Qudit, a quantum system that can exist in a superposition of several states, offers additional degree of functionality for quantum technologies as compared to a qubit that comprises two quantum states only. Here, we demonstrate the optical initialization, read-out, and radio-frequency manipulation of 4-level qudits associated with spin-3/2 Si vacancies in silicon carbide.

Due to spin-dependent photoluminescence (PL) cycle, optical pumping gives rise to a difference in the occupancies of the sublevels with spin projections ±1/2 and ±3/2, which is termed a quadrupole spin polarization. Such polarization can be controlled by external magnetic fields and probed as the variation of the PL intensity.  A static magnetic field lifts the spin degeneracy, which allows one to individually address spin transitions using AC field with corresponding radio frequencies. Radio-frequency pump-probe technique was proposed to select a homogeneous ensemble of qudits and coherently manipulate them [1]. The coupling between spin sublevels occurs also in certain static magnetic fields when the sublevel energies come close. The decrease of the quadrupole polarization at the level anticrossings leads to an abrupt change of the PL intensity, which can be used for detection of small variations of magnetic field or temperature [2]. The use on spin-mechanical resonators was proposed to further increase the sensitivity [3].

[1] V.A. Soltamov, C. Kasper, A.V. Poshakinskiy et al, Nat. Commun. 10, 1678 (2019).

[2] D. Simin, V.A. Soltamov, A.V. Poshakinskiy et al, Phys. Rev. X 6, 031014 (2016).

[3] A.V. Poshakinskiy and G.V. Astakhov, Phys. Rev. B 100, 094104 (2019).