Hyperfine level ($F=|I-J|,\dots ,I+J$)

An energy level resolved by coupling the nuclear spin $I$ to electronic total angular momentum $J$. For a rotationally invariant Hamiltonian, a fixed $F$ has $2F+1$ degenerate magnetic sublevels. Spectral component counts identify the number of upper hyperfine levels only when lower hyperfine structure, selection rules, unresolved overlaps and missing lines have been accounted for.

A qubit encoded in two resolved hyperfine levels of the same electronic ground state. Such states avoid optical excited-state decay and can support coherent radiofrequency or microwave control through a magnetic dipole transition. Technical magnetic noise and differential shifts can still dephase them; first-order field insensitivity requires additional choices of states and operating point.