Dynamical decoupling protocols with nuclear spin state selectivity

The ability to initialise nuclear spins, which are typically in a mixed state even at low temperature, is a key requirement of many protocols used in quantum computing and simulations as well as in magnetic resonance spectroscopy and imaging. Yet, it remains a challenging task that typically involves complex and inefficient protocols, limiting the fidelity of ensuing operations or the measurement sensitivity. We introduce here a class of dynamical nuclear spin state selective (DNSS) protocols which, when applied to a polarised electron spin such as the nitrogen-vacancy (NV) centre in diamond, permit the addressing of selected nuclear states of the mixture. It works by splitting the underlying eigenstates into two distinct symmetries dependent on the nuclear spin state, and independent of the electron-nuclear coupling strength. As a particular example, we show that DNSS is achievable by simply introducing a detuning in the common Carr-Purcell-Meiboom-Gill (CPMG) protocol, where the state selection is then controlled by the inter-pulse spacing. This approach offers advantages in ultra-high fidelity initialisation of nuclear registers, ensemble polarisation and single-gate manipulation of nuclei.