Research Overview

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 zero temperature, 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.

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 ten years. Besides their beauty in terms of fundamental physics, they have applications in precision measurement, interferometry, and atom lasers (see below). 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.

Ultrafast Optics is the study of laser systems that use femtosecond pulses (that's 0.000000000000001 seconds). This area of physics has immediate applications in micro- and nano-machining and biological imaging. For instance, cells can be observed without destroying them in the process, allowing one to make real-time videos of their behavior. Fundamental physics issues include relativistic interactions between light and matter, ion acceleration, and nonlinear optics. Ultrafast optics have also been used to observe such formerly elusive phenomena as the real-time dynamics of the solid to liquid transition. For a full description of experimental work in ultrafast optics at the Colorado School of Mines, see the web pages of Prof. Chip Durfee and Prof. Jeff Squier.

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 magnetics group of Prof. Carl Patton at Colorado State University has recently discovered fractals in magnetic feedback rings. Remarkably, a simple theory based on the nonlinear Schrodinger equation explains the results. This 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 (see below).

Atom Lasers are "lasers" made of matter-waves rather than light. This is one fundamental application of Bose-Einstein condensates. Shown at the left is one of the first experiments, at Yale University in 1998, in which a BEC is dropped down through a laser standing wave. This light crystal causes an interference pattern in the matter wave as it tunnels from well to well, leading to the observed series of coherent pulses. Unlike a conventional laser, an atom laser does not propagate at the speed of light, but accelerates with gravity like any other material object. Also, unlike photons, which do not interact, a matter-wave is a much more complicated, self-interacting object. One proposal of mine has been to make a pulsed atom laser from atoms with attractive interactions. This leads to a series of self-cooling mini-BEC's which can be fed onto waveguides written on a microchip. One can utilize these pulses to carry information in atom circuits.

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.

Matter Wave Solitons are localized waves which do not disperse. They have a number of beautiful mathematical properties. Solitons are to nonlinear equations what plane or sinusoidal waves are to linear ones. In the image at the left, from an experiment at Rice University, 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 supefluidity 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.

Fermionic Condensates are a radical new development in the field of ultracold atoms and molecules. Recall that all particles in the Universe are either fermions or bosons. Bosons prefer to be in the same state; fermions are excluded from doing so. The essential idea of a fermionic condensate is that fermions can pair to make bosons. When the pairing is very weak, so that many pairs pass through any unit volume, one has a Bardeen-Cooper-Schrieffer (BCS) state (Nobel prize, 1957), i.e., a superconductor. As the pairing becomes quite strong, so that in any unit volume one finds at most one tightly bound pair, one has effective bosons, and the system can condense to make a BEC. The process of tuning the interactions between the fermions from weak to strong is called the BCS-BEC crossover, and is a twenty year standing problem in quantum many body theory. Shown at the left is a condensate made of fermionic atoms, in this case Potassium 40, at JILA. This is a very exciting area for both experimentalists, who are now able to make very clean and precise measurements of the basic quantum many body physics of fermions and bosons, and theorists, who are are now completely revising their understanding.