# Observatoire de Paris - Systèms de Réferénce Temps Espace

Our aim is to realize a guided interferometer with atoms confined in a vertical optical lattice. In this novel interferometer scheme, ^{87}Rb atoms will be prepared in a quantum superposition of their two hyperfine ground states (F=1 and F=2, both in the magnetically insensitive m_{f}=0 sub-state, where F denotes the combined nuclear and electronic angular momentum of the atom). The local gravitational field is measured by allowing these quantum states to evolve via separate trajectories, thus accumulating a quantum phase difference ΔΦ=mgΔzT/h related to their different gravitational potential energy (cold-atom interferometer). Here m is the mass of the atom, g is the gravitation, Δz is the height difference in the gravitational field, h is Planck’s constant and T is the duration of the interferometer. For ^{87}Rb, a height difference of 100μm and readout expected to be with mrad accuracy would lead to a sensitivity of 10^{-9} g/s. In contrast to standard atom interferometer approaches, the two states will not be split in momentum space but in their location in an optical lattice, challenging the assumption that precision measurements necessarily require a freely falling regime. This guided atom interferometric gravity sensor would set a new standard in atom interferometry and remove current precision boundaries due to finite interrogation times (set by the space needed to accommodate the trajectory of freely falling atoms). By analyzing and measuring the parameters of this guided system, in particular with respect to the influence of the lattice potential, this project will lay the scientific foundations for future interferometer sensors as well as for optical lattice quantum information systems, which also rely on the ability to manipulate quantum superposition states with low decoherence.