Coherence-preserving cooling of nuclear spin qubits in a weak magnetic field

Nuclear spin memories of divalent neutral atoms can allow spin-preserving resolved-sideband cooling in a strong magnetic field [Phys. Rev. Lett. 99, 123001 (2007)]. We present a theory for cooling $^{87}$Sr nuclear-spin qubits in a weak magnetic field. The theory depends on laser excitation of $5s5p~^1P_1$ to a nearby state which results in $m_J$-dependent AC Stark shifts large compared to the hyperfine interaction. This effectively suppresses the nuclear-spin mixing due to the hyperfine interaction. Sideband cooling via the clock state quenched by the AC Stark-shifted $^1P_1$ state leads to nuclear-spin-preserving spontaneous emission back to the ground state. More than being compatible with low magnetic fields, the theory is applicable when the nuclear spin qubits are defined by the two lowest Zeeman substates.