Collaborative Research: Joint NSF-BSF Proposal: Nonlinear Dynamics with Gross-Pitaevskii Breathers

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The principle of energy conservation dictates that the total energy of any closed system does not change with time. For most highly complex interacting systems, energy is the only such conserved quantity, but there are exceptions to this rule. In rare situations, even quite complex systems may have additional invariant quantities whose existence constrains the possible physical configurations of the system. These extra invariants generally arise when the system possesses some degree of symmetry. The resulting constraints---the so-called conservation laws---are responsible, for example, for the clock-like regularity of the motion of Newton's cradle, for the existence of perfectly straight stable ocean-shore waves, and for the simplicity of the shape of the planetary orbits. The goal of this project is to learn to employ such non-standard conservation laws as a tool to stabilize atom interferometers; quantum mechanical devices used in ultra-sensitive detectors of gravitational and other fields. In addition, the project may shed light on the manner by which complex systems, once disturbed, return to equilibrium, and the time-scale required for that relaxation. This work involves exciting certain highly stable modes, so-called "atomic breathers", of an atom interferometer, and then studying the relaxation of these modes as they encounter a potential barrier. The high degree of sensitivity of the interferometer provides an opportunity for much more careful scrutiny of non-equilibrium processes than has been possible previously. There are three major components of the proposal: a study of the relaxation dynamics of the breathers, including effects of symmetry-breaking; the development of an experimental protocol for the creation of highly-stable breathers; and an assessment of the stability of the breathers against dissociation and decay. The group of four principal investigators possess combine unique skill sets ideally suited for these tasks: it includes experimental techniques for manipulating bosonic solitons (breathers made of bosonic atoms), theoretical quantum, mean-field, and classical nonequilibrium dynamics, Inverse Scattering Transform and nonlinear perturbation theory, and applications of the Bethe ansatz. The tight coupling of theory and experiment is a crucial aspect of this project and will be essential for its success.