Quantum many-body effects in optical cavity QED

Light forces offer ample possibilities to manipulate suitably polarizable particles in laser fields. In contrast to free space the back action of the particles on the field within an optical resonator plays a central part in the atom field dynamics and opens a wealth of new applications from cavity cooling to the implementation of quantum gates. Many limitations of laser cooling are lifted due to suppressed spontaneous emission and new physical phenomena appear as all particles in the cavity are collectively coupled to the same field. Particles effectively interact via the cavity field essentially over a long distance, which can be tailored by the choice of pump and resonator geometry. Important theoretical suggestions as laser cooling without spontaneous emission and steady state lasing of a single atom trapped in a high-Q cavity field just recently have been demonstrated experimentally. As a striking example for cavity-mediated motional coupling, numerical simulations exhibit the self-organization of laser driven atoms in cavities into regular patterns, which maximize the cooperative directional scattering of light into the cavity field. This formation of a regular pattern via self-organization starts only above a certain threshold of the pump strength and the particle number and bears many signatures of a phase transition. For suitably chosen geometry the pattern is stabilized as inelastic scattering extracts kinetic energy from the particle motion. Recent experiments have produced strong evidence for the existence and efficiency of this new mechanism, which could be the basis of a much more efficient and wider applicable laser cooling technology in particular for molecules. Selforganization and collective atomic motion have also been observed in high $Q$ optical ring cavities. The central goal of this theoretical research project is to investigate quantum statistical aspects of cavity mediated atomic interactions in more detail in the regime of very low temperatures close T=0.. In particular the effect of atomic selforganization opens intriguing questions here. What is required to start the selforganisation process at T=0? When does it yield a stable final equilibrium? How does the process scale with atom number, cavity volume and pump strength? What are the ultimate limits on forces and temperatures? Can it be interpreted in the spirit of a quantum phase transition? Finding answers to these questions requires developing new theoretical approaches involving approximate analytic models and refined numerical simulations for the multi-particle quantum dynamics. Experimentalists now started to investigate the quantum motion of ultracold atoms (BEC) trapped in a cavity field. Here the optical potential itself has quantum properties and the self-organisation would dynamically form macroscopic superposition of the different possible final states via a stimulated coherent process. In principle the ground state of the system then can be a superposition of two macroscopically distinct atomic distributions (phases). Extending cavity mediated interaction to ultracold atoms in optical lattices will add new long range interactions between atoms at different sites, which could lead to important changes for the study of phase transitions in these systems. Furthermore the process of self-organized, super radiant, cold molecule formation by cavity field induced photo-associations could provide for a source of externally and vibrational cold molecules.

Light forces offer ample possibilities to manipulate suitably polarizable particles in laser fields. In contrast to free space the back action of the particles on the field within an optical resonator plays a central part in the atom field dynamics and opens a wealth of new applications from cavity cooling to the implementation of quantum gates. Many limitations of laser cooling are lifted due to suppressed spontaneous emission and new physical phenomena appear as all particles in the cavity are collectively coupled to the same field. Particles effectively interact via the cavity field essentially over a long distance, which can be tailored by the choice of pump and resonator geometry. Important theoretical suggestions as laser cooling without spontaneous emission and steady state lasing of a single atom trapped in a high-Q cavity field just recently have been demonstrated experimentally. As a striking example for cavity-mediated motional coupling, numerical simulations exhibit the self-organization of laser driven atoms in cavities into regular patterns, which maximize the cooperative directional scattering of light into the cavity field. This formation of a regular pattern via self-organization starts only above a certain threshold of the pump strength and the particle number and bears many signatures of a phase transition. For suitably chosen geometry the pattern is stabilized as inelastic scattering extracts kinetic energy from the particle motion. Recent experiments have produced strong evidence for the existence and efficiency of this new mechanism, which could be the basis of a much more efficient and wider applicable laser cooling technology in particular for molecules. Selforganization and collective atomic motion have also been observed in high $Q$ optical ring cavities. The central goal of this theoretical research project is to investigate quantum statistical aspects of cavity mediated atomic interactions in more detail in the regime of very low temperatures close T=0. In particular the effect of atomic selforganization opens intriguing questions here. What is required to start the selforganisation process at T=0? When does it yield a stable final equilibrium? How does the process scale with atom number, cavity volume and pump strength? What are the ultimate limits on forces and temperatures? Can it be interpreted in the spirit of a quantum phase transition? Finding answers to these questions requires developing new theoretical approaches involving approximate analytic models and refined numerical simulations for the multi-particle quantum dynamics. Experimentalists now started to investigate the quantum motion of ultracold atoms (BEC) trapped in a cavity field. Here the optical potential itself has quantum properties and the self-organisation would dynamically form macroscopic superposition of the different possible final states via a stimulated coherent process. In principle the ground state of the system then can be a superposition of two macroscopically distinct atomic distributions (phases). Extending cavity mediated interaction to ultracold atoms in optical lattices will add new long range interactions between atoms at different sites, which could lead to important changes for the study of phase transitions in these systems. Furthermore the process of self-organized, super radiant, cold molecule formation by cavity field induced photo-associations could provide for a source of externally and vibrational cold molecules.