nano-sized building blocks. But unlike their atomic counterparts, these building blocks each contain a few hundred to a few thousand atoms and can be designed in a myriad of different shapes and material compositions. Furthermore, individual particles can be surrounded with a thin shell of organic molecules that modulate the interparticle spacing and thus the local coupling. In this way, nanoparticle aggregates combine the unique electronic, magnetic and optical properties of quantum-confined inorganic solids with the flexibility afforded by embedding them into a tunable organic matrix. We have been investigating the two-dimensional limit of nanoparticle solids: sheets of close-packed nanoparticles that are precisely one single particle thick. Our research tackles questions such as: What are the physical principles underlying the self-assembly of individual nanoparticles into extended, close-packed monolayers? How does charge transport occur through the resulting particle arrays? Can one freely suspend nanoparticle monolayers and what are the properties of such ultra-thin sheets? This effort combines fundamental science with an exploration of new applications in sensing, nano-mechanics and nano-filtration, and it utilizes experimental techniques ranging from scanning probe and electron microscopy (AFM, SEM, TEM), electron-beam lithography and ion-beam cutting, to charge transport measurements.
Macroscopic Particle Systems. A second effort in my group concerns the behavior of large numbers of interacting particles that are larger than a few microns and thus too large to be affected by Brownian motion. In this ‘macroscopic’ limit thermal energies are irrelevant and this makes such systems outstanding candidates for investigating key issues in far-from-equilibrium physics. We have been focusing on two classes of systems: dry granular materials consisting of large aggregates of macroscopic particles that interact primarily on contact, and dense suspensions where the particles are embedded in a liquid. Much of our work on the complex behavior of dry granular materials, which can show both solid- and liquid-like responses to applied forcing, has been done in collaboration with Sidney Nagel’s group. Current projects investigate the quasi-static behavior of granular matter (in particular, the packing properties and stress response of non-spherical particles), rapid interactions in flowing granular systems (using our unique apparatus for studying freely falling granular streams), and applications of granular jamming (for example, to new types of robotic systems). In dense suspensions both nonlinear, dissipative particle contact interactions and stresses arising from the presence of the surrounding liquid come into play. This makes dense suspensions a model system for tuning across the full spectrum from liquid to solid behavior. Our current research in this area seeks to answer questions such as: Why does the viscosity of suspensions increase with increased forcing (a counter-intuitive phenomenon known as shear-thickening)? How are stresses transmitted through these highly dissipative materials? Does a suspension break into droplets like a liquid or rupture like a solid? This effort uses an array of techniques that include high-speed video, rheometry, magnetic resonance imaging (MRI), x-ray tomography (at the Advanced Photon Source), and 3D printing.
- Eric Brown, Nicole A. Forman, Carlos S. Orellana, Hanjun Zhang, Ben Maynor, Douglas Betts, Joseph M. DeSimone, and Heinrich M. Jaeger, “Generality of shear thickening in suspensions”, Nature Materials 9, 220 - 224 (2010).
- Eric Brown, Nicholas Rodenberg, John Amend, Annan Mozeika, Erik Steltz, Mitchell R. Zakin, Hod Lipson, and Heinrich M. Jaeger, “Universal Robotic Gripper based on the Jamming of Granular Material”, Proc. Nat’l Acad. Sci. 107, 18809–18814 (2010).
- Jinbo He, Pongsakorn Kanjanaboos, N. Laszlo Frazer, Adam Weis, Xiao-Min Lin, Heinrich M. Jaeger, “Fabrication and Mechanical properties of large-scale freestanding nanoparticle membranes”, Small 6 (13), 1449-1456 (2010).
- Heinrich M. Jaeger and Andrea J. Liu, “Far-From-Equilibrium Physics: An Overview”, arXiv:1009.4874 (2010).
- John R. Royer, Daniel J. Evans, Loreto Oyarte, Qiti Guo, Eliot Kapit, Matthias E. Möbius, Scott R. Waitukaitis, and Heinrich M. Jaeger, “High-speed tracking of rupture and clustering in freely falling granular streams”, Nature 459, 1110 (2009).
- Ling-Nan Zou, Xiang Cheng, Mark L. Rivers, Heinrich M. Jaeger, and Sidney R. Nagel. “The packing of granular polymer chains”, Science 326, 408-410 (2009).
- Klara E. Mueggenburg, Xiao-Min Lin, Rodney H. Goldsmith, and Heinrich M. Jaeger, “Elastic membranes of close-packed nanoparticle arrays”, Nature Materials 6, 656 - 660 (2007).
- Terry P. Bigioni, Xiao-Min Lin, Toan T. Nguyen, Eric Corwin, Thomas A. Witten, and Heinrich M. Jaeger, “Kinetically-Driven Self-Assembly of Highly-Ordered Nanocrystal Monolayers”, Nature Materials 5, 265-270 (2006).
- John R. Royer, Eric I. Corwin, Andrew Flior, Maria-Luisa Cordero, Mark Rivers, Peter Eng, and Heinrich M. Jaeger, “Formation of Granular Jets Observed by High-Speed X-ray Radiography”, Nature Physics 1, 164-167 (2005).
- Heinrich M. Jaeger, Sidney R. Nagel, and Robert P. Behringer, "Granular Solids, Liquids and Gases", Rev. Mod. Phys. 68, 1259 (1996).
Ph.D., Princeton, 1992.
Prof., Dept. Physics, James Franck Inst., and the College
Experimental condensed matter physics, fractional quantum Hall effect, semi-conductor physics.
Woowon Kang's homepage
My research centers on the studies of novel, quantum mechanical effects in low-dimensional condensed matter systems. The collective response of a system consisting of many identical particles differs considerably from its single-particle behavior due to interaction between different particles. Unusual behaviors and phase transitions emerge as a classical system adiabatically enters the quantum regime. Model systems of interest include low-dimensional semiconductors and a class of charge-transfer molecular conductors. These systems serve as table-top testbed to study new types of ground states and excitations. Currently ongoing projects include:
- Tunneling between one dimensional, chiral edge states
- Spin physics in the fractional quantum Hall effect
- Superconductivity and spin density waves in molecular conductors
- Light emission in sonoluminescence
- Hysteresis and Spin Transitions in the Fractional Quantum Hall Effect. H. Cho, J.B. Young, W. Kang, K.L. Campman, A.C. Gossard, M. Bichler, and W. Wegscheider. Phys. Rev. Lett. 81, 2522, 1998.
- Negative Hall Plateaus and Quantum Hall Effect in TMTSF2PF6. H. Cho and W. Kang. Phys. Rev. B 59, 9814, 1999.
- Quantum Hall Effect and Anomalous Transport in TMTSF2PF6. J. Eom, H. Cho and W. Kang. J. Phys. IV 9, 191, 1999.
- Quantum Hall Ferromagnetism in a Two-Dimensional Electron System. J. Eom, H. Cho, W. Kang, K.L. Campman, A.C. Gossard, M. Bichler, and W. Wegscheider. Science 289, 2320, 2000.
- Tunneling between the Edges of Two Lateral Quantum Hall Systems. W. Kang, H.L. Stormer, K.B. Baldwin, L.N. Pfeiffer, and K.W. West. Nature 403, 59, 2000.
- Hysteresis, Spin Transitions, and Magnetic Ordering in the Fractional Quantum Hall Effect. H. Cho, J.B. Young, W. Kang, K.L. Campman, A.C. Gossard, M. Bichler, and W. Wegscheider. Physica A 6 , 18, 2000 .
- Line emission in single-bubble sonoluminescence. J. B. Young, J.A. Nelson, and W. Kang. Phys. Rev. Lett. 86, 2673, 2001.
Ph.D., Princeton, 1974.
Stein-Freiler Distinguished Service Prof., Dept. Physics, James Franck Inst., Enrico Fermi Inst., and the College
Experimental physics, condensed-matter physics, non-linear dynamics.
Sidney Nagel's homepage
Many complex phenomena are so familiar that we hardly realize that they defy our normal intuition; we forget to ask whether or not they are understood. Examples of such poorly understood behavior include the anomalous flow of granular material, the long messy tendrils left by honey spooned from one dish to another, the pesky rings deposited by spilled coffee on a table after the liquid evaporates or the common splash of a drop of liquid onto a countertop. Aside from being uncommonly beautiful to see, many of these phenomena involve non-linear behavior where the system is far from equilibrium. Most of the world we know is beyond description by equilibrium theories, and understanding far-from-equilibrium behavior is one of the great challenges of modern physics -- these are phenomena that can lead the inquisitive into new realms of physics. Problems such as these fuel much of my research effort. Here are a few of the topics on which my group is currently working:
Jamming. One emphasis of my work is to understand the properties of disordered materials. Such materials have many common features that are different from their crystalline counterparts. One example is of particular note. By varying some external parameter, these materials can become structurally arrested - that is they jam. We are interested in understanding what controls the onset of rigidity in a wide variety of situations. Do all jammed systems have a common set of inherent properties? If so, can we learn about the nature of glasses (where the ability to flow has been lost when the temperature is dropped to too low a value) by studying the jamming that occurs in a granular material such as a sand pile as it suddenly stops flowing? In an effort to deal with diverse phenomena where systems become stuck in a region far from equilibrium (e.g., at the glass transition and in clogged granular materials flowing - unsuccessfully - through a pipe), we have been investigating, along with Andrea Liu at the University of Pennsylvania, whether there can be a more general way of looking at these systems in terms of a Jamming Phase Diagram. Such a concept would relate the physics of granular materials with those of glasses. In our studies, we have concentrated on the elementary excitations, i.e., vibrations, of marginally jammed systems and have found that the nature of the vibrations are inherently different from what is expected in crystals. This discovery brings a new perspective to understanding the nature of amorphous matter in general.
Granular Materials. In collaboration with the group of Heinrich Jaeger, we have been studying the properties of granular media. Despite their ubiquity and the simplicity with which they can be described, we understand very little about how these materials (e.g., sand) behave. In these studies we enter a new area of physics in which we are studying a statistical system of many particles but where the temperature is totally irrelevant. Thus, these systems are unavoidably always out of equilibrium, and we must come up with new concepts in order to understand and predict their properties.
Singularities in Free-surface Flows. A drop falling from a faucet is a common example of a liquid fissioning into two or more pieces. The cascade of structure that is produced in this process is of uncommon beauty. As the drop falls, a long neck, connecting two masses of fluid, stretches out and then breaks. What is the shape of the drop at the instant of breaking apart? Something dire must happen to the mathematical description of the liquid at that point since the drop undergoes a topological transition where it starts out as a single, connected fluid and ends up in two or more separate pieces. This is an example of a finite-time singularity since the drop breakup occurs in a short time after the drop becomes unstable and starts to fall. At the transition, a singularity occurs since the radius of the neck holding the drop to the nozzle becomes vanishingly thin. As its radius goes to zero, the curvature diverges and the surface tension forces become infinite. How can such dramatic dynamics occur in something that had such smooth and innocuous initial conditions and forcing terms? Using photographic and electronic techniques, we have been studying transitions such as these to understand how the non-linearities in the governing equations (in this case the Navier-Stokes equations) can be tamed and understood. Singularities of this kind occur in many areas of physics from stellar structure to turbulence to bacterial colony growth. The drop breakup problem is one of the simplest places to probe directly the singularity itself. In collaboration with Wendy Zhang, we have uncovered a variety of different singularities - some of which surprisingly retain a memory of their initial conditions throughout the entire breakup process.
Splashing. How does a drop of liquid splash when it hits a solid surface like a piece of glass? Our intuition tells us it must splash and eject thousands of tiny droplets. We would expect the same behavior anywhere - here on Earth, on Mars and on the Moon. We would be wrong! We have found that we can suppress splashing completely by removing the surrounding air. A drop which splashes in Chicago would not necessarily splash on the top of Mt. Everest where the pressure is less and would definitely not splash on the Moon which has no atmosphere.
- Toward the zero surface tension limit in granular fingering instability, Xiang Cheng, Lei Xu, Aaron Patterson, Heinrich M. Jaeger and S. R. Nagel, Nature Physics 4, 234 (2008).
- Coalescence in low-viscosity liquids, Sarah C. Case and S. R. Nagel, Phys. Rev. Lett. 100, 084503 (2008).
- Energy transport in jammed sphere packings, Ning Xu, Vincenzo Vitelli, Matthieu Wyart, Andrea J. Liu, S. R. Nagel, Phys. Rev. Lett. 102, 038001 (2009).
- Memory-encoding vibrations in a disconnecting air bubble, Laura E. Schmidt, Nathan C. Keim, Wendy W. Zhang, and S. R. Nagel, Nature Physics 5, 343 (2009).
- Thermal Vestige of the Zero-Temperature Jamming Transition, Zexin Zhang, Ning Xu, D. T. N. Chen, P. Yunker, A. M. Alsayed, K. B. Aptowicz, P. Habdas, Andrea J. Liu, S. R. Nagel and Arjun G. Yodh, Nature 459, 230 (2009).
- Excitations of Ellipsoid Packings near Jamming, Zorana Zeravcic, Ning Xu, Andrea J. Liu, S. R. Nagel and Wim van Saarloos, Europhys. Lett. 87, 26001 (2009).
- The packing of granular polymer chains, Ling-Nan Zou, Xiang Cheng, Mark L. Rivers, Heinrich M. Jaeger, S. R. Nagel, Science 326, 408 (2009).
- Equivalence of glass transition and colloidal glass transition in the hard-sphere limit, Ning Xu, Thomas K. Haxton, Andrea J. Liu, S. R. Nagel, Phys. Rev. Lett. 103, 245701 (2009).
- Anharmonicity and quasi-localization of the excess low-frequency vibrations in jammed solids, Ning Xu, Vincenzo Vitelli, Andrea J. Liu, and S. R. Nagel, Europhys. Lett. 90, 56001 (2010).
- Glassy dynamics in thermally-activated list sorting, Ling-Nan Zou, S. R. Nagel, Phys. Rev. Lett. 104, 257201 (2010).
- The jamming transition and the marginally jammed solid, Andrea J. Liu and S. R. Nagel, Annual Reviews of Cond. Mat. Phys. 1, 347 (2010).
- Thin Film Formation During Splashing of Viscous Liquids, Michelle M. Driscoll, Cacey S. Stevens, S. R. Nagel, Phys. Rev. E 82, 036302 (2010).
Ph.D., Princeton, 1982.
John T. Wilson Distinguished Service Professor, Dept. Physics, James Franck Inst., and the College, and Provost, University of Chicago.
Experimental physics, solid state physics, low-temperature physics.
Thomas Rosenbaum's homepage
At temperatures near absolute zero, new collective phenomena become possible. The quantum mechanical nature of materials is highlighted at the low temperatures, leading to a different class of phase transitions and to states with unusual excitation spectra. I use dilution refrigerator techniques to explore quantum magnets and glasses with connections both to quantum phase transitions and to the encoding of information, metal-insulator transitions with choreographed charge and spin degrees of freedom, new magnetoresistive compounds, and exotic superconductivity. MilliKelvin temperatures often are combined with symmetry-breaking fields (such as uniaxial stress or magnetic fields), diamond anvil cell pressures, and x-ray and neutron scattering to help constrain theory on fundamental grounds. These disparate topics are united by the theme of the interplay of correlation effects and disorder and by the issue of how macroscopic order can emerge from microscopic disorder.
- Quantum and Classical Routes to Linear Magnetoresistance, J. Hu and T.F. Rosenbaum, Nature Materials 7, 697 (2008).
- Macroscopic Signature of Protected Spins in a Dense Frustrated Magnet, S. Ghosh, T.F. Rosenbaum, and G. Aeppli, Phys. Rev. Lett. 101, 157205 (2008).
- Breakdown of the Bardeen-Cooper-Schrieffer Ground State at a Quantum Phase Transition, R. Jaramillo et al., Nature 459, 405 (2009).
- Switchable Hardening of a Ferromagnet at Fixed Temperature, D.M. Silevitch, G. Aeppli, and T.F. Rosenbaum, Proc. Nat. Acad. Sci. 107, 2797 (2010).
- Signatures of Quantum Criticality in Pure Cr at High Pressure, R. Jaramillo, Y. Feng, J. Wang, and T.F. Rosenbaum, Proc. Nat. Acad. Sci. 107, 13631 (2010). [Editors’ Choice: An Orderly Transition, Science 329, 729 (2010).]
- Magnetism, Structure, and Charge Correlation at a Pressure-Induced Mott-Hubbard Insulator-Metal Transition, Y. Feng et al., Phys. Rev. B 83, 035106 (2011).
Ph.D., Yale, 2007.
Asst. Prof., Dept. Physics, James Franck Inst., and the College.
Experimental condensed matter physics, quantum computing, superconducting circuits, electrons on helium.
David Schuster's homepage
Quantum mechanical effects form the basis of nearly all modern electronics and light generation. The discreteness of energy transitions underlies the remarkable stability of lasers and atomic clocks which can be precise to an astonishing part in 1e-17. It is also used as the basis of nearly every standard of measurement including voltage, resistance, current, temperature, and soon mass. It also provides the non-linearity exploited by transistors. Interference is employed by most exquisite modern sensors including the SQuID, atomic magnetometers, and gravity gradiometers.
Though these devices rely on quantum mechanics they operate on classical signals and information. Fully quantum mechanical systems could in principle exploit entanglement to solve certain problems exponentially faster and enhance metrology.
My group studies fully quantum systems experimentally, employing a technique known as circuit quantum electrodynamics. In this method microwave photons are manipulated by superconducting circuits which maintain quantum coherence. These circuits are readily manipulated and have the potential to interact with many quantum systems. In particular, I plan to use them as a "quantum bus" to explore and connect other quantum systems together.
Initial research projects include: Quantum coherent superconducting circuits, Electrons floating on superfluid helium, and Solid-state electron spins.
- D. I. Schuster, A. Fragner, M. I. Dykman, S. A. Lyon, R. J. Schoelkopf. Proposal for manipulating and detecting spin and orbital states of trapped electrons on helium using cavity quantum electrodynamics. Phys. Rev. Lett. 105, 040503 (2010)
- D. I. Schuster, A. P. Sears, E. Ginossar, L. DiCarlo, L. Frunzio, J. J. L. Morton, H. Wu, G. A. D. Briggs, R. J. Schoelkopf Phys. Rev. Lett. 105, 140501 (2010)
- A. A. Houck, D. I. Schuster, J. M. Gambetta, J. A. Schreier, B. R. Johnson, J. M. Chow, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin and R. J. Schoelkopf. Generating single microwave photons in a circuit. Nature 449, 328-331 (2007)
- D. I. Schuster, A. A. Houck, J. A. Schreier, A. Wallraff, J. M. Gambetta, A. Blais, L. Frunzio, J. Majer, B. Johnson, M. H. Devoret, S. M. Girvin and R. J. Schoelkopf. Resolving photon number states in a superconducting circuit. Nature Vol 445 515 (2007)
- A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin and R. J. Schoelkopf. Circuit quantum electrodynamics: Coherent coupling of a single photon to a Cooper pair box. Nature 431 162 (2004)