Extended Data Fig. 2: Experimental sequences.
From: Quantum thermalization and Floquet engineering in a spin ensemble with a clock transition
a, The simplified energy level diagram for a 171Yb3+ ion in a YVO4 crystal. Both the ground and optically excited states exhibit fine structures labeled as {\(\left\vert 0\right\rangle ,\left\vert 1\right\rangle ,\left\vert {\rm{Aux}}\right\rangle\)} and {\({\left\vert 0\right\rangle }_{e},{\left\vert 1\right\rangle }_{e},{\left\vert {\rm{Aux}}\right\rangle }_{e}\)}, respectively. Microwave spin transitions occur at frequencies fg ≈ 0.675 GHz and fe ≈ 3.37 GHz for the ground and excited states, respectively. The optical transitions A and F occur near a wavelength of 984 nm, with a separation of 6.118 GHz. Note that transition A is coupled to the cavity mode used for fast spin state readout, while transition F is not coupled to the cavity mode and is driven for optical initialization. b, Experimental sequences include state initialization, spin dynamics control, and optical readout. c, Control of the average spin-spin interaction strength J within the qubit manifold {\(\left\vert 0\right\rangle ,\left\vert 1\right\rangle\)} (orange shaded area). Adjusting the driving amplitude on the F transition during initialization effectively controls the transfer of population from the auxiliary state \(\left\vert {\rm{Aux}}\right\rangle\) to the qubit manifold {\(\left\vert 0\right\rangle ,\left\vert 1\right\rangle\)} (blue arrows). Subsequently, a combination of optical pulses driving the A transition and microwave pulses driving the fg transition is applied to polarize the spin state to \(\left\vert 0\right\rangle\) (red arrows). A higher (smaller) population in the qubit manifold corresponds to a larger (smaller) average interaction strength J.
