Cavity enhanced detection of cold molecules

Abstract

Cold quantum gases are versatile tools not only to investigate quantum many-body physics and ultracold chemistry, but also for testing fundamental theories. Many degenerate quantum gases, however, consist of atoms and provide only short-range interactions between different particles limiting research opportunities. Hence, shortly after the production of the first atomic gases an interest arose in ensembles of cold polar molecules that exhibit adjustable long-range anisotropic dipole-dipole interactions to expand research fields further. Loading such a molecular cloud into an optical lattice provides an excellent experimental control regarding particle-particle interactions and to simulate condensed matter physics.

Experiments with cold quantum gases require imaging techniques to determine properties like the number of atoms and molecules or the position of single particles. For atomic ensembles, absorption or fluorescence techniques are often utilised since atoms usually provide closed cycling transitions allowing to scatter a large number of photons for the imaging signal. The internal level structure of molecules, though, is more complex compared to atoms due to additional rovibrational states and many molecules do not provide closed cycling transitions. For these molecules new imaging techniques need to be developed.

In the first part of the thesis a theoretical background of the imaging technique is provided, starting with a classical approach. The advantages of a classical theory are an intuitive understanding of the detection method and an applicability to spherical nanoparticles, which can then be utilised as test objects for the proposed imaging scheme. The resolution capability of the detection technique is discussed and the important role of small cavity waists for high resolutions is highlighted. In a next step, a full quantum mechanical approach is presented and compared to the classical theory. It is shown that both theories are equivalent except for vacuum fluctuations, a pure quantum physical effect important to determine quantum noise correctly.

After introducing theoretical backgrounds, cavity geometries suitable for the detection of molecules are discussed. Properties, directly important for the imaging process, e.\;g. waist, mode number and linewidth, and technical aspects like misalignment sensitivity are taken into account. A simultaneous optimisation of all these properties is not possible since they are partially contradicting each other. However, a balance between these different aspects is found. Two cavity geometrics, feasible for imaging NaK molecules, a hemispherical resonator and a concentric cavity are proposed.

Finally, an experimental setup to demonstrate the general feasibility of the imaging technique is developed. Titania and silver are identified as materials for nanoparticles best suited to imitate NaK molecules. Imaging resonators are designed and an alignment procedure for these cavities is presented.