  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.
