  Self-organization, and transitions from reversible to irreversible behaviour,
of interacting particle assemblies driven by externally imposed stresses or
deformation is of interest in comprehending diverse phenomena in soft matter.
They have been investigated in a wide range of systems, such as colloidal
suspensions, glasses, and granular matter. In different density and driving
regimes, such behaviour is related to yielding of amorphous solids, jamming,
and memory formation, \emph{etc.} How these phenomena are related to each other
has not, however, been much studied. In order to obtain a unified view of the
different regimes of behaviour, and transitions between them, we investigate
computationally the response of soft sphere assemblies to athermal cyclic shear
deformation over a wide range of densities and amplitudes of shear deformation.
Cyclic shear deformation induces transitions from reversible to irreversible
behaviour in both unjammed and jammed soft sphere packings. Well above
isotropic jamming density ($\bf{\phi_J}$), this transition corresponds to
yielding. In the vicinity of the jamming point, up to a higher density limit we
designate ${\bf \phi_J^{cyc}}$, an unjammed phase emerges between a localised,
\emph{absorbing} phase, and a diffusive, {\emph irreversible} phase. The
emergence of the unjammed phase signals the shifting of the jamming point to
higher densities as a result of annealing, and opens a window where shear
jamming becomes possible for frictionless packings. Below $\bf{\phi_J}$, two
distinct localised states, termed point and loop reversibile, are observed. We
characterise in detail the different regimes and transitions between them, and
obtain a unified density-shear amplitude phase diagram.
