Strongly correlated states in quantum optical systems

The goal of this project is to develop a theory of novel phenomena, which join two broad and intensively developing fields of modern physics: quantum optics and ultracold quantum gases. A unified theoretical approach will consider both light and matter at an ultimate quantum level, the level that only very recently became accessible experimentally. Moreover, the theoretical models will be also applied to solid-state systems used in quantum nanophotonics (polaritons in microcavities and fibers). On the one hand, classical optics, treating light as classical electromagnetic waves, has become one of the most developed and fruitful fields of physics. Quantum optics, which considers the light as quantum particles, photons, thus going beyond the mean-field (classical) description of the electromagnetic waves, is also currently a well- developed field. On the other hand, cooling and manipulating atoms by laser fields became a standard procedure, which led to the foundation of a new field of atom physics: atom optics. It was shown that the matter waves of atoms can be treated similarly to light waves in classical optics and can be manipulated using the forces and potentials of laser light beams. The quantum properties of matter waves beyond the mean-field description became accessible after 1995, when the first Bose-Einstein condensate (BEC) and many other fascinating quantum states of bosonic and fermionic atoms were obtained. However, up to now, the absolute majority of even very involved setups and theoretical models of quantum atom optics treats light as an essentially classical auxiliary tool to prepare and probe fascinating atomic states. The general goal of this project is to close the gap between quantum optics and quantum atom optics by merging them. The project will address phenomena, where the quantum natures of both light and atomic motion are equally important. Thus, quantum optics with quantum gases will be considered as an ultimate quantum limit of light- matter interaction. Since 2005, there are only three experiments in the world, where the setups of quantum optics and ultracold gases were joined. The development of a general theory is timely for this emerging direction of quantum physics. The project will provide cycling of ideas between different disciplines. During the last decade, the field of quantum gases was influenced by condensed matter models. However, the standard models do not consider the quantization of light, i.e., trapping potentials. So, the novel theoretical models and approaches have to be developed within this project. The main object of study will be the gas of ultracold atoms (both bosonic and fermionic) trapped in a quantum periodic potential provided by the modes of a high-Q cavity. The modification of known many-body phases of trapped atoms as well as the appearance of novel phases essentially due to the quantum and dynamical nature of the trapping potentials will be demonstrated. The theory of quantum measurements and control of strongly correlated systems by optical methods will be presented. The Condensed Matter Theory group in Harvard is one of the world leaders in applying its deep background in condensed matter to the systems of ultracold atoms. Using their know-how, I will be able to apply the most advanced tools of quantum many-body physics available in the world to the systems, which we consider in Austria. The development of a novel direction, which theoretically we have initiated in Austria and establishing the international network including theorists and experimentalists will enable the Austrian science to keep its leading position in that field and to be the main focus of attraction for further research projects with international funding. Quantum optics with quantum gases will enable the unprecedented control of light and matter. It will find applications in the following areas. (I) Novel non-destructive detectors of atomic states using light scattering. (II) Quantum information processing: novel protocols will be developed using the multipartite entangled states naturally appearing at this level of interaction. (III) Quantum interferometry and metrology: the entangled states of massive particles is a resource to approach the ultimate Heisenberg limit, which can be used in the gravitational wave detectors and novel quantum nanolithography. (IV) The general approaches can be applied to other fields: molecular physics, semiconductor and superconductor systems. Applications of nanophotonic systems are more industry-oriented: quantum-noise-limited devices for classical information processing.