Dark spin-cats as biased qubits

Abstract: We present a biased atomic qubit, universally implementable across all atomic platforms, encoded as a spin-cat' within ground state Zeeman levels. The key characteristic of our configuration is the coupling of the ground state spin manifold of size $F_g \gg 1$ to an excited Zeeman spin manifold of size $F_e = F_g - 1$ using light. This coupling results in eigenstates of the driven atom that include exactly two dark states in the ground state manifold, which are decoupled from light and immune to spontaneous emission from the excited states. These dark states constitute thespin-cat', leading to the designation dark spin-cat'. We demonstrate that under strong Rabi drive and for large $F_g$, thedark spin-cat' is autonomously stabilized against common noise sources and encodes a qubit with significantly biased noise. Specifically, the bit-flip error rate decreases exponentially with $F_g$ relative to the dephasing rate. We provide an analysis of dark spin-cats, their robustness to noise, and discuss bias-preserving single qubit and entangling gates, exemplified on a Rydberg tweezer platform.