Research Overview

The Carr Theoretical Physics Group works primarily in quantum many body theory, nonlinear dynamics, and artificial solid state materials, although our interests extend into many fields of physics and both science and mathematics as a whole. For a brief description of some specific areas we are working in at the moment, please see the summaries below. For a list of people and projects, see the group page.

Quantum Phase Transitions Quantum Phase Transitions are phase transitions which are not caused by a temperature change, as in a solid to liquid transition, but by an external parameter in the system. They are most clearly observed at very low temperatures, where quantum mechanical effects are often strongest. Shown at the left is an interference experiment at the University of Munich in Germany on ultracold bosonic atoms trapped in laser standing waves. The standing waves make an egg crate, and the atoms sit in the wells of the crate. In each panel, the peaks of the crate have been made successively higher. Then the lasers have been turned off and the whole system has been allowed to expand, resulting in a matter-wave interference pattern. The interference peaks gradually wash out from the top left to lower right panels. This is a realization of the phase-number uncertainty relationship. When the peaks of the egg crate are low, the atoms tunnel from well to well, the phase is maximally certain, and one has a superfluid. When the peaks are high, the atoms are prevented from tunneling, the number of atoms in each well is maximally certain, one has what is called a Mott insulator, and the relative phase between wells in unknown, which destroys the interference pattern. For an introduction to quantum phase transitions, see Subir Sachdev's book.

Ultracold Molecules in Optical Lattices Ultracold Molecules have recently been brought to the edge of quantum degeneracy at JILA at the University of Colorado and at the University of Innsbruck. Ultracold molecules in optical lattices represent a designer solid state system which can be shaped to any crystal structure and can be used to explore condensed matter physics in a well-controlled system. These molecules can have temperatures smaller than one millionth of one Kelvin. Molecules have internal rotational, vibrational, and other degrees of freedom which give them an unprecedented level of versatility for applications in quantum computing, quantum information processing, and quantum simulations. Moreover, cold and ultracold molecules bring a new idea of chemistry into play in which, for example, chemical reactions can be Bose-enhanced. The picture to the left shows heteronuclear diatomic molecules with an electric field to create a dipole moment. This leads to long range interactions, an exciting new possibility to realize a strongly interacting ultracold system. The pale purple arrows represent laser beams used to create the oscillatory standing wave, or optical lattice potential depicted.

Graphene Nanoengineering Graphene nanoengineering seeks to manipulate a newly created two-dimensional solid state material, graphene, to obtain novel electronic, mechanical, magnetic, thermal, and chemical properties. We are used to processor speed in computers doubling every two years (Moore's law). However, we are out of room in silicon to write smaller features. In order to increase computing speed we need new materials and new ideas. Graphene is an excellent candidate because of its high mobility at room temperature, among other reasons. There is a lot of excitement about graphene on many fronts, from fundamental theory to applications. The picture at the left shows a graphene metacrystal, which is made by laying down a pattern of defects on a 2D carbon surface. Another such pattern leads to a new allotrope of carbon in two dimensions, which we call dimerite. Examples of different allotropes of carbon in three dimensions are graphite (pencil lead) and diamond. Graphene is a 2D allotrope of carbon which takes the form of a honeycomb lattice, just like a beehive. Dimerite is based on converting 4 hexagons into a pair of pentagons and a pair of septagons by introducing an Inverse Stone-Thrower-Wales defect in a regular pattern. A review on the electronic properties of graphene can be found here.

Spin Wave Fractals Spin wave fractals refer to fractal patterns in excitations of the local magnetic moment of thin ferromagnetic films. Fractals are self-similar structures which repeat at progressively finer scales. For instance, in the fern at the left, the pattern of each frond is repeated in each of its sections. Each section has a subsection which in turn repeats the original pattern, and so forth. Fractals occur frequently in Nature. The Magnetic Materials and Applied Magnetics Laboratory at Colorado State University has recently discovered fractals and chaos in magnetic feedback rings. We believe a simple theory based on a modified nonlinear Schrodinger equation can explain the results. The nonlinear Schrodinger equation has very special mathematical properties, including an infinite number of conservation laws. Spin waves in ferromagnetic feedback rings have been used to generate a whole host of intriguing nonlinear phenomena, including bright and dark soliton trains.

Bose-Einstein Condensates Bose Einstein Condensates (BEC's) were predicted in 1924 and realized in 1995 at JILA at the University of Colorado and at the Massachusetts Institute of Technology, for which the investigators jointly received the 2001 Nobel prize, as well as at Rice University, where the observation of a BEC remained controversial until 1997. The picture at the left shows the original JILA experiment. As the temperature decreases, a macroscopic number of Rubidium atoms, in this case about a million, "Bose condense" into the same state. This means they all have the same energy and momentum. Since they are held in a harmonic trap, entering the same momentum state means they also condense in space -- thus the formation of the peak in the rightmost image. All particles in the Universe are divided into two categories: bosons and fermions. Bosons prefer to be in the same state -- this is the essential principle behind a laser, where all the photons, which are also bosons, "lase" in a beam of a single color. BEC's are extremely versatile and have generated an extraordinary amount of research activity all around the world over the last fifteen years. Besides their beauty in terms of fundamental physics, they have applications in precision measurement, interferometry, and atom lasers. For a great review from the quantum many body perspective by a Nobel prize winning theorist (2003), see Tony Leggett's article in Review of Modern Physics.

Macroscopic Quantum Tunnelling Macroscopic Quantum Tunneling is the study of what quantum mechanical tunneling means for a many-body wavefunction. The essential idea of tunneling is that the probability distribution of a particle can extend through a potential barrier: put an atom in a closed container, and everyone once in a while it pops out. This is in severe contrast to something like a marble in a jar. One of the fundamental questions in quantum mechanics is how the microscopic behavior of things like atoms becomes the macroscopic behavior of things like marbles. The picture at the left shows a potential barrier in blue. The red curve shows a many body wavefunction, in this case the mean field of a Bose-Einstein condensate. The green line sketches the path atoms take as they tunnel through the barrier. This is a bit like testing gravitational attraction at different length scales: does gravity really work the same on the scale of astronomical units as it does on the scale of micrometers? Here we are asking if quantum mechanics works in the same way for a million atoms in synch as it does for a single one in isolation.

Emergent Phenomena Emergent phenomena refers to complex properties of a system whose constituents are simple. For example, consciousness could be considered an emergent phenomenon in a collection of neurons; the great red spot of Jupiter is an emergent property of its atmosphere. Shown at the left are matter wave solitons, a specific example of an emergent property in a Bose-Einstein condensate. Solitons are localized waves which do not disperse. They have a number of beautiful mathematical properties, and are to nonlinear equations what plane or sinusoidal waves are to linear ones. The image shows an experiment at Rice University in which a train of solitons is created from a Bose-Einstein condensate condensate with attractive interactions. Each of the peaks acts like an independent particle which runs up and down the blue strip. The attractive interactions exactly and robustly balance the dispersion, or quantum pressure, which would otherwise cause the solitons to spread out like a wavepacket. Solitons appear in many places in Nature, including fiber optics, plasmas, DNA, and as tsunamis in the ocean. They have been observed in many contexts in Bose-Einstein condensates. Solitons are fundamental to the definition of superfluidity in one dimension in the same way that their higher dimensional cousins, vortices, are key to defining superfluidity in two and three dimensions. A superfluid is a special quantum mechanical state which flows with zero friction. Solitons are sufficiently important to be directly in the title of a major scientific journal, Chaos, Solitons, and Fractals. Solitons, vortices, and other emergent phenomena described by nonlinear wave equations are an important subject of study in our group.

Macroscopic Superposition States Macroscopic superposition states bring quantum mechanics up from the single particle atomic or subatomic level to the macroscopic world we live in. One of the more radical predictions of quantum mechanics is that a particle can be both here and there simultaneously. We have very good evidence that this is true, in the form of interference patterns and other measurable predictions. But is this radical idea true at macrosopic scales? The picture at the left shows a cat in a box. The apparatus next to the cat represents a radioactive device which hinges on the decay of a single unstable nucleus. If the nucleus decays, a vial of poison is broken and the cat dies (no actual cats were harmed in this thought experiment). The decay process is quantum mechanical, so that the nucleus is in a superposition of two states, decayed and "un-decayed", so to speak. Before the observor opens the box, is the cat alive or dead? Quantum mechanics says that the cat is both alive and dead. Can we actually set up such an experiment in physics, to realize these completely counter-intuitive results? Creating macroscopic superposition states is an extension of quantum information processing, for which there are many candidates. Particularly promising possibilities are Bose-Einstein condensates in a double well and superconducting current loops.