Self-organization in two and three dimensions and new excitation geometries

Natalia Masalaeva, (previously Arthur Jungkind), UINN (WP2) Universität Innsbruck

The project addresses theoretically the quantum dynamics of fluctuations and the non-destructive measurement of phase transitions in different pumping schemes. A range of analytical and numerical methods based on the standard master equation, with can be analytically mapped to Boltzmann equation and studied in a linearized form, is used. Numerical simulations will be based on the open source C++QED object oriented framework developed in Innsbruck.

Objectives: 1. Theoretical modelling of self-ordering using polarization gradient pump geometries. 2. Self-ordering threshold and ordered state classification for transverse and longitudinal lin-perp lin pump. 3. Study of cavity field fluctuation spectra for nondestructive
observation of phase transitions in intra-cavity optical lattices. 4. Modelling cavity mediated long range interactions in externally prescribed incommensurate optical lattices. 5. Self trapping and self ordering of particles in confined 1D geometries as optical nanofibres based on dipole-dipole interaction
Expected Results: 1. Vlasov description of coupled atom field dynamics to study self-ordering thresholds. 2. Phase characterization and diagram for an ultracold gas in optical resonators with polarization gradient pump fields. 3. Fluctuation spectra and soft mode structure around threshold for real time analysis of superfluid to Mott insulator transition. 4. Particle pairing and entanglement and density field correlations. 5. Stability properties of dipole-dipole induced crystalline structures in 1D traps and its connection to multiple scattering
Planned secondmens: 1. ETHZ, 2. USAAR, 3. USTRAT 4. UMIL, . 5. Barracuda