Delayed entanglement echo for individual control of a large number of nuclear spins

Methods for achieving quantum control and detection of individual nuclear spins by single electrons of solid-state defects play a central role for quantum information processing and nano-scale nuclear magnetic resonance (NMR). However, with standard techniques, no more than 8 nuclear spins have been resolved. Here we develop a method that improves significantly the ability to spectrally resolve nuclear spins and demonstrate its capabilities with detailed numerical simulations by using a nitrogen-vacancy (NV) centre as model system. Based on delayed entanglement control, a technique combining microwave and radio-frequency (rf) fields, nuclei with resonances in a broad frequency band can be unambiguously and individually addressed by the sensor electron. Additionally the spectral resolution can extend beyond the electron spin relaxation time by using a long-lived qubit memory. Our method greatly increases the number of useful register qubits accessible to a defect centre and improves the signals of nano-scale NMR.