Abstract
Nuclear-spin memories of divalent neutral atoms can allow spin-preserving resolved-sideband cooling in a strong magnetic field [I. Reichenbach and I. H. Deutsch, Phys. Rev. Lett. 99, 123001 (2007)]. We present a theory for cooling $^{87}\mathrm{Sr}$ nuclear-spin qubits in a weak magnetic field. The theory depends on laser excitation of $5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ 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 $^{3}P_{1}$ 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.
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