  Dry granular materials such as sand, gravel, pills, or agricultural grains,
can become rigid when compressed or sheared. At low density, one can distort
the shape of a container of granular material without encountering any
resistance. Under isotropic compression, the material will reach a certain {\it
jamming} density and then resist further compression. {\em Shear jamming}
occurs when resistance to shear emerges in a system at a density lower than the
jamming density, and the elastic properties of such states have important
implications for industrial and geophysical processes. We report on
experimental observations of changes in the mechanical properties of a
shear-jammed granular material subjected to small-amplitude, quasi-static
cyclic shear. We study a layer of plastic discs confined to a shear cell, using
photoelasticimetry to measure all inter-particle vector forces. For
sufficiently small cyclic shear amplitudes and large enough initial shear, the
material evolves to an unexpected "ultra-stable" state in which all the
particle positions and inter-particle contact forces remain unchanged after
each complete shear cycle for thousands of cycles. The stress response of these
states to small imposed shear is nearly elastic, in contrast to the original
shear jammed state.
