Photon Superruid as a Complex Adaptative Medium Critical Phenomena and Spatial Solitons in Nonlinear Cavities 1. Names and Aaliates of Main Participants 2. Description of Proposed Research

We propose a comprehensive experimental and theoretical approach to a new state of light bearing strong analogies with the phenomena of superruidity and superconductivity. This is of interest in its own right but will also allow detailed studies of the dynamics of second order phase transitions, a subject which has recently attracted considerable interest, including mention in the '96 Nobel prize announcement (www.nobel.se/laureates/physics-1996-press.html). The collaboration between LANL and UCB, if funded, would aaord a perfect match of theoretical expertise with the novel experimental setting. Apart from fundamental implications for our understanding of superruidity, it holds great promise of a range of applications in laser industries. The experiment taking place at Prof. Chiao's group at U.C. Berkeley propagates light in a Fabry-Perot cavity lled with a gas of alkali atoms which constitutes a nonlinear optical medium, and provides a state-of-the-art new example of a complex adaptative medium. Under suitable experimentally adjustable circumstances the photons interact strongly with each other (via the atoms), giving rise to large-scale collective behavior manifested in the formation of spatial solitons and in the occurrence of bulk critical phenomena. FIG. 1. Phase of the complex order parameter , winding around a 1D path. The topological nature of these phase windings leads to soliton stability. The experimental setting is such that the sign and strength of the photon-photon interaction can be changed via the detuning of the frequency of an external laser across an atomic resonance. This permits the easy realization of a variety of experimental situations, unlike in traditional superruid and superconducting materials. In addition, the boundary conditions imposed by the cavity generate a small mass for the photons and can thereby enforce an experimentally adjustable dimensional reduction of the system from 3 to 2 or 1 spatial dimensions. The paraxial ray approximation appropriate for these cavities then further reduces the relativistic photon gas system to that of a dilute, weakly-interacting, nonrelativistic Bose gas (with an easily adjustable interaction strength) which, in the case of repulsive photon-photon interactions, we shall call a \photon uid." A careful treatment of Maxwell's equations in the nonlinear FP medium results in the description of the photon uid by a many body Schrr odinger equation or equivalently by a nonrelativistic quantum eld theory. In the high-nesse limit, the corresponding free energy F has the canonical Ginzburg-Landau (GL) form 1], F = Z d 2 x ? h 2 2m r 2 + …