A Straight Forward Method to Read the Nuclear Qudit of $4f$ Single-Molecule Magnets : $^{163}$DyPc$_2$

Nuclear spins in $4f$ single-molecule magnets (SMMs) are promising qubits or qudits candidates for quantum information processing due to their relative isolation and reduced susceptibility to environmental disturbances, while hyperfine coupling with the $4f$ moments enables readout and control. So far, the nuclear spin states of individual TbPc$_2$ SMMs have been detected in transport measurements via the spin-cascade effect, in which transitions of the Tb$^{3+}$ magnetic moment coupled to the unpaired ligand electron manifest as conductance jumps in spin-polarized transport. The ligand electron also gives rise to a Kondo effect through its interaction with the metallic contacts. By sweeping a magnetic field along the easy axis of the Tb$^{3+}$ moment, the system is tuned to avoided crossings of the hyperfine levels, such that the magnetic field at which the conductance jumps occur indicates the nuclear spin state. Here, we present a method to read the nuclear spin of $^{163}$DyPc$_2$ ($I=5/2$) using millikelvin spin-polarized scanning tunneling microscopy without the need for magnetic-field sweeps. Instead, hyperfine interactions modify the statistics of the telegraph noise generated by reversals of the Dy$^{3+}$ moment, thereby revealing the nuclear spin state. We observe nuclear spin relaxation times $T_1$ in excess of minutes at \SI{35}{mK}. Furthermore, we drive nuclear spin transitions using a radio-frequency field and detect the resulting nuclear magnetic resonance directly in the tunneling current, as the conductance near the split Kondo peaks depends on the nuclear spin state.