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Magnetic resonance imaging (MRI) is a powerful technique for investigatingthe microscopic properties and dynamics of physical systems. In this work wedemonstrate state-sensitive MRI of ultracold atoms in an optical lattice.Single-shot spatial resolution is 120 nm, well below the lattice spacing, andnumber sensitivity is +/-2.4 for 150 atoms on a single site, well belowPoissonian atom-number fluctuations. We achieve this by combininghigh-spatial-resolution control over the atomic spin using an atom chip,together with nearly quantum-limited spin measurement, obtained by dispersivelycoupling the atoms to light in a high-finesse optical cavity. The MRI isminimally disruptive of the atoms' internal state, preserving the magnetisationof the gas for subsequent experiments. Using this technique, we observe thenonequilibrium transport dynamics of the atoms among individual lattice sites.We see the atom cloud initially expand ballistically, followed by the onset ofinteraction-inhibited transport.

Cavity-aided magnetic-resonance microscopy of atoms in optical lattices