Single Spin Resolved Quantum Metrology in Optical Lattices

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This project aims at the realization of single spin resolved detection of ultracold atoms in two dimensional optical lattices and its application to quantum metrology. At the heart of the detection technique will be a quantum spin pump, providing robust (topologically protected) spatial separation of the two involved spin states. This will enable full local qubit readout in two-dimensional atomic arrays, a fundamental requirement for quantum simulation and quantum information, which has not yet been demonstrated so far. Importantly, the technique will be generally applicable to two-dimensional ultracold lattice systems including alkaline-earth like atoms. The latter is important in the wider context of this project proposal, which is accompanying a Heisenberg professorship proposal at the University of Tübingen. One of the ongoing research efforts at the Center for Quantum Science in Tübingen - in close collaboration with Japanese research partners - is the realization of a compact and continuous alkaline-earth atom based optical lattice clock. On longer time scale, the techniques developed within the proposed project will allow us to realize quantum enhanced measurements in this optical clock.Single spin resolved readout and, hence, the detection of the parity of the magnetization, is required to make use of maximally entangled states for quantum metrology, which promise ultimate measurement precision at the Heisenberg limit. One-axis twisting dynamics, producing spin squeezing on short evolution times, indeed results in maximally entangled NOON states at longer times. This time is half-way to the revival time of the global magnetization, i.e. the time set by the inverse interaction strength. In between complicated non-gaussian states are produced that are in general difficult to characterize. Here local single spin resolved detection promises new insight as it allows one to characterize the system not only by global observable but also by local multi-point correlations.We propose to use long-range interactions between ten to hundred atoms in a two-dimensional optical lattice to implement one-axis twisting like quantum dynamics. The interaction is induced by near-resonant laser coupling to Rydberg states (aka Rydberg dressing). With such a setting, we recently demonstrated coherence times as long as 100 inverse interaction times, while the time scale for spin squeezing in this system is one tenth of the inverse interaction time. Thus, fully coherent evolution even to the time to produce NOON states seems within reach. We will additionally explore feasible schemes to realize a Loschmidt echo sequence, based on which much more general entangled states can be used for quantum metrology.