# Implementing an Optical Accordion Lattice for the Realization of a Quantized Otto Cycle

### Abstract

This thesis presents design and characterization of a versatile optical standingwave trap for lithium atoms. Using this trap, an implementation of a quantized Otto cycle with the sodium-lithium mixture experiment that cools down a cloud of sodium atoms to quantum degeneracy while conserving the number of atoms may be possible. Three key characteristics which are crucial to the quantum Otto cycle are described: First, spatial movement of the lithium cloud is implemented by adjusting the relative phase of the two interfering beams up to $\Delta \theta = 3\pi$. Second, the energy level spacing in the trap are adjustable by controlling the laser intensity. Third, the spatial overlap between clouds of sodium and lithium atoms can be optimized by an accordion setup with two electric tunable lenses which allows to change the periodicity of the standing-wave dynamically by a factor of two. Furthermore, the stability of the setup is characterized. An estimate on the trap storage time based on heating rates by spontaneous emission, intensity and trap center fluctuations is given. In the current setup, the storage time is limited by detuning and power of the laser. With a 5nm blue-detuned setup the estimated storage time is up to 4s, whereas intensity and trap center fluctuations would allow for a estimated lifetime of bigger than 80s. The longterm trap center stability was characterized and substantially improved by temperature stabilization of the electro-optical modulator crystal to approximately $0.3/\pi = 12 h$. In the near future, this setup will be installed on the main experiment, allowing the sodium-lithium experiment to become a test-bed for quantum thermodynamics.

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