  Working with nuclear magnetic resonance (NMR) in quadrupolar spin systems, in
this paper we transfer the concept of atomic coherent state to the nuclear spin
context, where it is referred to as pseudo-nuclear spin coherent state
(pseudo-NSCS). Experimentally, we discuss the initialization of the
pseudo-NSCSs and also their quantum control, implemented by polar and azimuthal
rotations. Theoretically, we compute the geometric phases acquired by an
initial pseudo-NSCS on undergoing three distinct cyclic evolutions: $ i) $ the
free evolution of the NMR quadrupolar system and, by analogy with the evolution
of the NMR quadrupolar system, that of $ii)$ single-mode and $ iii)$ two-mode
Bose-Einstein Condensate like system. By means of these analogies, we derive,
through spin angular momentum operators, results equivalent to those presented
in the literature for orbital angular momentum operators. The pseudo-NSCS
description is a starting point to introduce the spin squeezed state and
quantum metrology into nuclear spin systems of liquid crystal or solid matter.
