Dark-cat encoding in atomic levels - Part I

Neutral atoms become one of the most promising platforms for quantum information and simulation purposes. Finding hardware-efficient way to encode quantum information and performing error correction is still an important problem for this system. In our work, we show how decoherence-free qubits can be efficiently encoded in the large spin hyperfine ground state of lanthanide atoms. In particular, they are encoded in the dark states of a Raman-coupled hyperfine structure. This encoding resembles cat code structure in bosonic systems, which shares common features like autonomous stabilization and biased-noise structure, as bit-flip error is suppressed exponentially as the system size becomes larger. In the first part, we will go through the system setup, explain the analogy with bosonic cat, and uncover the mechanism behind autonomous stabilization as well as the biased noise structure.