# Exploring the nonequilibrium dynamics of superconductors

Our group has developed a new optical technique for determining precisely the diffusion coefficient and scattering rates of “quasiparticles” in high-Tc superconductors. Our initial results, from single crystals of YBa2Cu3O6.5, reveal that high-energy quasiparticles in such materials propagate remarkably far, several hundreds of nanometers, before either thermalizing with other excitations, such as phonons, or pairing with each other to form “Cooper pairs.”

Superconductivity occurs when two electrons come together to form a so-called “Cooper pair.” The pairs coalesce into a resistanceless charged fluid, which leads to the macroscopic observation of zero electrical resistance. This state of zero resistance can persist even when some of the pairs separate (the unpaired electrons that form in this process are called quasiparticles in the language of condensed matter physics). Viewed from this perspective, quasiparticles have a shadowy existence, as their contribution to resistance is completely “short-circuited” by the Cooper pair condensate. Nevertheless, in the wider world of superconductivity and its applications, quasiparticles play a crucial role. In x-ray detectors, quasiparticles carry the charge that is detected when a photon impinges on a superconductor. In another rapidly growing area, superconducting Josephson junctions are under investigation as a possible solid state quantum computer. In such devices quasiparticles are a major source of undesired “decoherence.” Thus, the dynamics of quasiparticles, specifically their rates of diffusion, scattering, trapping, and recombination, are critical for the both the applications and fundamental understanding of superconductivity.

Because quasiparticles do not contribute to the resistance of a superconductor, prior investigations of their dynamics have been indirect. In our new technique, two ultrashort laser pulses incident on the sample at a carefully controlled angle create a standing wave of intensity. This form of excitation generates a periodic variation in the density of quasiparticles at the superconductor’s surface. Because the index of refraction at the surface depends on the local quasiparticle density, the surface of the superconductor becomes a diffraction grating. The amplitude of the grating, and hence the crest to trough variation in quasiparticle density, can be measured by a probe beam arriving at the sample after a variable delay time on the order of picoseconds (see figure). Following its creation, the grating decays due to the combined effects of recombination (in which quasiparticles reform superconducting Cooper pairs) and diffusion. By adjusting the angle between the two pulses that create the quasiparticles, gratings with spatial periods between 2 and 5 microns were made. Analysis of the decay rate of the grating as a function of the spatial period allowed the effects of recombination and diffusion to be separated. Our research team found diffusion coefficients of 20, or 24 cm2/s (depending on orientation with respect to the crystal axes) and a recombination lifetime that reached 100 picoseconds at low quasiparticle density. Together these parameters imply a quasiparticle diffusion length of approximately 400 nm, which is remarkably large for high-energy quasiparticles.

The results represent the first direct study of the dynamics of quasiparticles in a high Tc superconductor. The surprising discovery that they can propagate over relatively large distances provides a challenge to theorists to explain, as well as opportunities for applications that involve detection of nonequilibrium quasiparticles.